WorldWideScience

Sample records for linear fractional programming

  1. An Approach for Solving Linear Fractional Programming Problems

    OpenAIRE

    Andrew Oyakhobo Odior

    2012-01-01

    Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebr...

  2. An approach for solving linear fractional programming problems ...

    African Journals Online (AJOL)

    The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality ...

  3. A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems

    Directory of Open Access Journals (Sweden)

    Tunjo Perić

    2014-12-01

    Full Text Available This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.

  4. An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem

    Directory of Open Access Journals (Sweden)

    Meriem Ait Mehdi

    2014-01-01

    Full Text Available We describe an improvement of Chergui and Moulaï’s method (2008 that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.

  5. Analysis of the efficiency of the linearization techniques for solving multi-objective linear fractional programming problems by goal programming

    Directory of Open Access Journals (Sweden)

    Tunjo Perić

    2017-01-01

    Full Text Available This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1 Taylor’s polynomial linearization approximation, (2 the method of variable change, and (3 a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a using the optimal value of the objective functions as the decision makers’ aspirations, and (b the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.

  6. SLFP: a stochastic linear fractional programming approach for sustainable waste management.

    Science.gov (United States)

    Zhu, H; Huang, G H

    2011-12-01

    A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.

  7. Solving a class of generalized fractional programming problems using the feasibility of linear programs.

    Science.gov (United States)

    Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

    2017-01-01

    This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

  8. A generalized fuzzy credibility-constrained linear fractional programming approach for optimal irrigation water allocation under uncertainty

    Science.gov (United States)

    Zhang, Chenglong; Guo, Ping

    2017-10-01

    The vague and fuzzy parametric information is a challenging issue in irrigation water management problems. In response to this problem, a generalized fuzzy credibility-constrained linear fractional programming (GFCCFP) model is developed for optimal irrigation water allocation under uncertainty. The model can be derived from integrating generalized fuzzy credibility-constrained programming (GFCCP) into a linear fractional programming (LFP) optimization framework. Therefore, it can solve ratio optimization problems associated with fuzzy parameters, and examine the variation of results under different credibility levels and weight coefficients of possibility and necessary. It has advantages in: (1) balancing the economic and resources objectives directly; (2) analyzing system efficiency; (3) generating more flexible decision solutions by giving different credibility levels and weight coefficients of possibility and (4) supporting in-depth analysis of the interrelationships among system efficiency, credibility level and weight coefficient. The model is applied to a case study of irrigation water allocation in the middle reaches of Heihe River Basin, northwest China. Therefore, optimal irrigation water allocation solutions from the GFCCFP model can be obtained. Moreover, factorial analysis on the two parameters (i.e. λ and γ) indicates that the weight coefficient is a main factor compared with credibility level for system efficiency. These results can be effective for support reasonable irrigation water resources management and agricultural production.

  9. Fractional order differentiation by integration: An application to fractional linear systems

    KAUST Repository

    Liu, Dayan

    2013-02-04

    In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.

  10. Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

    Directory of Open Access Journals (Sweden)

    Bin Wang

    2015-01-01

    Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

  11. Analysis of fractional non-linear diffusion behaviors based on Adomian polynomials

    Directory of Open Access Journals (Sweden)

    Wu Guo-Cheng

    2017-01-01

    Full Text Available A time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.

  12. Stochastic Fractional Programming Approach to a Mean and Variance Model of a Transportation Problem

    Directory of Open Access Journals (Sweden)

    V. Charles

    2011-01-01

    Full Text Available In this paper, we propose a stochastic programming model, which considers a ratio of two nonlinear functions and probabilistic constraints. In the former, only expected model has been proposed without caring variability in the model. On the other hand, in the variance model, the variability played a vital role without concerning its counterpart, namely, the expected model. Further, the expected model optimizes the ratio of two linear cost functions where as variance model optimize the ratio of two non-linear functions, that is, the stochastic nature in the denominator and numerator and considering expectation and variability as well leads to a non-linear fractional program. In this paper, a transportation model with stochastic fractional programming (SFP problem approach is proposed, which strikes the balance between previous models available in the literature.

  13. Reduction of Linear Programming to Linear Approximation

    OpenAIRE

    Vaserstein, Leonid N.

    2006-01-01

    It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.

  14. A Simulation-Based Linear Fractional Programming Model for Adaptable Water Allocation Planning in the Main Stream of The Songhua River Basin, China

    Directory of Open Access Journals (Sweden)

    Qiang Fu

    2018-05-01

    Full Text Available The potential influence of natural variations in a climate system on global warming can change the hydrological cycle and threaten current strategies of water management. A simulation-based linear fractional programming (SLFP model, which integrates a runoff simulation model (RSM into a linear fractional programming (LFP framework, is developed for optimal water resource planning. The SLFP model has multiple objectives such as benefit maximization and water supply minimization, balancing water conflicts among various water demand sectors, and addressing complexities of water resource allocation system. Lingo and Excel programming solutions were used to solve the model. Water resources in the main stream basin of the Songhua River are allocated for 4 water demand sectors in 8 regions during two planning periods under different scenarios. Results show that the increase or decrease of water supply to the domestic sector is related to the change in population density at different regions in different target years. In 2030, the water allocation in the industrial sector decreased by 1.03–3.52% compared with that in 2020, while the water allocation in the environmental sector increased by 0.12–1.29%. Agricultural water supply accounts for 54.79–77.68% of total water supply in different regions. These changes in water resource allocation for various sectors were affected by different scenarios in 2020; however, water resource allocation for each sector was relatively stable under different scenarios in 2030. These results suggest that the developed SLFP model can help to improve the adjustment of water use structure and water utilization efficiency.

  15. Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

    Directory of Open Access Journals (Sweden)

    Ai-Min Yang

    2014-01-01

    Full Text Available The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

  16. Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays

    Directory of Open Access Journals (Sweden)

    Tadeusz Kaczorek

    2013-06-01

    Full Text Available Necessary and sufficient conditions for the asymptotic stability of positive fractional continuous-time linear systems with many delays are established. It is shown that: 1 the asymptotic stability of the positive fractional system is independent of their delays, 2 the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.

  17. The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

    Science.gov (United States)

    Narayanamoorthy, S; Kalyani, S

    2015-01-01

    An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  18. The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

    Directory of Open Access Journals (Sweden)

    S. Narayanamoorthy

    2015-01-01

    Full Text Available An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  19. Optimization of refinery product blending by using linear programming

    International Nuclear Information System (INIS)

    Ristikj, Julija; Tripcheva-Trajkovska, Loreta; Rikaloski, Ice; Markovska, Liljana

    1999-01-01

    The product slate of a simple refinery consists mainly of liquefied petroleum gas, leaded and unleaded gasoline, jet fuel, diesel fuel, extra light heating oil and fuel oil. The quality of the oil products (fuels) for sale has to comply with the adopted standards for liquid fuels, and the produced quantities have to be comply with the market needs. The oil products are manufactured by blending two or more different fractions which quantities and physical-chemical properties depend on the crude oil type, the way and conditions of processing, and at the same time the fractions are used to blend one or more products. It is in producer's interest to do the blending in an optimal way, namely, to satisfy the requirements for the oil products quality and quantity with a maximal usage of the available fractions and, of course, with a maximal profit out of the sold products. This could be accomplished by applying linear programming, that is by using a linear model for oil products blending optimization. (Author)

  20. On the discretization of linear fractional representations of LPV systems

    NARCIS (Netherlands)

    Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.

    2012-01-01

    Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a

  1. An iterative method for tri-level quadratic fractional programming problems using fuzzy goal programming approach

    Science.gov (United States)

    Kassa, Semu Mitiku; Tsegay, Teklay Hailay

    2017-08-01

    Tri-level optimization problems are optimization problems with three nested hierarchical structures, where in most cases conflicting objectives are set at each level of hierarchy. Such problems are common in management, engineering designs and in decision making situations in general, and are known to be strongly NP-hard. Existing solution methods lack universality in solving these types of problems. In this paper, we investigate a tri-level programming problem with quadratic fractional objective functions at each of the three levels. A solution algorithm has been proposed by applying fuzzy goal programming approach and by reformulating the fractional constraints to equivalent but non-fractional non-linear constraints. Based on the transformed formulation, an iterative procedure is developed that can yield a satisfactory solution to the tri-level problem. The numerical results on various illustrative examples demonstrated that the proposed algorithm is very much promising and it can also be used to solve larger-sized as well as n-level problems of similar structure.

  2. Semi-infinite fractional programming

    CERN Document Server

    Verma, Ram U

    2017-01-01

    This book presents a smooth and unified transitional framework from generalised fractional programming, with a finite number of variables and a finite number of constraints, to semi-infinite fractional programming, where a number of variables are finite but with infinite constraints. It focuses on empowering graduate students, faculty and other research enthusiasts to pursue more accelerated research advances with significant interdisciplinary applications without borders. In terms of developing general frameworks for theoretical foundations and real-world applications, it discusses a number of new classes of generalised second-order invex functions and second-order univex functions, new sets of second-order necessary optimality conditions, second-order sufficient optimality conditions, and second-order duality models for establishing numerous duality theorems for discrete minmax (or maxmin) semi-infinite fractional programming problems.   In the current interdisciplinary supercomputer-oriented research envi...

  3. Linear Programming (LP)

    International Nuclear Information System (INIS)

    Rogner, H.H.

    1989-01-01

    The submitted sections on linear programming are extracted from 'Theorie und Technik der Planung' (1978) by W. Blaas and P. Henseler and reformulated for presentation at the Workshop. They consider a brief introduction to the theory of linear programming and to some essential aspects of the SIMPLEX solution algorithm for the purposes of economic planning processes. 1 fig

  4. ALPS: A Linear Program Solver

    Science.gov (United States)

    Ferencz, Donald C.; Viterna, Larry A.

    1991-01-01

    ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

  5. On the linear programming bound for linear Lee codes.

    Science.gov (United States)

    Astola, Helena; Tabus, Ioan

    2016-01-01

    Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.

  6. Interactive Approach for Multi-Level Multi-Objective Fractional Programming Problems with Fuzzy Parameters

    Directory of Open Access Journals (Sweden)

    M.S. Osman

    2018-03-01

    Full Text Available In this paper, an interactive approach for solving multi-level multi-objective fractional programming (ML-MOFP problems with fuzzy parameters is presented. The proposed interactive approach makes an extended work of Shi and Xia (1997. In the first phase, the numerical crisp model of the ML-MOFP problem has been developed at a confidence level without changing the fuzzy gist of the problem. Then, the linear model for the ML-MOFP problem is formulated. In the second phase, the interactive approach simplifies the linear multi-level multi-objective model by converting it into separate multi-objective programming problems. Also, each separate multi-objective programming problem of the linear model is solved by the ∊-constraint method and the concept of satisfactoriness. Finally, illustrative examples and comparisons with the previous approaches are utilized to evince the feasibility of the proposed approach.

  7. Linear fractional diffusion-wave equation for scientists and engineers

    CERN Document Server

    Povstenko, Yuriy

    2015-01-01

    This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

  8. A METHOD FOR SOLVING LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS BASED ON MULTIOBJECTIVE LINEAR PROGRAMMING TECHNIQUE

    OpenAIRE

    M. ZANGIABADI; H. R. MALEKI

    2007-01-01

    In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, w...

  9. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    KAUST Repository

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  10. Parameters and Fractional Differentiation Orders Estimation for Linear Continuous-Time Non-Commensurate Fractional Order Systems

    KAUST Repository

    Belkhatir, Zehor

    2017-05-31

    This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.

  11. Linear-Algebra Programs

    Science.gov (United States)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  12. Joint estimation of the fractional differentiation orders and the unknown input for linear fractional non-commensurate system

    KAUST Repository

    Belkhatir, Zehor

    2015-11-05

    This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.

  13. Quadratic-linear pattern in cancer fractional radiotherapy. Equations for a computering program

    International Nuclear Information System (INIS)

    Burgos, D.; Bullejos, J.; Garcia Puche, J.L.; Pedraza, V.

    1990-01-01

    Knowledge of equivalence between different tratment schemes with the same iso-effect is the essential thing in clinical cancer radiotherapy. For this purpose it is very useful the group of ideas derived from quadratic-linear pattern (Q-L) proposed in order to analyze cell survival curve to radiation. Iso-effect definition caused by several irradiation rules is done by extrapolated tolerance dose (ETD). Because equations for ETD are complex, a computering program have been carried out. In this paper, iso-effect equations for well defined therapeutic situations and flow diagram proposed for resolution, have been studied. (Author)

  14. Elementary linear programming with applications

    CERN Document Server

    Kolman, Bernard

    1995-01-01

    Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear program

  15. Projective Synchronization of N-Dimensional Chaotic Fractional-Order Systems via Linear State Error Feedback Control

    Directory of Open Access Journals (Sweden)

    Baogui Xin

    2012-01-01

    Full Text Available Based on linear feedback control technique, a projective synchronization scheme of N-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.

  16. Linear programming

    CERN Document Server

    Solow, Daniel

    2014-01-01

    This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.

  17. Menu-Driven Solver Of Linear-Programming Problems

    Science.gov (United States)

    Viterna, L. A.; Ferencz, D.

    1992-01-01

    Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).

  18. 14 CFR 91.1411 - Continuous airworthiness maintenance program use by fractional ownership program manager.

    Science.gov (United States)

    2010-01-01

    ... program use by fractional ownership program manager. 91.1411 Section 91.1411 Aeronautics and Space FEDERAL... airworthiness maintenance program use by fractional ownership program manager. Fractional ownership program... through 91.1443. Any program manager who elects to maintain the program aircraft using a continuous...

  19. Linear Programming and Network Flows

    CERN Document Server

    Bazaraa, Mokhtar S; Sherali, Hanif D

    2011-01-01

    The authoritative guide to modeling and solving complex problems with linear programming-extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research

  20. A Solution to the Fundamental Linear Fractional Order Differential Equation

    Science.gov (United States)

    Hartley, Tom T.; Lorenzo, Carl F.

    1998-01-01

    This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.

  1. Uniqueness of non-linear ground states for fractional Laplacians in R

    DEFF Research Database (Denmark)

    Frank, Rupert L.; Lenzmann, Enno

    2013-01-01

    We prove uniqueness of ground state solutions Q = Q(|x|) ≥ 0 of the non-linear equation (−Δ)sQ+Q−Qα+1=0inR,where 0 fractional Laplacian in one dimension. In particular, we answer affirmatively an open question...... recently raised by Kenig–Martel–Robbiano and we generalize (by completely different techniques) the specific uniqueness result obtained by Amick and Toland for s=12 and α = 1 in [5] for the Benjamin–Ono equation. As a technical key result in this paper, we show that the associated linearized operator L...... + = (−Δ) s +1−(α+1)Q α is non-degenerate; i.e., its kernel satisfies ker L + = span{Q′}. This result about L + proves a spectral assumption, which plays a central role for the stability of solitary waves and blowup analysis for non-linear dispersive PDEs with fractional Laplacians, such as the generalized...

  2. Asymptotic behavior of solutions of linear multi-order fractional differential equation systems

    OpenAIRE

    Diethelm, Kai; Siegmund, Stefan; Tuan, H. T.

    2017-01-01

    In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of line...

  3. Comparison of open-source linear programming solvers.

    Energy Technology Data Exchange (ETDEWEB)

    Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph

    2013-10-01

    When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.

  4. Linear programming foundations and extensions

    CERN Document Server

    Vanderbei, Robert J

    2001-01-01

    Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...

  5. Ada Linear-Algebra Program

    Science.gov (United States)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  6. A linear programming manual

    Science.gov (United States)

    Tuey, R. C.

    1972-01-01

    Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

  7. Financial Planning with Fractional Goals

    OpenAIRE

    Goedhart, Marc; Spronk, Jaap

    1995-01-01

    textabstractWhen solving financial planning problems with multiple goals by means of multiple objective programming, the presence of fractional goals leads to technical difficulties. In this paper we present a straightforward interactive approach for solving such linear fractional programs with multiple goal variables. The approach is illustrated by means of an example in financial planning.

  8. Linear genetic programming

    CERN Document Server

    Brameier, Markus

    2007-01-01

    Presents a variant of Genetic Programming that evolves imperative computer programs as linear sequences of instructions, in contrast to the more traditional functional expressions or syntax trees. This book serves as a reference for researchers, but also contains sufficient introduction for students and those who are new to the field

  9. Application of the principal fractional meta-trigonometric functions for the solution of linear commensurate-order time-invariant fractional differential equations.

    Science.gov (United States)

    Lorenzo, C F; Hartley, T T; Malti, R

    2013-05-13

    A new and simplified method for the solution of linear constant coefficient fractional differential equations of any commensurate order is presented. The solutions are based on the R-function and on specialized Laplace transform pairs derived from the principal fractional meta-trigonometric functions. The new method simplifies the solution of such fractional differential equations and presents the solutions in the form of real functions as opposed to fractional complex exponential functions, and thus is directly applicable to real-world physics.

  10. The linear programming bound for binary linear codes

    NARCIS (Netherlands)

    Brouwer, A.E.

    1993-01-01

    Combining Delsarte's (1973) linear programming bound with the information that certain weights cannot occur, new upper bounds for dmin (n,k), the maximum possible minimum distance of a binary linear code with given word length n and dimension k, are derived.

  11. Linear Programming across the Curriculum

    Science.gov (United States)

    Yoder, S. Elizabeth; Kurz, M. Elizabeth

    2015-01-01

    Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…

  12. Linear programming

    CERN Document Server

    Karloff, Howard

    1991-01-01

    To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...

  13. Fuzzy Multi-objective Linear Programming Approach

    Directory of Open Access Journals (Sweden)

    Amna Rehmat

    2007-07-01

    Full Text Available Traveling salesman problem (TSP is one of the challenging real-life problems, attracting researchers of many fields including Artificial Intelligence, Operations Research, and Algorithm Design and Analysis. The problem has been well studied till now under different headings and has been solved with different approaches including genetic algorithms and linear programming. Conventional linear programming is designed to deal with crisp parameters, but information about real life systems is often available in the form of vague descriptions. Fuzzy methods are designed to handle vague terms, and are most suited to finding optimal solutions to problems with vague parameters. Fuzzy multi-objective linear programming, an amalgamation of fuzzy logic and multi-objective linear programming, deals with flexible aspiration levels or goals and fuzzy constraints with acceptable deviations. In this paper, a methodology, for solving a TSP with imprecise parameters, is deployed using fuzzy multi-objective linear programming. An example of TSP with multiple objectives and vague parameters is discussed.

  14. Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System

    Directory of Open Access Journals (Sweden)

    Z.H. Wang

    2011-01-01

    Full Text Available Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots. The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.

  15. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  16. Investigating Integer Restrictions in Linear Programming

    Science.gov (United States)

    Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.

    2015-01-01

    Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…

  17. Underprediction of human skin erythema at low doses per fraction by the linear quadratic model

    International Nuclear Information System (INIS)

    Hamilton, Christopher S.; Denham, James W.; O'Brien, Maree; Ostwald, Patricia; Kron, Tomas; Wright, Suzanne; Doerr, Wolfgang

    1996-01-01

    Background and purpose. The erythematous response of human skin to radiotherapy has proven useful for testing the predictions of the linear quadratic (LQ) model in terms of fractionation sensitivity and repair half time. No formal investigation of the response of human skin to doses less than 2 Gy per fraction has occurred. This study aims to test the validity of the LQ model for human skin at doses ranging from 0.4 to 5.2 Gy per fraction. Materials and methods. Complete erythema reaction profiles were obtained using reflectance spectrophotometry in two patient populations: 65 patients treated palliatively with 5, 10, 12 and 20 daily treatment fractions (varying thicknesses of bolus, various body sites) and 52 patients undergoing prostatic irradiation for localised carcinoma of the prostate (no bolus, 30-32 fractions). Results and conclusions. Gender, age, site and prior sun exposure influence pre- and post-treatment erythema values independently of dose administered. Out-of-field effects were also noted. The linear quadratic model significantly underpredicted peak erythema values at doses less than 1.5 Gy per fraction. This suggests that either the conventional linear quadratic model does not apply for low doses per fraction in human skin or that erythema is not exclusively initiated by radiation damage to the basal layer. The data are potentially explained by an induced repair model

  18. Linear and integer programming made easy

    CERN Document Server

    Hu, T C

    2016-01-01

    Linear and integer programming are fundamental toolkits for data and information science and technology, particularly in the context of today’s megatrends toward statistical optimization, machine learning, and big data analytics. Drawn from over 30 years of classroom teaching and applied research experience, this textbook provides a crisp and practical introduction to the basics of linear and integer programming. The authors’ approach is accessible to students from all fields of engineering, including operations research, statistics, machine learning, control system design, scheduling, formal verification, and computer vision. Readers will learn to cast hard combinatorial problems as mathematical programming optimizations, understand how to achieve formulations where the objective and constraints are linear, choose appropriate solution methods, and interpret results appropriately. •Provides a concise introduction to linear and integer programming, appropriate for undergraduates, graduates, a short cours...

  19. PCX, Interior-Point Linear Programming Solver

    International Nuclear Information System (INIS)

    Czyzyk, J.

    2004-01-01

    1 - Description of program or function: PCX solves linear programming problems using the Mehrota predictor-corrector interior-point algorithm. PCX can be called as a subroutine or used in stand-alone mode, with data supplied from an MPS file. The software incorporates modules that can be used separately from the linear programming solver, including a pre-solve routine and data structure definitions. 2 - Methods: The Mehrota predictor-corrector method is a primal-dual interior-point method for linear programming. The starting point is determined from a modified least squares heuristic. Linear systems of equations are solved at each interior-point iteration via a sparse Cholesky algorithm native to the code. A pre-solver is incorporated in the code to eliminate inefficiencies in the user's formulation of the problem. 3 - Restriction on the complexity of the problem: There are no size limitations built into the program. The size of problem solved is limited by RAM and swap space on the user's computer

  20. Influence of the void fraction in the linear reactivity model

    International Nuclear Information System (INIS)

    Castillo, J.A.; Ramirez, J.R.; Alonso, G.

    2003-01-01

    The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)

  1. Analytical approach to linear fractional partial differential equations arising in fluid mechanics

    International Nuclear Information System (INIS)

    Momani, Shaher; Odibat, Zaid

    2006-01-01

    In this Letter, we implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear fractional partial differential equations arising in fluid mechanics. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these methods, the solution takes the form of a convergent series with easily computable components. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. Some numerical examples are presented to illustrate the efficiency and reliability of the two methods

  2. Refining and end use study of coal liquids II - linear programming analysis

    Energy Technology Data Exchange (ETDEWEB)

    Lowe, C.; Tam, S.

    1995-12-31

    A DOE-funded study is underway to determine the optimum refinery processing schemes for producing transportation fuels that will meet CAAA regulations from direct and indirect coal liquids. The study consists of three major parts: pilot plant testing of critical upgrading processes, linear programming analysis of different processing schemes, and engine emission testing of final products. Currently, fractions of a direct coal liquid produced form bituminous coal are being tested in sequence of pilot plant upgrading processes. This work is discussed in a separate paper. The linear programming model, which is the subject of this paper, has been completed for the petroleum refinery and is being modified to handle coal liquids based on the pilot plant test results. Preliminary coal liquid evaluation studies indicate that, if a refinery expansion scenario is adopted, then the marginal value of the coal liquid (over the base petroleum crude) is $3-4/bbl.

  3. Linear programming using Matlab

    CERN Document Server

    Ploskas, Nikolaos

    2017-01-01

    This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book  are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus.  The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting ru...

  4. Ranking Forestry Investments With Parametric Linear Programming

    Science.gov (United States)

    Paul A. Murphy

    1976-01-01

    Parametric linear programming is introduced as a technique for ranking forestry investments under multiple constraints; it combines the advantages of simple tanking and linear programming as capital budgeting tools.

  5. ALPS - A LINEAR PROGRAM SOLVER

    Science.gov (United States)

    Viterna, L. A.

    1994-01-01

    Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.

  6. Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems

    Directory of Open Access Journals (Sweden)

    Hai Zhang

    2014-01-01

    Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.

  7. Linear programming mathematics, theory and algorithms

    CERN Document Server

    1996-01-01

    Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.

  8. A New Finite Continuation Algorithm for Linear Programming

    DEFF Research Database (Denmark)

    Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa

    1996-01-01

    We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an $\\ell_1$ minimization problem augmented with the addition of a linear term. This nondifferentiable problem is approximated...... by a smooth problem. It is shown that the minimizers of the smooth problem define a family of piecewise-linear paths as a function of a smoothing parameter. Based on this property, a finite algorithm that traces these paths to arrive at an optimal solution of the linear program is developed. The smooth...

  9. Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

    KAUST Repository

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating

  10. Interior Point Method for Solving Fuzzy Number Linear Programming Problems Using Linear Ranking Function

    Directory of Open Access Journals (Sweden)

    Yi-hua Zhong

    2013-01-01

    Full Text Available Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.

  11. Stochastic multiresonance for a fractional linear oscillator with time-delayed kernel and quadratic noise

    Science.gov (United States)

    Guo, Feng; Wang, Xue-Yuan; Zhu, Cheng-Yin; Cheng, Xiao-Feng; Zhang, Zheng-Yu; Huang, Xu-Hui

    2017-12-01

    The stochastic resonance for a fractional oscillator with time-delayed kernel and quadratic trichotomous noise is investigated. Applying linear system theory and Laplace transform, the system output amplitude (SPA) for the fractional oscillator is obtained. It is found that the SPA is a periodical function of the kernel delayed-time. Stochastic multiplicative phenomenon appears on the SPA versus the driving frequency, versus the noise amplitude, and versus the fractional exponent. The non-monotonous dependence of the SPA on the system parameters is also discussed.

  12. A program package for solving linear optimization problems

    International Nuclear Information System (INIS)

    Horikami, Kunihiko; Fujimura, Toichiro; Nakahara, Yasuaki

    1980-09-01

    Seven computer programs for the solution of linear, integer and quadratic programming (four programs for linear programming, one for integer programming and two for quadratic programming) have been prepared and tested on FACOM M200 computer, and auxiliary programs have been written to make it easy to use the optimization program package. The characteristics of each program are explained and the detailed input/output descriptions are given in order to let users know how to use them. (author)

  13. EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.

    Science.gov (United States)

    Jarvis, John J.; And Others

    Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…

  14. Sparsity Prevention Pivoting Method for Linear Programming

    DEFF Research Database (Denmark)

    Li, Peiqiang; Li, Qiyuan; Li, Canbing

    2018-01-01

    When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

  15. Sparsity Prevention Pivoting Method for Linear Programming

    DEFF Research Database (Denmark)

    Li, Peiqiang; Li, Qiyuan; Li, Canbing

    2018-01-01

    . The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...

  16. Timetabling an Academic Department with Linear Programming.

    Science.gov (United States)

    Bezeau, Lawrence M.

    This paper describes an approach to faculty timetabling and course scheduling that uses computerized linear programming. After reviewing the literature on linear programming, the paper discusses the process whereby a timetable was created for a department at the University of New Brunswick. Faculty were surveyed with respect to course offerings…

  17. Methods for optimizing over the efficient and weakly efficient sets of an affine fractional vector optimization program

    DEFF Research Database (Denmark)

    Le, T.H.A.; Pham, D. T.; Canh, Nam Nguyen

    2010-01-01

    Both the efficient and weakly efficient sets of an affine fractional vector optimization problem, in general, are neither convex nor given explicitly. Optimization problems over one of these sets are thus nonconvex. We propose two methods for optimizing a real-valued function over the efficient...... and weakly efficient sets of an affine fractional vector optimization problem. The first method is a local one. By using a regularization function, we reformulate the problem into a standard smooth mathematical programming problem that allows applying available methods for smooth programming. In case...... the objective function is linear, we have investigated a global algorithm based upon a branch-and-bound procedure. The algorithm uses Lagrangian bound coupling with a simplicial bisection in the criteria space. Preliminary computational results show that the global algorithm is promising....

  18. High-order sliding mode observer for fractional commensurate linear systems with unknown input

    KAUST Repository

    Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem

    2017-01-01

    In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

  19. High-order sliding mode observer for fractional commensurate linear systems with unknown input

    KAUST Repository

    Belkhatir, Zehor

    2017-05-20

    In this paper, a high-order sliding mode observer (HOSMO) is proposed for the joint estimation of the pseudo-state and the unknown input of fractional commensurate linear systems with single unknown input and a single output. The convergence of the proposed observer is proved using a Lyapunov-based approach. In addition, an enhanced variant of the proposed fractional-HOSMO is introduced to avoid the peaking phenomenon and thus to improve the estimation results in the transient phase. Simulation results are provided to illustrate the performance of the proposed fractional observer in both noise-free and noisy cases. The effect of the observer’s gains on the estimated pseudo-state and unknown input is also discussed.

  20. Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions

    KAUST Repository

    Belkhatir, Zehor

    2017-06-28

    This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input’s amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.

  1. An Instructional Note on Linear Programming--A Pedagogically Sound Approach.

    Science.gov (United States)

    Mitchell, Richard

    1998-01-01

    Discusses the place of linear programming in college curricula and the advantages of using linear-programming software. Lists important characteristics of computer software used in linear programming for more effective teaching and learning. (ASK)

  2. A unified framework for testing in the linear regression model under unknown order of fractional integration

    DEFF Research Database (Denmark)

    Christensen, Bent Jesper; Kruse, Robinson; Sibbertsen, Philipp

    We consider hypothesis testing in a general linear time series regression framework when the possibly fractional order of integration of the error term is unknown. We show that the approach suggested by Vogelsang (1998a) for the case of integer integration does not apply to the case of fractional...

  3. Portfolio optimization using fuzzy linear programming

    Science.gov (United States)

    Pandit, Purnima K.

    2013-09-01

    Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.

  4. The time-walk of analog constant fraction discriminators using very fast scintillator detectors with linear and non-linear energy response

    Energy Technology Data Exchange (ETDEWEB)

    Regis, J.-M., E-mail: regis@ikp.uni-koeln.de [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Rudigier, M.; Jolie, J.; Blazhev, A.; Fransen, C.; Pascovici, G.; Warr, N. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany)

    2012-08-21

    The electronic {gamma}-{gamma} fast timing technique allows for direct nuclear lifetime determination down to the few picoseconds region by measuring the time difference between two coincident {gamma}-ray transitions. Using high resolution ultra-fast LaBr{sub 3}(Ce) scintillator detectors in combination with the recently developed mirror symmetric centroid difference method, nuclear lifetimes are measured with a time resolving power of around 5 ps. The essence of the method is to calibrate the energy dependent position (centroid) of the prompt response function of the setup which is obtained for simultaneously occurring events. This time-walk of the prompt response function induced by the analog constant fraction discriminator has been determined by systematic measurements using different photomultiplier tubes and timing adjustments of the constant fraction discriminator. We propose a universal calibration function which describes the time-walk or the combined {gamma}-{gamma} time-walk characteristics, respectively, for either a linear or a non-linear amplitude versus energy dependency of the scintillator detector output pulses.

  5. The application of the linear-quadratic model to fractionated radiotherapy when there is incomplete normal tissue recovery between fractions, and possible implications for treatments involving multiple fractions per day

    International Nuclear Information System (INIS)

    Dale, R.G.

    1986-01-01

    By extending a previously developed mathematical model based on the linear-quadratic dose-effect relationship, it is possible to examine the consequences of performing fractionated treatments for which there is insufficient time between fractions to allow complete damage repair. Equations are derived which give the relative effectiveness of such treatments in terms of tissue-repair constants (μ values) and α/β ratios, and these are then applied to some examples of treatments involving multiple fractions per day. The interplay of the various mechanisms involved (including repopulation effects) and their possible influence on treatments involving closely spaced fractions are examined. If current indications of the differences in recovery rates between early- and late-reacting normal tissues are representative, then it is shown that such differences may limit the clinical potential of accelerated fractionation regimes, where several fractions per day are given in a relatively short overall time. (author)

  6. Results of fractionated stereotactic radiotherapy with linear accelerator

    Energy Technology Data Exchange (ETDEWEB)

    Aoki, Masahiko; Watanabe, Sadao [Aomori Prefectural Central Hospital (Japan); Mariya, Yasushi [and others

    1997-03-01

    A lot of clinical data about stereotactic radiotherapy (SRT) were reported, however, standard fractionated schedules were not shown. In this paper, our clinical results of SRT, 3 fractions of 10 Gy, are reported. Between February 1992 and March 1995, we treated 41 patients with 7 arteriovenous malformations and 41 intracranial tumors using a stereotactic technique implemented by a standard 10MV X-ray linear accelerator. Average age was 47.4 years (range 3-80 years) and average follow-up time was 16.7 months (range 3.5-46.1 months). The patients received 3 fractions of 10 Gy for 3 days delivered by multiple arc narrow beams under 3 cm in width and length. A three-pieces handmade shell was used for head fixation without any anesthetic procedures. Three-dimensional treatment planning system (Focus) was applied for the dose calculation. All patients have received at least one follow-up radiographic study and one clinical examination. In four of the 7 patients with AVM the nidus has become smaller, 9 of the 21 patients with benign intracranial tumors and 9 of the 13 patients with intracranial malignant tumors have shown complete or partial response to the therapy. In 14 patients, diseases were stable or unevaluable due to the short follow-up time. In 5 patients (3 with astrocytoma, 1 each with meningioma and craniopharyngioma), diseases were progressive. Only 1 patient with falx meningioma had minor complication due to the symptomatic brain edema around the tumor. Although, further evaluation of target control (i.e. tumor and nidus) and late normal tissue damage is needed, preliminary clinical results indicate that SRT with our methods is safe and effective. (author)

  7. Evaluation of uneven fractionation radiotherapy of cervical lymph node-metastases by linear quadratic model

    International Nuclear Information System (INIS)

    Sasaki, Takehito; Kamata, Rikisaburo; Urahashi, Shingo; Yamaguchi, Tetsuji.

    1993-01-01

    One hundred and sixty-nine cervical lymph node-metastases from head and neck squamous cell carcinomas treated with either even fractionation or uneven fractionation regimens were analyzed in the present investigation. Logistic multivariate regression analysis indicated that: type of fractionation (even vs uneven), size of metastases, T value of primary tumors, and total dose are independent variables out of 18 variables that significantly influenced the rate of tumor clearance. The data, with statistical bias corrected by the regression equation, indicated that the uneven fractionation scheme significantly improved the rate of tumor clearance for the same size of metastases, total dose, and overall time compared to the even fractionation scheme. Further analysis by a linear-quadratic cell survival model indicated that the clinical improvement by uneven fractionation might not be explained entirely by a larger dose per fraction. It is suggested that tumor cells irradiated with an uneven fractionation regimen might repopulate more slowly, or they might be either less hypoxic or redistributed in a more radiosensitive phase in the cell cycle than those irradiated with even fractionation. This conclusion is clearly not definite, but it is suitable, pending the results of further investigation. (author)

  8. Joint shape segmentation with linear programming

    KAUST Repository

    Huang, Qixing; Koltun, Vladlen; Guibas, Leonidas

    2011-01-01

    program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape

  9. A Primal-Dual Interior Point-Linear Programming Algorithm for MPC

    DEFF Research Database (Denmark)

    Edlund, Kristian; Sokoler, Leo Emil; Jørgensen, John Bagterp

    2009-01-01

    Constrained optimal control problems for linear systems with linear constraints and an objective function consisting of linear and l1-norm terms can be expressed as linear programs. We develop an efficient primal-dual interior point algorithm for solution of such linear programs. The algorithm...

  10. A Fuzzy Linear Programming Approach for Aggregate Production Planning

    DEFF Research Database (Denmark)

    Iris, Cagatay; Cevikcan, Emre

    2014-01-01

    a mathematical programming framework for aggregate production planning problem under imprecise data environment. After providing background information about APP problem, together with fuzzy linear programming, the fuzzy linear programming model of APP is solved on an illustrative example for different a...

  11. On the exactness of the cavity method for weighted b-matchings on arbitrary graphs and its relation to linear programs

    International Nuclear Information System (INIS)

    Bayati, Mohsen; Borgs, Christian; Chayes, Jennifer; Zecchina, Riccardo

    2008-01-01

    We consider the general problem of finding the minimum weight b-matching on arbitrary graphs. We prove that, whenever the linear programing relaxation of the problem has no fractional solutions, then the cavity or belief propagation equations converge to the correct solution both for synchronous and asynchronous updating. (letter)

  12. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

    OpenAIRE

    Zuidwijk, Rob

    2005-01-01

    textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...

  13. Output feedback control of linear fractional transformation systems subject to actuator saturation

    Science.gov (United States)

    Ban, Xiaojun; Wu, Fen

    2016-11-01

    In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.

  14. LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections

    International Nuclear Information System (INIS)

    2007-01-01

    1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table

  15. Game Theory and its Relationship with Linear Programming Models ...

    African Journals Online (AJOL)

    Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.

  16. Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing.

    Science.gov (United States)

    Yang, Changju; Kim, Hyongsuk

    2016-08-19

    A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model.

  17. Evaluation of film dosemeters by linear programming

    International Nuclear Information System (INIS)

    Kragh, P.; Nitschke, J.

    1992-01-01

    An evaluation method for multi-component dosemeters is described which uses linear programming in order to decrease the dependence on energy and direction. The results of this method are more accurate than those obtained with the evaluation methods so far applied in film dosimetry. In addition, systematic errors can be given when evaluating individual measurements. Combined linear programming, as a special case of the presented method, is described taking a film dosemeter of particular type as an example. (orig.) [de

  18. Optimization Research of Generation Investment Based on Linear Programming Model

    Science.gov (United States)

    Wu, Juan; Ge, Xueqian

    Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.

  19. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

    KAUST Repository

    Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

  20. An algebraic fractional order differentiator for a class of signals satisfying a linear differential equation

    KAUST Repository

    Liu, Da-Yan

    2015-04-30

    This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.

  1. 175 Years of Linear Programming

    Indian Academy of Sciences (India)

    polynomial-time solvability of linear programming, that is, testing if a polyhedron Q E ~ ... Q is rational, i.e. all extreme points and rays of Q are ra- tional vectors or ..... rithrll terminates with an interior solution, a post-processing step is usually ...

  2. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

    Science.gov (United States)

    El-Gebeily, M.; Yushau, B.

    2008-01-01

    In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

  3. A Sawmill Manager Adapts To Change With Linear Programming

    Science.gov (United States)

    George F. Dutrow; James E. Granskog

    1973-01-01

    Linear programming provides guidelines for increasing sawmill capacity and flexibility and for determining stumpagepurchasing strategy. The operator of a medium-sized sawmill implemented improvements suggested by linear programming analysis; results indicate a 45 percent increase in revenue and a 36 percent hike in volume processed.

  4. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Science.gov (United States)

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-08-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  5. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    International Nuclear Information System (INIS)

    Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao

    2016-01-01

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  6. Response analysis of a class of quasi-linear systems with fractional derivative excited by Poisson white noise

    Energy Technology Data Exchange (ETDEWEB)

    Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong; Jia, Wantao [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)

    2016-08-15

    The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.

  7. 175 Years of Linear Programming

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. 175 Years of Linear Programming - Max Flow = Min Cut. Vijay Chandru M R Rao. Series Article Volume 4 Issue 10 October 1999 pp 22-39. Fulltext. Click here to view fulltext PDF. Permanent link:

  8. 175 Years of Linear Programming

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 5. 175 Years of Linear Programming - Pune's Gift. Vijay Chandru M R Rao. Series Article Volume 4 Issue 5 May ... Computer Science and Automation, IISc Bangalore 560012, India. Director, Indian Institute of Management, Bannerghatta Road, ...

  9. Linear-quadratic model underestimates sparing effect of small doses per fraction in rat spinal cord

    International Nuclear Information System (INIS)

    Shun Wong, C.; Toronto University; Minkin, S.; Hill, R.P.; Toronto University

    1993-01-01

    The application of the linear-quadratic (LQ) model to describe iso-effective fractionation schedules for dose fraction sizes less than 2 Gy has been controversial. Experiments are described in which the effect of daily fractionated irradiation given with a wide range of fraction sizes was assessed in rat cervical spine cord. The first group of rats was given doses in 1, 2, 4, 8 and 40 fractions/day. The second group received 3 initial 'top-up'doses of 9 Gy given once daily, representing 3/4 tolerance, followed by doses in 1, 2, 10, 20, 30 and 40 fractions/day. The fractionated portion of the irradiation schedule therefore constituted only the final quarter of the tolerance dose. The endpoint of the experiments was paralysis of forelimbs secondary to white matter necrosis. Direct analysis of data from experiments with full course fractionation up to 40 fractions/day (25.0-1.98 Gy/fraction) indicated consistency with the LQ model yielding an α/β value of 2.41 Gy. Analysis of data from experiments in which the 3 'top-up' doses were followed by up to 10 fractions (10.0-1.64 Gy/fraction) gave an α/β value of 3.41 Gy. However, data from 'top-up' experiments with 20, 30 and 40 fractions (1.60-0.55 Gy/fraction) were inconsistent with LQ model and gave a very small α/β of 0.48 Gy. It is concluded that LQ model based on data from large doses/fraction underestimates the sparing effect of small doses/fraction, provided sufficient time is allowed between each fraction for repair of sublethal damage. (author). 28 refs., 5 figs., 1 tab

  10. Non-linear programming method in optimization of fast reactors

    International Nuclear Information System (INIS)

    Pavelesku, M.; Dumitresku, Kh.; Adam, S.

    1975-01-01

    Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)

  11. Analytic central path, sensitivity analysis and parametric linear programming

    NARCIS (Netherlands)

    A.G. Holder; J.F. Sturm; S. Zhang (Shuzhong)

    1998-01-01

    textabstractIn this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face

  12. Linear program differentiation for single-channel speech separation

    DEFF Research Database (Denmark)

    Pearlmutter, Barak A.; Olsson, Rasmus Kongsgaard

    2006-01-01

    Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver....... For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied...... to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single...

  13. Linear combination of forecasts with numerical adjustment via MINIMAX non-linear programming

    Directory of Open Access Journals (Sweden)

    Jairo Marlon Corrêa

    2016-03-01

    Full Text Available This paper proposes a linear combination of forecasts obtained from three forecasting methods (namely, ARIMA, Exponential Smoothing and Artificial Neural Networks whose adaptive weights are determined via a multi-objective non-linear programming problem, which seeks to minimize, simultaneously, the statistics: MAE, MAPE and MSE. The results achieved by the proposed combination are compared with the traditional approach of linear combinations of forecasts, where the optimum adaptive weights are determined only by minimizing the MSE; with the combination method by arithmetic mean; and with individual methods

  14. Performance of a fully automated program for measurement of left ventricular ejection fraction

    International Nuclear Information System (INIS)

    Douglass, K.H.; Tibbits, P.; Kasecamp, W.; Han, S.T.; Koller, D.; Links, J.M.; Wagner, H.H. Jr.

    1982-01-01

    A fully automated program developed by us for measurement of left ventricular ejection fraction from equilibrium gated blood studies was evaluated in 130 additional patients. Both of 6-min (130 studies) and 2-min (142 studies in 31 patients) gated blood pool studies were acquired and processed. The program successfully generated ejection fractions in 86% of the studies. These automatically generated ejection fractions were compared with ejection fractions derived from manually drawn regions the interest. When studies were acquired for 6-min with the patient at rest, the correlation between automated and manual ejection fractions was 0.92. When studies were acquired for 2-min, both at rest and during bicycle exercise, the correlation was 0.81. In 25 studies from patients who also underwent contrast ventriculography, the program successfully generated regions of interest in 22 (88%). The correlation between the ejection fraction determined by contrast ventriculography and the automatically generated radionuclide ejection fraction was 0.79. (orig.)

  15. Very Low-Cost Nutritious Diet Plans Designed by Linear Programming.

    Science.gov (United States)

    Foytik, Jerry

    1981-01-01

    Provides procedural details of Linear Programing, developed by the U.S. Department of Agriculture to devise a dietary guide for consumers that minimizes food costs without sacrificing nutritional quality. Compares Linear Programming with the Thrifty Food Plan, which has been a basis for allocating coupons under the Food Stamp Program. (CS)

  16. Portfolio optimization by using linear programing models based on genetic algorithm

    Science.gov (United States)

    Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.

    2018-01-01

    In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.

  17. A new algorithm for generalized fractional programs

    NARCIS (Netherlands)

    J.B.G. Frenk (Hans); A.I. Barros (Ana); S. Schaible; S. Zhang (Shuzhong)

    1996-01-01

    textabstractA new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized

  18. A uniform law for convergence to the local times of linear fractional stable motions

    OpenAIRE

    Duffy, James A.

    2016-01-01

    We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.

  19. An easy way to obtain strong duality results in linear, linear semidefinite and linear semi-infinite programming

    NARCIS (Netherlands)

    Pop, P.C.; Still, Georg J.

    1999-01-01

    In linear programming it is known that an appropriate non-homogeneous Farkas Lemma leads to a short proof of the strong duality results for a pair of primal and dual programs. By using a corresponding generalized Farkas lemma we give a similar proof of the strong duality results for semidefinite

  20. The simplex method of linear programming

    CERN Document Server

    Ficken, Frederick A

    1961-01-01

    This concise but detailed and thorough treatment discusses the rudiments of the well-known simplex method for solving optimization problems in linear programming. Geared toward undergraduate students, the approach offers sufficient material for readers without a strong background in linear algebra. Many different kinds of problems further enrich the presentation. The text begins with examinations of the allocation problem, matrix notation for dual problems, feasibility, and theorems on duality and existence. Subsequent chapters address convex sets and boundedness, the prepared problem and boun

  1. Some Properties of Multiple Parameters Linear Programming

    Directory of Open Access Journals (Sweden)

    Maoqin Li

    2010-01-01

    Full Text Available We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function f can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of f at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.

  2. Some Properties of Multiple Parameters Linear Programming

    Directory of Open Access Journals (Sweden)

    Yan Hong

    2010-01-01

    Full Text Available Abstract We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.

  3. Generalized prolate spheroidal wave functions for optical finite fractional Fourier and linear canonical transforms.

    Science.gov (United States)

    Pei, Soo-Chang; Ding, Jian-Jiun

    2005-03-01

    Prolate spheroidal wave functions (PSWFs) are known to be useful for analyzing the properties of the finite-extension Fourier transform (fi-FT). We extend the theory of PSWFs for the finite-extension fractional Fourier transform, the finite-extension linear canonical transform, and the finite-extension offset linear canonical transform. These finite transforms are more flexible than the fi-FT and can model much more generalized optical systems. We also illustrate how to use the generalized prolate spheroidal functions we derive to analyze the energy-preservation ratio, the self-imaging phenomenon, and the resonance phenomenon of the finite-sized one-stage or multiple-stage optical systems.

  4. A LINEAR PROGRAMMING ALGORITHM FOR LEAST-COST SCHEDULING

    Directory of Open Access Journals (Sweden)

    AYMAN H AL-MOMANI

    1999-12-01

    Full Text Available In this research, some concepts of linear programming and critical path method are reviewed to describe recent modeling structures that have been of great value in analyzing extended planning horizon project time-cost trade-offs problems. A simplified representation of a small project and a linear programming model is formulated to represent this system. Procedures to solve these various problems formulations were cited and the final solution is obtained using LINDO program. The model developed represents many restrictions and management considerations of the project. It could be used by construction managers in a planning stage to explore numerous possible opportunities to the contractor and predict the effect of a decision on the construction to facilitate a preferred operating policy given different management objectives. An implementation using this method is shown to outperform several other techniques and a large class of test problems. Linear programming show that the algorithm is very promising in practice on a wide variety of time-cost trade-offs problems. This method is simple, applicable to a large network, and generates a shorter computational time at low cost, along with an increase in robustness.

  5. Applied Research of Enterprise Cost Control Based on Linear Programming

    Directory of Open Access Journals (Sweden)

    Yu Shuo

    2015-01-01

    This paper researches the enterprise cost control through the linear programming model, and analyzes the restriction factors of the labor of enterprise production, raw materials, processing equipment, sales price, and other factors affecting the enterprise income, so as to obtain an enterprise cost control model based on the linear programming. This model can calculate rational production mode in the case of limited resources, and acquire optimal enterprise income. The production guiding program and scheduling arrangement of the enterprise can be obtained through calculation results, so as to provide scientific and effective guidance for the enterprise production. This paper adds the sensitivity analysis in the linear programming model, so as to learn about the stability of the enterprise cost control model based on linear programming through the sensitivity analysis, and verify the rationality of the model, and indicate the direction for the enterprise cost control. The calculation results of the model can provide a certain reference for the enterprise planning in the market economy environment, which have strong reference and practical significance in terms of the enterprise cost control.

  6. Optical Measurement of Radiocarbon below Unity Fraction Modern by Linear Absorption Spectroscopy.

    Science.gov (United States)

    Fleisher, Adam J; Long, David A; Liu, Qingnan; Gameson, Lyn; Hodges, Joseph T

    2017-09-21

    High-precision measurements of radiocarbon ( 14 C) near or below a fraction modern 14 C of 1 (F 14 C ≤ 1) are challenging and costly. An accurate, ultrasensitive linear absorption approach to detecting 14 C would provide a simple and robust benchtop alternative to off-site accelerator mass spectrometry facilities. Here we report the quantitative measurement of 14 C in gas-phase samples of CO 2 with F 14 C radiocarbon measurement science including the study of biofuels and bioplastics, illicitly traded specimens, bomb dating, and atmospheric transport.

  7. Joint shape segmentation with linear programming

    KAUST Repository

    Huang, Qixing

    2011-01-01

    We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms single-shape segmentation techniques. © 2011 ACM.

  8. Analysis of blood pressure signal in patients with different ventricular ejection fraction using linear and non-linear methods.

    Science.gov (United States)

    Arcentales, Andres; Rivera, Patricio; Caminal, Pere; Voss, Andreas; Bayes-Genis, Antonio; Giraldo, Beatriz F

    2016-08-01

    Changes in the left ventricle function produce alternans in the hemodynamic and electric behavior of the cardiovascular system. A total of 49 cardiomyopathy patients have been studied based on the blood pressure signal (BP), and were classified according to the left ventricular ejection fraction (LVEF) in low risk (LR: LVEF>35%, 17 patients) and high risk (HR: LVEF≤35, 32 patients) groups. We propose to characterize these patients using a linear and a nonlinear methods, based on the spectral estimation and the recurrence plot, respectively. From BP signal, we extracted each systolic time interval (STI), upward systolic slope (BPsl), and the difference between systolic and diastolic BP, defined as pulse pressure (PP). After, the best subset of parameters were obtained through the sequential feature selection (SFS) method. According to the results, the best classification was obtained using a combination of linear and nonlinear features from STI and PP parameters. For STI, the best combination was obtained considering the frequency peak and the diagonal structures of RP, with an area under the curve (AUC) of 79%. The same results were obtained when comparing PP values. Consequently, the use of combined linear and nonlinear parameters could improve the risk stratification of cardiomyopathy patients.

  9. Arc-Search Infeasible Interior-Point Algorithm for Linear Programming

    OpenAIRE

    Yang, Yaguang

    2014-01-01

    Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the propo...

  10. Linear Programming and Its Application to Pattern Recognition Problems

    Science.gov (United States)

    Omalley, M. J.

    1973-01-01

    Linear programming and linear programming like techniques as applied to pattern recognition problems are discussed. Three relatively recent research articles on such applications are summarized. The main results of each paper are described, indicating the theoretical tools needed to obtain them. A synopsis of the author's comments is presented with regard to the applicability or non-applicability of his methods to particular problems, including computational results wherever given.

  11. Object matching using a locally affine invariant and linear programming techniques.

    Science.gov (United States)

    Li, Hongsheng; Huang, Xiaolei; He, Lei

    2013-02-01

    In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

  12. A non-invasive method for fractionated steriotactic irradiation of brain tumors with linear accelerator

    International Nuclear Information System (INIS)

    Hariz, M.I.; Laitinen, L.V.; Henriksson, R.; Saeterborg, N.-E.; Loefroth, P.-O.

    1990-01-01

    A new technique for fractionated stereotactic irradiation of intracranial lesions is described. The treatment is based on a versatile, non-invasive interface for stereotactic localization of the brain target imaged by computed tomography (CT), angiography or magnetic resonance tomography (MRT), and subsequent repetitive stereotactic irradiation of the target using a linear accelerator. The fractionation of the stereotactic irradiation was intended to meet the requirements of the basic principles of radiobiology. The radiophysical evaluation using phantoms, and the clinical results in a small number of patients, demonstrated a good reproducibilit between repeated positionings of the target in the isocenter of the accelerator, and a high degree of accuracy in the treatment of brain lesions. (authors). 28 refs.; 11 figs.; 1 tab

  13. A Fuzzy Approach Using Generalized Dinkelbach’s Algorithm for Multiobjective Linear Fractional Transportation Problem

    Directory of Open Access Journals (Sweden)

    Nurdan Cetin

    2014-01-01

    Full Text Available We consider a multiobjective linear fractional transportation problem (MLFTP with several fractional criteria, such as, the maximization of the transport profitability like profit/cost or profit/time, and its two properties are source and destination. Our aim is to introduce MLFTP which has not been studied in literature before and to provide a fuzzy approach which obtain a compromise Pareto-optimal solution for this problem. To do this, first, we present a theorem which shows that MLFTP is always solvable. And then, reducing MLFTP to the Zimmermann’s “min” operator model which is the max-min problem, we construct Generalized Dinkelbach’s Algorithm for solving the obtained problem. Furthermore, we provide an illustrative numerical example to explain this fuzzy approach.

  14. Application of the simplex method of linear programming model to ...

    African Journals Online (AJOL)

    This work discussed how the simplex method of linear programming could be used to maximize the profit of any business firm using Saclux Paint Company as a case study. It equally elucidated the effect variation in the optimal result obtained from linear programming model, will have on any given firm. It was demonstrated ...

  15. An introduction to fuzzy linear programming problems theory, methods and applications

    CERN Document Server

    Kaur, Jagdeep

    2016-01-01

    The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.

  16. An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

    Science.gov (United States)

    Zhao, Yingfeng; Liu, Sanyang

    2016-01-01

    We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

  17. A Direct Heuristic Algorithm for Linear Programming

    Indian Academy of Sciences (India)

    Abstract. An (3) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure.

  18. Train Repathing in Emergencies Based on Fuzzy Linear Programming

    Directory of Open Access Journals (Sweden)

    Xuelei Meng

    2014-01-01

    Full Text Available Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  19. Train repathing in emergencies based on fuzzy linear programming.

    Science.gov (United States)

    Meng, Xuelei; Cui, Bingmou

    2014-01-01

    Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  20. Study and program implementation of transient curves' piecewise linearization

    International Nuclear Information System (INIS)

    Shi Yang; Zu Hongbiao

    2014-01-01

    Background: Transient curves are essential for the stress analysis of related equipment in nuclear power plant (NPP). The actually operating data or the design transient data of a NPP usually consist of a large number of data points with very short time intervals. To simplify the analysis, transient curves are generally piecewise linearized in advance. Up to now, the piecewise linearization of transient curves is accomplished manually, Purpose: The aim is to develop a method for the piecewise linearization of transient curves, and to implement it by programming. Methods: First of all, the fitting line of a number of data points was obtained by the least square method. The segment of the fitting line is set while the accumulation error of linearization exceeds the preset limit with the increasing number of points. Then the linearization of subsequent data points was begun from the last point of the preceding curve segment to get the next segment in the same way, and continue until the final data point involved. Finally, averaging of junction points is taken for the segment connection. Results: A computer program named PLTC (Piecewise Linearization for Transient Curves) was implemented and verified by the linearization of the standard sine curve and typical transient curves of a NPP. Conclusion: The method and the PLTC program can be well used to the piecewise linearization of transient curves, with improving efficiency and precision. (authors)

  1. Linear Programming for Vocational Education Planning. Interim Report.

    Science.gov (United States)

    Young, Robert C.; And Others

    The purpose of the paper is to define for potential users of vocational education management information systems a quantitative analysis technique and its utilization to facilitate more effective planning of vocational education programs. Defining linear programming (LP) as a management technique used to solve complex resource allocation problems…

  2. The Computer Program LIAR for Beam Dynamics Calculations in Linear Accelerators

    International Nuclear Information System (INIS)

    Assmann, R.W.; Adolphsen, C.; Bane, K.; Raubenheimer, T.O.; Siemann, R.H.; Thompson, K.

    2011-01-01

    Linear accelerators are the central components of the proposed next generation of linear colliders. They need to provide acceleration of up to 750 GeV per beam while maintaining very small normalized emittances. Standard simulation programs, mainly developed for storage rings, do not meet the specific requirements for high energy linear accelerators. We present a new program LIAR ('LInear Accelerator Research code') that includes wakefield effects, a 6D coupled beam description, specific optimization algorithms and other advanced features. Its modular structure allows to use and to extend it easily for different purposes. The program is available for UNIX workstations and Windows PC's. It can be applied to a broad range of accelerators. We present examples of simulations for SLC and NLC.

  3. The Use of Linear Programming for Prediction.

    Science.gov (United States)

    Schnittjer, Carl J.

    The purpose of the study was to develop a linear programming model to be used for prediction, test the accuracy of the predictions, and compare the accuracy with that produced by curvilinear multiple regression analysis. (Author)

  4. The RANDOM computer program: A linear congruential random number generator

    Science.gov (United States)

    Miles, R. F., Jr.

    1986-01-01

    The RANDOM Computer Program is a FORTRAN program for generating random number sequences and testing linear congruential random number generators (LCGs). The linear congruential form of random number generator is discussed, and the selection of parameters of an LCG for a microcomputer described. This document describes the following: (1) The RANDOM Computer Program; (2) RANDOM.MOD, the computer code needed to implement an LCG in a FORTRAN program; and (3) The RANCYCLE and the ARITH Computer Programs that provide computational assistance in the selection of parameters for an LCG. The RANDOM, RANCYCLE, and ARITH Computer Programs are written in Microsoft FORTRAN for the IBM PC microcomputer and its compatibles. With only minor modifications, the RANDOM Computer Program and its LCG can be run on most micromputers or mainframe computers.

  5. Using linear programming to analyze and optimize stochastic flow lines

    DEFF Research Database (Denmark)

    Helber, Stefan; Schimmelpfeng, Katja; Stolletz, Raik

    2011-01-01

    This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time...... programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines....

  6. Near-Regular Structure Discovery Using Linear Programming

    KAUST Repository

    Huang, Qixing; Guibas, Leonidas J.; Mitra, Niloy J.

    2014-01-01

    as an optimization and efficiently solve it using linear programming techniques. Our optimization has a discrete aspect, that is, the connectivity relationships among the elements, as well as a continuous aspect, namely the locations of the elements of interest. Both

  7. NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program

    OpenAIRE

    Chermakani, Deepak Ponvel

    2012-01-01

    We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the time parameter that tends to positive infinity. The number of variables, constraints, and rational linear functions in the objective, of the real-variable problem is bounded by a polynomial ...

  8. Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs

    NARCIS (Netherlands)

    R.A. Zuidwijk (Rob)

    2005-01-01

    textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an

  9. Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae

    Science.gov (United States)

    Rosu, Grigore; Havelund, Klaus

    2001-01-01

    The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.

  10. Prediction of protein interaction hot spots using rough set-based multiple criteria linear programming.

    Science.gov (United States)

    Chen, Ruoying; Zhang, Zhiwang; Wu, Di; Zhang, Peng; Zhang, Xinyang; Wang, Yong; Shi, Yong

    2011-01-21

    Protein-protein interactions are fundamentally important in many biological processes and it is in pressing need to understand the principles of protein-protein interactions. Mutagenesis studies have found that only a small fraction of surface residues, known as hot spots, are responsible for the physical binding in protein complexes. However, revealing hot spots by mutagenesis experiments are usually time consuming and expensive. In order to complement the experimental efforts, we propose a new computational approach in this paper to predict hot spots. Our method, Rough Set-based Multiple Criteria Linear Programming (RS-MCLP), integrates rough sets theory and multiple criteria linear programming to choose dominant features and computationally predict hot spots. Our approach is benchmarked by a dataset of 904 alanine-mutated residues and the results show that our RS-MCLP method performs better than other methods, e.g., MCLP, Decision Tree, Bayes Net, and the existing HotSprint database. In addition, we reveal several biological insights based on our analysis. We find that four features (the change of accessible surface area, percentage of the change of accessible surface area, size of a residue, and atomic contacts) are critical in predicting hot spots. Furthermore, we find that three residues (Tyr, Trp, and Phe) are abundant in hot spots through analyzing the distribution of amino acids. Copyright © 2010 Elsevier Ltd. All rights reserved.

  11. Program LINEAR (version 79-1): linearize data in the evaluated nuclear data file/version B (ENDF/B) format

    International Nuclear Information System (INIS)

    Cullen, D.E.

    1979-01-01

    Program LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form (i.e., removes points not needed for linear interpolability). The main advantage of the code is that it allows subsequent codes to consider only linear-linear data. A listing of the source deck is available on request

  12. General guidelines solution for linear programming with fuzzy coefficients

    Directory of Open Access Journals (Sweden)

    Sergio Gerardo de los Cobos Silva

    2013-08-01

    Full Text Available This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp. This work presents some examples based on [1].

  13. A linear programming approach for placement of applicants to academic programs

    OpenAIRE

    Kassa, Biniyam Asmare

    2013-01-01

    This paper reports a linear programming approach for placement of applicants to study programs developed and implemented at the college of Business & Economics, Bahir Dar University, Bahir Dar, Ethiopia. The approach is estimated to significantly streamline the placement decision process at the college by reducing required man hour as well as the time it takes to announce placement decisions. Compared to the previous manual system where only one or two placement criteria were considered, the ...

  14. Propagation dynamics of super-Gaussian beams in fractional Schrödinger equation: from linear to nonlinear regimes.

    Science.gov (United States)

    Zhang, Lifu; Li, Chuxin; Zhong, Haizhe; Xu, Changwen; Lei, Dajun; Li, Ying; Fan, Dianyuan

    2016-06-27

    We have investigated the propagation dynamics of super-Gaussian optical beams in fractional Schrödinger equation. We have identified the difference between the propagation dynamics of super-Gaussian beams and that of Gaussian beams. We show that, the linear propagation dynamics of the super-Gaussian beams with order m > 1 undergo an initial compression phase before they split into two sub-beams. The sub-beams with saddle shape separate each other and their interval increases linearly with propagation distance. In the nonlinear regime, the super-Gaussian beams evolve to become a single soliton, breathing soliton or soliton pair depending on the order of super-Gaussian beams, nonlinearity, as well as the Lévy index. In two dimensions, the linear evolution of super-Gaussian beams is similar to that for one dimension case, but the initial compression of the input super-Gaussian beams and the diffraction of the splitting beams are much stronger than that for one dimension case. While the nonlinear propagation of the super-Gaussian beams becomes much more unstable compared with that for the case of one dimension. Our results show the nonlinear effects can be tuned by varying the Lévy index in the fractional Schrödinger equation for a fixed input power.

  15. Non-linear nuclear engineering models as genetic programming application

    International Nuclear Information System (INIS)

    Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S.

    1997-01-01

    This work presents a Genetic Programming paradigm and a nuclear application. A field of Artificial Intelligence, based on the concepts of Species Evolution and Natural Selection, can be understood as a self-programming process where the computer is the main agent responsible for the discovery of a program able to solve a given problem. In the present case, the problem was to find a mathematical expression in symbolic form, able to express the existent relation between equivalent ratio of a fuel cell, the enrichment of fuel elements and the multiplication factor. Such expression would avoid repeatedly reactor physics codes execution for core optimization. The results were compared with those obtained by different techniques such as Neural Networks and Linear Multiple Regression. Genetic Programming has shown to present a performance as good as, and under some features superior to Neural Network and Linear Multiple Regression. (author). 10 refs., 8 figs., 1 tabs

  16. Sensitivity analysis of linear programming problem through a recurrent neural network

    Science.gov (United States)

    Das, Raja

    2017-11-01

    In this paper we study the recurrent neural network for solving linear programming problems. To achieve optimality in accuracy and also in computational effort, an algorithm is presented. We investigate the sensitivity analysis of linear programming problem through the neural network. A detailed example is also presented to demonstrate the performance of the recurrent neural network.

  17. The evaporative fraction as a measure of surface energy partitioning

    Energy Technology Data Exchange (ETDEWEB)

    Nichols, W.E. [Pacific Northwest Lab., Richland, WA (United States); Cuenca, R.H. [Oregon State Univ., Corvallis, OR (United States)

    1990-12-31

    The evaporative fraction is a ratio that expresses the proportion of turbulent flux energy over land surfaces devoted to evaporation and transpiration (evapotranspiration). It has been used to characterize the energy partition over land surfaces and has potential for inferring daily energy balance information based on mid-day remote sensing measurements. The HAPEX-MOBILHY program`s SAMER system provided surface energy balance data over a range of agricultural crops and soil types. The databases from this large-scale field experiment was analyzed for the purpose of studying the behavior and daylight stability of the evaporative fraction in both ideal and general meteorological conditions. Strong linear relations were found to exist between the mid-day evaporative fraction and the daylight mean evaporative fraction. Statistical tests however rejected the hypothesis that the two quantities were equal. The relations between the evaporative fraction and the surface soil moisture as well as soil moisture in the complete vegetation root zone were also explored.

  18. FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.

    Science.gov (United States)

    Li, Pu; Chen, Bing

    2011-04-01

    Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.

  19. A study on rheological characteristics of roller milled fenugreek fractions.

    Science.gov (United States)

    Sakhare, Suresh D; Inamdar, Aashitosh A; Prabhasankar, P

    2016-01-01

    Fenugreek seeds were fractionated by roller milling to get various fractions. The roller milled fractions and whole fenugreek flour (WFF) were evaluated for the flow behavior and time-dependent flow properties using a rotational viscometer at the temperatures of 10-60 (0)C. The samples subjected to a programmed shear rate increase linearly from 0 to 300 s(-1) in 3 min and successive decrease linearly shear rate from 300 s(-1) to 0 in 3 min. The roller milled fractions and WFF paste exhibited non-Newtonian pseudoplastic behavior. Difference in hysteresis loop area was observed among the roller milled fractions and WFF, being more noticeable at lower temperatures. Power law and Casson models were used to predict flow properties of samples. The power law model described well the flow behavior of the roller milled fractions and WFF at temperatures tested. Except flour (FL) fraction, consistency coefficient, m, increased with the temperature both in the forward and backward measurements. The roller milled fractions and WFF exhibited rheopectic behavior that increased viscosity with increasing the shear speed and the temperature. For all the sample tested, initial shear stress increased with increase in shear rate and temperature.

  20. Generalised Assignment Matrix Methodology in Linear Programming

    Science.gov (United States)

    Jerome, Lawrence

    2012-01-01

    Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

  1. Different elution modes and field programming in gravitational field-flow fractionation. III. Field programming by flow-rate gradient generated by a programmable pump.

    Science.gov (United States)

    Plocková, J; Chmelík, J

    2001-05-25

    Gravitational field-flow fractionation (GFFF) utilizes the Earth's gravitational field as an external force that causes the settlement of particles towards the channel accumulation wall. Hydrodynamic lift forces oppose this action by elevating particles away from the channel accumulation wall. These two counteracting forces enable modulation of the resulting force field acting on particles in GFFF. In this work, force-field programming based on modulating the magnitude of hydrodynamic lift forces was implemented via changes of flow-rate, which was accomplished by a programmable pump. Several flow-rate gradients (step gradients, linear gradients, parabolic, and combined gradients) were tested and evaluated as tools for optimization of the separation of a silica gel particle mixture. The influence of increasing amount of sample injected on the peak resolution under flow-rate gradient conditions was also investigated. This is the first time that flow-rate gradients have been implemented for programming of the resulting force field acting on particles in GFFF.

  2. Fuzzy linear programming approach for solving transportation

    Indian Academy of Sciences (India)

    Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at ...

  3. The Non-Linear Relationship between BMI and Health Care Costs and the Resulting Cost Fraction Attributable to Obesity.

    Science.gov (United States)

    Laxy, Michael; Stark, Renée; Peters, Annette; Hauner, Hans; Holle, Rolf; Teuner, Christina M

    2017-08-30

    This study aims to analyse the non-linear relationship between Body Mass Index (BMI) and direct health care costs, and to quantify the resulting cost fraction attributable to obesity in Germany. Five cross-sectional surveys of cohort studies in southern Germany were pooled, resulting in data of 6757 individuals (31-96 years old). Self-reported information on health care utilisation was used to estimate direct health care costs for the year 2011. The relationship between measured BMI and annual costs was analysed using generalised additive models, and the cost fraction attributable to obesity was calculated. We found a non-linear association of BMI and health care costs with a continuously increasing slope for increasing BMI without any clear threshold. Under the consideration of the non-linear BMI-cost relationship, a shift in the BMI distribution so that the BMI of each individual is lowered by one point is associated with a 2.1% reduction of mean direct costs in the population. If obesity was eliminated, and the BMI of all obese individuals were lowered to 29.9 kg/m², this would reduce the mean direct costs by 4.0% in the population. Results show a non-linear relationship between BMI and health care costs, with very high costs for a few individuals with high BMI. This indicates that population-based interventions in combination with selective measures for very obese individuals might be the preferred strategy.

  4. Large-scale linear programs in planning and prediction.

    Science.gov (United States)

    2017-06-01

    Large-scale linear programs are at the core of many traffic-related optimization problems in both planning and prediction. Moreover, many of these involve significant uncertainty, and hence are modeled using either chance constraints, or robust optim...

  5. Linear decomposition approach for a class of nonconvex programming problems.

    Science.gov (United States)

    Shen, Peiping; Wang, Chunfeng

    2017-01-01

    This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

  6. A Recurrent Neural Network for Nonlinear Fractional Programming

    Directory of Open Access Journals (Sweden)

    Quan-Ju Zhang

    2012-01-01

    Full Text Available This paper presents a novel recurrent time continuous neural network model which performs nonlinear fractional optimization subject to interval constraints on each of the optimization variables. The network is proved to be complete in the sense that the set of optima of the objective function to be minimized with interval constraints coincides with the set of equilibria of the neural network. It is also shown that the network is primal and globally convergent in the sense that its trajectory cannot escape from the feasible region and will converge to an exact optimal solution for any initial point being chosen in the feasible interval region. Simulation results are given to demonstrate further the global convergence and good performance of the proposing neural network for nonlinear fractional programming problems with interval constraints.

  7. International program on linear electric motors

    Energy Technology Data Exchange (ETDEWEB)

    Dawson, G.E.; Eastham, A.R.; Parker, J.H.

    1992-05-01

    The International Program on Linear Electric Motors (LEM) was initiated for the purposes of commumication and coordination between various centers of expertise in LEM technology in Germany, Japan and Canada. Furthermore, it was intended to provide assessment and support of the planning of technological developments and for dissemination of information to researchers, service operators and policy makers, and to ensure that full advantage can be taken if opportunities for technology transfer occur. In the process, the program was able to provide closer contacts between researchers, to enhance and encourage collaborative research and development, and to facilitate joint ventures in advanced transportation technologies. Work done under the program is documented, and seminar materials presented by Canadian researchers in Italy, and by Italian researchers at Queen's University in Canada are presented. Five separate abstracts have been prepared for the main body of the report and the seminar materials.

  8. Evaluating forest management policies by parametric linear programing

    Science.gov (United States)

    Daniel I. Navon; Richard J. McConnen

    1967-01-01

    An analytical and simulation technique, parametric linear programing explores alternative conditions and devises an optimal management plan for each condition. Its application in solving policy-decision problems in the management of forest lands is illustrated in an example.

  9. Numerical analysis of non-linear vibrations of a fractionally damped cylindrical shell under the conditions of combinational internal resonance

    Directory of Open Access Journals (Sweden)

    Rossikhin Yury A.

    2018-01-01

    Full Text Available Non-linear damped vibrations of a cylindrical shell embedded into a fractional derivative medium are investigated for the case of the combinational internal resonance, resulting in modal interaction, using two different numerical methods with further comparison of the results obtained. The damping properties of the surrounding medium are described by the fractional derivative Kelvin-Voigt model utilizing the Riemann-Liouville fractional derivatives. Within the first method, the generalized displacements of a coupled set of nonlinear ordinary differential equations of the second order are estimated using numerical solution of nonlinear multi-term fractional differential equations by the procedure based on the reduction of the problem to a system of fractional differential equations. According to the second method, the amplitudes and phases of nonlinear vibrations are estimated from the governing nonlinear differential equations describing amplitude-and-phase modulations for the case of the combinational internal resonance. A good agreement in results is declared.

  10. C-program LINOP for the evaluation of film dosemeters by linear optimization. User manual

    International Nuclear Information System (INIS)

    Kragh, P.

    1995-11-01

    Linear programming results in an optimal measuring value for film dosemeters. The Linop program was developed to be used for linear programming. The program permits the evaluation and control of film dosemeters and of all other multi-component dosemeters. This user manual for the Linop program contains the source program, a description of the program and installation and use instructions. The data sets with programs and examples are available upon request. (orig.) [de

  11. A property of assignment type mixed integer linear programming problems

    NARCIS (Netherlands)

    Benders, J.F.; van Nunen, J.A.E.E.

    1982-01-01

    In this paper we will proof that rather tight upper bounds can be given for the number of non-unique assignments that are achieved after solving the linear programming relaxation of some types of mixed integer linear assignment problems. Since in these cases the number of splitted assignments is

  12. Comparison of linear, mixed integer and non-linear programming methods in energy system dispatch modelling

    DEFF Research Database (Denmark)

    Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian

    2014-01-01

    In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...

  13. Fundamental solution of the problem of linear programming and method of its determination

    Science.gov (United States)

    Petrunin, S. V.

    1978-01-01

    The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.

  14. Visual Outcome in Meningiomas Around Anterior Visual Pathways Treated With Linear Accelerator Fractionated Stereotactic Radiotherapy

    International Nuclear Information System (INIS)

    Stiebel-Kalish, Hadas; Reich, Ehud; Gal, Lior; Rappaport, Zvi Harry; Nissim, Ouzi; Pfeffer, Raphael; Spiegelmann, Roberto

    2012-01-01

    Purpose: Meningiomas threatening the anterior visual pathways (AVPs) and not amenable for surgery are currently treated with multisession stereotactic radiotherapy. Stereotactic radiotherapy is available with a number of devices. The most ubiquitous include the gamma knife, CyberKnife, tomotherapy, and isocentric linear accelerator systems. The purpose of our study was to describe a case series of AVP meningiomas treated with linear accelerator fractionated stereotactic radiotherapy (FSRT) using the multiple, noncoplanar, dynamic conformal rotation paradigm and to compare the success and complication rates with those reported for other techniques. Patients and Methods: We included all patients with AVP meningiomas followed up at our neuro-ophthalmology unit for a minimum of 12 months after FSRT. We compared the details of the neuro-ophthalmologic examinations and tumor size before and after FSRT and at the end of follow-up. Results: Of 87 patients with AVP meningiomas, 17 had been referred for FSRT. Of the 17 patients, 16 completed >12 months of follow-up (mean 39). Of the 16 patients, 11 had undergone surgery before FSRT and 5 had undergone FSRT as first-line management. Tumor control was achieved in 14 of the 16 patients, with three meningiomas shrinking in size after RT. Two meningiomas progressed, one in an area that was outside the radiation field. The visual function had improved in 6 or stabilized in 8 of the 16 patients (88%) and worsened in 2 (12%). Conclusions: Linear accelerator fractionated RT using the multiple noncoplanar dynamic rotation conformal paradigm can be offered to patients with meningiomas that threaten the anterior visual pathways as an adjunct to surgery or as first-line treatment, with results comparable to those reported for other stereotactic RT techniques.

  15. Mixed integer (0-1) fractional programming for decision support in paper production industry

    NARCIS (Netherlands)

    Claassen, G.D.H.

    2014-01-01

    This paper presents an effective and efficient method for solving a special class of mixed integer fractional programming (FP) problems. We take a classical reformulation approach for continuous FP as a starting point and extend it for solving a more general class of mixed integer (0–1) fractional

  16. A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson

    DEFF Research Database (Denmark)

    Harrod, Steven

    2009-01-01

    The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...

  17. Fractionation of human serum lipoproteins and simultaneous enzymatic determination of cholesterol and triglycerides

    International Nuclear Information System (INIS)

    Qureshi, Rashid Nazir; Kok, Wim Th.; Schoenmakers, Peter J.

    2009-01-01

    A method based on Asymmetric Flow Field-Flow Fractionation (AF4) was developed to separate different types of lipoproteins from human serum. The emphasis in the method optimization was on the possibilities to characterize the largest lipoprotein fractions (LDL and VLDL), which is usually not possible with the size-exclusion chromatography methods applied in routine analysis. Different channel geometries and flow programs were tested and compared. The use of a short fractionation channel was shown to give less sample dilution at the same fractionation power compared to a conventional, long channel. Different size selectivities were obtained with an exponential decay and a linear cross flow program. The ratio of the UV absorption signal to the light scattering signal was used to validate the relation between retention time and size of the fractionated particles. An experimental setup was developed for the simultaneous determination of the cholesterol and triglycerides distribution over the lipoprotein fractions, based on enzymatic reactions followed by UV detection at 500 nm. Coiled and knitted PTFE tubing reactors were compared. An improved peak sharpness and sensitivity were observed with the knitted tubing reactor. After optimization of the experimental conditions a satisfactory linearity and precision (2-3% rsd for cholesterol and 5-6% rsd for triglycerides) were obtained. Finally, serum samples, a pooled sample from healthy volunteers and samples of sepsis patients, were analyzed with the method developed. Lipoprotein fractionation and cholesterol and triglyceride distributions could be correlated with the clinical background of the samples.

  18. Fractionation of human serum lipoproteins and simultaneous enzymatic determination of cholesterol and triglycerides

    Energy Technology Data Exchange (ETDEWEB)

    Qureshi, Rashid Nazir [Polymer-Analysis Group, van' t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam (Netherlands); Kok, Wim Th., E-mail: W.Th.Kok@uva.nl [Polymer-Analysis Group, van' t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam (Netherlands); Schoenmakers, Peter J. [Polymer-Analysis Group, van' t Hoff Institute for Molecular Sciences, University of Amsterdam, Nieuwe Achtergracht 166, 1018WV Amsterdam (Netherlands)

    2009-11-03

    A method based on Asymmetric Flow Field-Flow Fractionation (AF4) was developed to separate different types of lipoproteins from human serum. The emphasis in the method optimization was on the possibilities to characterize the largest lipoprotein fractions (LDL and VLDL), which is usually not possible with the size-exclusion chromatography methods applied in routine analysis. Different channel geometries and flow programs were tested and compared. The use of a short fractionation channel was shown to give less sample dilution at the same fractionation power compared to a conventional, long channel. Different size selectivities were obtained with an exponential decay and a linear cross flow program. The ratio of the UV absorption signal to the light scattering signal was used to validate the relation between retention time and size of the fractionated particles. An experimental setup was developed for the simultaneous determination of the cholesterol and triglycerides distribution over the lipoprotein fractions, based on enzymatic reactions followed by UV detection at 500 nm. Coiled and knitted PTFE tubing reactors were compared. An improved peak sharpness and sensitivity were observed with the knitted tubing reactor. After optimization of the experimental conditions a satisfactory linearity and precision (2-3% rsd for cholesterol and 5-6% rsd for triglycerides) were obtained. Finally, serum samples, a pooled sample from healthy volunteers and samples of sepsis patients, were analyzed with the method developed. Lipoprotein fractionation and cholesterol and triglyceride distributions could be correlated with the clinical background of the samples.

  19. Controller design approach based on linear programming.

    Science.gov (United States)

    Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa

    2013-11-01

    This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.

  20. Sensitivity Analysis of Linear Programming and Quadratic Programming Algorithms for Control Allocation

    Science.gov (United States)

    Frost, Susan A.; Bodson, Marc; Acosta, Diana M.

    2009-01-01

    The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.

  1. Scatter fractions from linear accelerators with x-ray energies from 6 to 24 MV.

    Science.gov (United States)

    Taylor, P L; Rodgers, J E; Shobe, J

    1999-08-01

    Computation of shielding requirements for a linear accelerator must take into account the amount of radiation scattered from the patient to areas outside the primary beam. Currently, the most frequently used data are from NCRP 49 that only includes data for x-ray energies up to 6 MV and angles from 30 degrees to 135 degrees. In this work we have determined by Monte Carlo simulation the scattered fractions of dose for a wide range of energies and angles of clinical significance including 6, 10, 18, and 24 MV and scattering angles from 10 degrees to 150 degrees. Calculations were made for a 400 cm2 circular field size impinging onto a spherical phantom. Scattered fractions of dose were determined at 1 m from the phantom. Angles from 10 degrees to 30 degrees are of concern for higher energies where the scatter is primarily in the forward direction. An error in scatter fraction may result in too little secondary shielding near the junction with the primary barrier. The Monte Carlo code ITS (Version 3.0) developed at Sandia National Laboratory and NIST was used to simulate scatter from the patient to the barrier. Of significance was the variation of calculated scattered dose with depth of measurement within the barrier indicating that accurate values may be difficult to obtain. Mean energies of scatter x-ray spectra are presented.

  2. Application of the method of continued fractions for electron scattering by linear molecules

    International Nuclear Information System (INIS)

    Lee, M.-T.; Iga, I.; Fujimoto, M.M.; Lara, O.; Brasilia Univ., DF

    1995-01-01

    The method of continued fractions (MCF) of Horacek and Sasakawa is adapted for the first time to study low-energy electron scattering by linear molecules. Particularly, we have calculated the reactance K-matrices for an electron scattered by hydrogen molecule and hydrogen molecular ion as well as by a polar LiH molecule in the static-exchange level. For all the applications studied herein. the calculated physical quantities converge rapidly, even for a strongly polar molecule such as LiH, to the correct values and in most cases the convergence is monotonic. Our study suggests that the MCF could be an efficient method for studying electron-molecule scattering and also photoionization of molecules. (Author)

  3. Spline smoothing of histograms by linear programming

    Science.gov (United States)

    Bennett, J. O.

    1972-01-01

    An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.

  4. Formulated linear programming problems from game theory and its ...

    African Journals Online (AJOL)

    Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.

  5. An algorithm for the solution of dynamic linear programs

    Science.gov (United States)

    Psiaki, Mark L.

    1989-01-01

    The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation

  6. MAGDM linear-programming models with distinct uncertain preference structures.

    Science.gov (United States)

    Xu, Zeshui S; Chen, Jian

    2008-10-01

    Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.

  7. An overview of solution methods for multi-objective mixed integer linear programming programs

    DEFF Research Database (Denmark)

    Andersen, Kim Allan; Stidsen, Thomas Riis

    Multiple objective mixed integer linear programming (MOMIP) problems are notoriously hard to solve to optimality, i.e. finding the complete set of non-dominated solutions. We will give an overview of existing methods. Among those are interactive methods, the two phases method and enumeration...... methods. In particular we will discuss the existing branch and bound approaches for solving multiple objective integer programming problems. Despite the fact that branch and bound methods has been applied successfully to integer programming problems with one criterion only a few attempts has been made...

  8. Accommodation of practical constraints by a linear programming jet select. [for Space Shuttle

    Science.gov (United States)

    Bergmann, E.; Weiler, P.

    1983-01-01

    An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.

  9. Coefficient of restitution in fractional viscoelastic compliant impacts using fractional Chebyshev collocation

    Science.gov (United States)

    Dabiri, Arman; Butcher, Eric A.; Nazari, Morad

    2017-02-01

    Compliant impacts can be modeled using linear viscoelastic constitutive models. While such impact models for realistic viscoelastic materials using integer order derivatives of force and displacement usually require a large number of parameters, compliant impact models obtained using fractional calculus, however, can be advantageous since such models use fewer parameters and successfully capture the hereditary property. In this paper, we introduce the fractional Chebyshev collocation (FCC) method as an approximation tool for numerical simulation of several linear fractional viscoelastic compliant impact models in which the overall coefficient of restitution for the impact is studied as a function of the fractional model parameters for the first time. Other relevant impact characteristics such as hysteresis curves, impact force gradient, penetration and separation depths are also studied.

  10. DESIGN OF EDUCATIONAL PROBLEMS ON LINEAR PROGRAMMING USING SYSTEMS OF COMPUTER MATHEMATICS

    Directory of Open Access Journals (Sweden)

    Volodymyr M. Mykhalevych

    2013-11-01

    Full Text Available From a perspective of the theory of educational problems a problem of substitution in the conditions of ICT use of one discipline by an educational problem of another discipline is represented. Through the example of mathematical problems of linear programming it is showed that a student’s method of operation in the course of an educational problem solving is determinant in the identification of an educational problem in relation to a specific discipline: linear programming, informatics, mathematical modeling, methods of optimization, automatic control theory, calculus etc. It is substantiated the necessity of linear programming educational problems renovation with the purpose of making students free of bulky similar arithmetic calculations and notes which often becomes a barrier to a deeper understanding of key ideas taken as a basis of algorithms used by them.

  11. Generalized Second-Order Parametric Optimality Conditions in Semiinfinite Discrete Minmax Fractional Programming and Second-Order Univexity

    Directory of Open Access Journals (Sweden)

    Ram Verma

    2016-02-01

    Full Text Available This paper deals with mainly establishing numerous sets of generalized second order paramertic sufficient optimality conditions for a semiinfinite discrete minmax fractional programming problem, while the results on semiinfinite discrete minmax fractional programming problem achieved based on some partitioning schemes under various types of generalized second order univexity assumptions. 

  12. Scattered fractions of dose from 18 and 25 MV X-ray radiotherapy linear accelerators

    International Nuclear Information System (INIS)

    Shobe, J.; Rodgers, J.E.; Taylor, P.L.; Jackson, J.; Popescu, G.

    1996-01-01

    Over the years, measurements have been made at a few energies to estimate the scattered fraction of dose from the patient in medical radiotherapy operations. This information has been a useful aid in the determination of shielding requirements for these facilities. With these measurements, known characteriztics of photons, and various other known parameters, Monte Carlo codes are being used to calculate the scattered fractions and hence the shielding requirements for the photons of other energies commonly used in radiotherapeutic applications. The National Institute of Standards and Technology (NIST) acquired a Sagittaire medical linear accelerator (linac) which was previously located at the Yale-New Haven Hospital. This linac provides an X-ray beam of 25 MV photons and electron beams with energies up to 32 MeV. The housing on the gantry was permanently removed from the accelerator during installation. A Varian Clinac 1800 linear accelerator was used to produce the 18 MV photons at the Frederick Memorial Hospital Regional Cancer Therapy Center in Frederick, MD. This paper represents a study of the photon dose scattered from a patient in typical radiation treatment situations as it relates to the dose delivered at the isocenter in water. The results of these measurements will be compared to Monte Carlo calculations. Photon spectral measurements were not made at this time. Neutron spectral measurements were made on this Sagittaire machine in its previous location and that work was not repeated here, although a brief study of the neutron component of the 18 and 25 MV linacs was performed utilizing thermoluminescent dosimetry (TLD) to determine the isotropy of the neutron dose. (author)

  13. Mathematical solution of multilevel fractional programming problem with fuzzy goal programming approach

    Science.gov (United States)

    Lachhwani, Kailash; Poonia, Mahaveer Prasad

    2012-08-01

    In this paper, we show a procedure for solving multilevel fractional programming problems in a large hierarchical decentralized organization using fuzzy goal programming approach. In the proposed method, the tolerance membership functions for the fuzzily described numerator and denominator part of the objective functions of all levels as well as the control vectors of the higher level decision makers are respectively defined by determining individual optimal solutions of each of the level decision makers. A possible relaxation of the higher level decision is considered for avoiding decision deadlock due to the conflicting nature of objective functions. Then, fuzzy goal programming approach is used for achieving the highest degree of each of the membership goal by minimizing negative deviational variables. We also provide sensitivity analysis with variation of tolerance values on decision vectors to show how the solution is sensitive to the change of tolerance values with the help of a numerical example.

  14. International program on linear electric motors. CIGGT report No. 92-1

    Energy Technology Data Exchange (ETDEWEB)

    Dawson, G.E.; Eastham, A.R.; Parker, J.H.

    1992-12-31

    The International Program for Linear Electric Motors (LEM) was begun in April 1989 to communicate and coordinate activities with centers of expertise in Germany, Canada, and Japan; to provide for the assessment and support of the planning of technological developments and for dissemination of information to researchers, service operators, and policy makers; and to ensure that full advantage can be taken if opportunities for technology transfer occur. This report documents the work done under the program, including standardizing linear induction motor (LIM) design characteristics; test procedures and measurement methods; rating; database for design data; criteria for evaluation of designs; computer programs for modelling performance; and a design study for an agreed application.

  15. Indirect synthesis of multi-degree of freedom transient systems. [linear programming for a kinematically linear system

    Science.gov (United States)

    Pilkey, W. D.; Chen, Y. H.

    1974-01-01

    An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.

  16. LCPT: a program for finding linear canonical transformations

    International Nuclear Information System (INIS)

    Char, B.W.; McNamara, B.

    1979-01-01

    This article describes a MACSYMA program to compute symbolically a canonical linear transformation between coordinate systems. The difficulties in implementation of this canonical small physics problem are also discussed, along with the implications that may be drawn from such difficulties about widespread MACSYMA usage by the community of computational/theoretical physicists

  17. Interior-Point Methods for Linear Programming: A Review

    Science.gov (United States)

    Singh, J. N.; Singh, D.

    2002-01-01

    The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with…

  18. Optimal homotopy asymptotic method for solving fractional relaxation-oscillation equation

    Directory of Open Access Journals (Sweden)

    Mohammad Hamarsheh

    2015-11-01

    Full Text Available In this paper, an approximate analytical solution of linear fractional relaxation-oscillation equations in which the fractional derivatives are given in the Caputo sense, is obtained by the optimal homotopy asymptotic method (OHAM. The studied OHAM is based on minimizing the residual error. The results given by OHAM are compared with the exact solutions and the solutions obtained by generalized Taylor matrix method. The reliability and efficiency of the proposed approach are demonstrated in three examples with the aid of the symbolic algebra program Maple.

  19. A Linear Programming Model to Optimize Various Objective Functions of a Foundation Type State Support Program.

    Science.gov (United States)

    Matzke, Orville R.

    The purpose of this study was to formulate a linear programming model to simulate a foundation type support program and to apply this model to a state support program for the public elementary and secondary school districts in the State of Iowa. The model was successful in producing optimal solutions to five objective functions proposed for…

  20. International Workshop on “Generalized Concavity, Fractional Programming and Economic Applications”

    CERN Document Server

    Castagnoli, Erio; Martein, Laura; Mazzoleni, Piera; Schaible, Siegfried

    1990-01-01

    Generalizations of convex functions have been used in a variety of fields such as economics. business administration. engineering. statistics and applied sciences.· In 1949 de Finetti introduced one of the fundamental of generalized convex functions characterized by convex level sets which are now known as quasiconvex functions. Since then numerous types of generalized convex functions have been defined in accordance with the need of particular applications.· In each case such functions preserve soine of the valuable properties of a convex function. In addition to generalized convex functions this volume deals with fractional programs. These are constrained optimization problems which in the objective function involve one or several ratios. Such functions are often generalized convex. Fractional programs arise in management science. economics and numerical mathematics for example. In order to promote the circulation and development of research in this field. an international workshop on "Generalized Concavi...

  1. Acoustic programming in step-split-flow lateral-transport thin fractionation.

    Science.gov (United States)

    Ratier, Claire; Hoyos, Mauricio

    2010-02-15

    We propose a new separation scheme for micrometer-sized particles combining acoustic forces and gravitational field in split-flow lateral-transport thin (SPLITT)-like fractionation channels. Acoustic forces are generated by ultrasonic standing waves set up in the channel thickness. We report on the separation of latex particles of two different sizes in a preliminary experiment using this proposed hydrodynamic acoustic sorter, HAS. Total binary separation of 5 and 10 microm diameter particles has been achieved. Numerical simulations of trajectories of particles flowing through a step-SPLITT under the conditions which combine acoustic standing waves and gravity show a very good agreement with the experiment. Calculations in order to compare separations obtained by the acoustic programming s-SPLITT fractionation and the conventional SPLITT fractionation show that the improvement in separation time is around 1 order of magnitude and could still be improved; this is the major finding of this work. This separation technique can be extended to biomimetic particles and blood cells.

  2. A Comparison of Traditional Worksheet and Linear Programming Methods for Teaching Manure Application Planning.

    Science.gov (United States)

    Schmitt, M. A.; And Others

    1994-01-01

    Compares traditional manure application planning techniques calculated to meet agronomic nutrient needs on a field-by-field basis with plans developed using computer-assisted linear programming optimization methods. Linear programming provided the most economical and environmentally sound manure application strategy. (Contains 15 references.) (MDH)

  3. Planning Student Flow with Linear Programming: A Tunisian Case Study.

    Science.gov (United States)

    Bezeau, Lawrence

    A student flow model in linear programming format, designed to plan the movement of students into secondary and university programs in Tunisia, is described. The purpose of the plan is to determine a sufficient number of graduating students that would flow back into the system as teachers or move into the labor market to meet fixed manpower…

  4. Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers.

    Science.gov (United States)

    Stamova, Ivanka; Stamov, Gani

    2017-12-01

    In this paper, we propose a fractional-order neural network system with time-varying delays and reaction-diffusion terms. We first develop a new Mittag-Leffler synchronization strategy for the controlled nodes via impulsive controllers. Using the fractional Lyapunov method sufficient conditions are given. We also study the global Mittag-Leffler synchronization of two identical fractional impulsive reaction-diffusion neural networks using linear controllers, which was an open problem even for integer-order models. Since the Mittag-Leffler stability notion is a generalization of the exponential stability concept for fractional-order systems, our results extend and improve the exponential impulsive control theory of neural network system with time-varying delays and reaction-diffusion terms to the fractional-order case. The fractional-order derivatives allow us to model the long-term memory in the neural networks, and thus the present research provides with a conceptually straightforward mathematical representation of rather complex processes. Illustrative examples are presented to show the validity of the obtained results. We show that by means of appropriate impulsive controllers we can realize the stability goal and to control the qualitative behavior of the states. An image encryption scheme is extended using fractional derivatives. Copyright © 2017 Elsevier Ltd. All rights reserved.

  5. Application of linear programming and perturbation theory in optimization of fuel utilization in a nuclear reactor

    International Nuclear Information System (INIS)

    Zavaljevski, N.

    1985-01-01

    Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time

  6. A Nutritional Analysis of the Food Basket in BIH: A Linear Programming Approach

    Directory of Open Access Journals (Sweden)

    Arnaut-Berilo Almira

    2017-04-01

    Full Text Available This paper presents linear and goal programming optimization models for determining and analyzing the food basket in Bosnia and Herzegovina (BiH in terms of adequate nutritional needs according to World Health Organization (WHO standards and World Bank (WB recommendations. A linear programming (LP model and goal linear programming model (GLP are adequate since price and nutrient contents are linearly related to food weight. The LP model provides information about the minimal value and the structure of the food basket for an average person in BiH based on nutrient needs. GLP models are designed to give us information on minimal deviations from nutrient needs if the budget is fixed. Based on these results, poverty analysis can be performed. The data used for the models consisted of 158 food items from the general consumption of the population of BiH according to COICOP classifications, with average prices in 2015 for these products.

  7. Weighted inequalities for fractional integral operators and linear commutators in the Morrey-type spaces

    Directory of Open Access Journals (Sweden)

    Hua Wang

    2017-01-01

    Full Text Available Abstract In this paper, we first introduce some new Morrey-type spaces containing generalized Morrey space and weighted Morrey space with two weights as special cases. Then we give the weighted strong type and weak type estimates for fractional integral operators I α $I_{\\alpha}$ in these new Morrey-type spaces. Furthermore, the weighted strong type estimate and endpoint estimate of linear commutators [ b , I α ] $[b,I_{\\alpha}]$ formed by b and I α $I_{\\alpha}$ are established. Also we study related problems about two-weight, weak type inequalities for I α $I_{\\alpha}$ and [ b , I α ] $[b,I_{\\alpha}]$ in the Morrey-type spaces and give partial results.

  8. Planning under uncertainty solving large-scale stochastic linear programs

    Energy Technology Data Exchange (ETDEWEB)

    Infanger, G. [Stanford Univ., CA (United States). Dept. of Operations Research]|[Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft

    1992-12-01

    For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.

  9. No-signaling quantum key distribution: solution by linear programming

    Science.gov (United States)

    Hwang, Won-Young; Bae, Joonwoo; Killoran, Nathan

    2015-02-01

    We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.

  10. Optimal selection for shielding materials by fuzzy linear programming

    International Nuclear Information System (INIS)

    Kanai, Y.; Miura, N.; Sugasawa, S.

    1996-01-01

    An application of fuzzy linear programming methods to optimization of a radiation shield is presented. The main purpose of the present study is the choice of materials and the search of the ratio of mixture-component as the first stage of the methodology on optimum shielding design according to individual requirements of nuclear reactor, reprocessing facility, shipping cask installing spent fuel, ect. The characteristic values for the shield optimization may be considered their cost, spatial space, weight and some shielding qualities such as activation rate and total dose rate for neutron and gamma ray (includes secondary gamma ray). This new approach can reduce huge combination calculations for conventional two-valued logic approaches to representative single shielding calculation by group-wised optimization parameters determined in advance. Using the fuzzy linear programming method, possibilities for reducing radiation effects attainable in optimal compositions hydrated, lead- and boron-contained materials are investigated

  11. A MICROCOMPUTER LINEAR PROGRAMMING PACKAGE: AN ALTERNATIVE TO MAINFRAMES

    OpenAIRE

    Laughlin, David H.

    1984-01-01

    This paper presents the capabilities and limitations of a microcomputer linear programming package. The solution algorithm is a version of the revised simplex. Rapid problem entry, user ease of operation, sensitivity analyses on objective function and right hand sides are advantages. A problem size of 150 activities and 64 constraints can be solved in present form. Due to problem size, limitations and lack of parametric and integer programming routines, this package is thought to have the mos...

  12. Micosoft Excel Sensitivity Analysis for Linear and Stochastic Program Feed Formulation

    Science.gov (United States)

    Sensitivity analysis is a part of mathematical programming solutions and is used in making nutritional and economic decisions for a given feed formulation problem. The terms, shadow price and reduced cost, are familiar linear program (LP) terms to feed formulators. Because of the nonlinear nature of...

  13. Linear Programming, the Simplex Algorithm and Simple Polytopes

    Directory of Open Access Journals (Sweden)

    Das Bhusan

    2010-09-01

    Full Text Available In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.

  14. Stability of multi-objective bi-level linear programming problems under fuzziness

    Directory of Open Access Journals (Sweden)

    Abo-Sinna Mahmoud A.

    2013-01-01

    Full Text Available This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC. First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.

  15. 175 Years of Linear Programming - Minimax and Cake Topography

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 7. 175 Years of Linear Programming - Minimax and Cake Topography. Vijay Chandru M R Rao. Series Article Volume 4 Issue 7 July 1999 pp 4-13. Fulltext. Click here to view fulltext PDF. Permanent link:

  16. Assembling networks of microbial genomes using linear programming.

    Science.gov (United States)

    Holloway, Catherine; Beiko, Robert G

    2010-11-20

    Microbial genomes exhibit complex sets of genetic affinities due to lateral genetic transfer. Assessing the relative contributions of parent-to-offspring inheritance and gene sharing is a vital step in understanding the evolutionary origins and modern-day function of an organism, but recovering and showing these relationships is a challenging problem. We have developed a new approach that uses linear programming to find between-genome relationships, by treating tables of genetic affinities (here, represented by transformed BLAST e-values) as an optimization problem. Validation trials on simulated data demonstrate the effectiveness of the approach in recovering and representing vertical and lateral relationships among genomes. Application of the technique to a set comprising Aquifex aeolicus and 75 other thermophiles showed an important role for large genomes as 'hubs' in the gene sharing network, and suggested that genes are preferentially shared between organisms with similar optimal growth temperatures. We were also able to discover distinct and common genetic contributors to each sequenced representative of genus Pseudomonas. The linear programming approach we have developed can serve as an effective inference tool in its own right, and can be an efficient first step in a more-intensive phylogenomic analysis.

  17. On the Approximate Solutions of Local Fractional Differential Equations with Local Fractional Operators

    Directory of Open Access Journals (Sweden)

    Hossein Jafari

    2016-04-01

    Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.

  18. Algorithmic Trading with Developmental and Linear Genetic Programming

    Science.gov (United States)

    Wilson, Garnett; Banzhaf, Wolfgang

    A developmental co-evolutionary genetic programming approach (PAM DGP) and a standard linear genetic programming (LGP) stock trading systemare applied to a number of stocks across market sectors. Both GP techniques were found to be robust to market fluctuations and reactive to opportunities associated with stock price rise and fall, with PAMDGP generating notably greater profit in some stock trend scenarios. Both algorithms were very accurate at buying to achieve profit and selling to protect assets, while exhibiting bothmoderate trading activity and the ability to maximize or minimize investment as appropriate. The content of the trading rules produced by both algorithms are also examined in relation to stock price trend scenarios.

  19. A novel recurrent neural network with finite-time convergence for linear programming.

    Science.gov (United States)

    Liu, Qingshan; Cao, Jinde; Chen, Guanrong

    2010-11-01

    In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.

  20. Development and adjustment of programs for solving systems of linear equations

    International Nuclear Information System (INIS)

    Fujimura, Toichiro

    1978-03-01

    Programs for solving the systems of linear equations have been adjusted and developed in expanding the scientific subroutine library SSL. The principal programs adjusted are based on the congruent method, method of product form of the inverse, orthogonal method, Crout's method for sparse system, and acceleration of iterative methods. The programs developed are based on the escalator method, direct parallel residue method and block tridiagonal method for band system. Described are usage of the programs developed and their future improvement. FORTRAN lists with simple examples in tests of the programs are also given. (auth.)

  1. Non-linear nuclear engineering models as genetic programming application; Modelos nao-lineares de engenharia nuclear como aplicacao de programacao genetica

    Energy Technology Data Exchange (ETDEWEB)

    Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S. [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia

    1997-12-01

    This work presents a Genetic Programming paradigm and a nuclear application. A field of Artificial Intelligence, based on the concepts of Species Evolution and Natural Selection, can be understood as a self-programming process where the computer is the main agent responsible for the discovery of a program able to solve a given problem. In the present case, the problem was to find a mathematical expression in symbolic form, able to express the existent relation between equivalent ratio of a fuel cell, the enrichment of fuel elements and the multiplication factor. Such expression would avoid repeatedly reactor physics codes execution for core optimization. The results were compared with those obtained by different techniques such as Neural Networks and Linear Multiple Regression. Genetic Programming has shown to present a performance as good as, and under some features superior to Neural Network and Linear Multiple Regression. (author). 10 refs., 8 figs., 1 tabs.

  2. A non-linear programming approach to the computer-aided design of regulators using a linear-quadratic formulation

    Science.gov (United States)

    Fleming, P.

    1985-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.

  3. Genetic programming over context-free languages with linear constraints for the knapsack problem: first results.

    Science.gov (United States)

    Bruhn, Peter; Geyer-Schulz, Andreas

    2002-01-01

    In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling complementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.

  4. The evaporative fraction as a measure of surface energy partitioning

    Energy Technology Data Exchange (ETDEWEB)

    Nichols, W.E. (Pacific Northwest Lab., Richland, WA (United States)); Cuenca, R.H. (Oregon State Univ., Corvallis, OR (United States))

    1990-01-01

    The evaporative fraction is a ratio that expresses the proportion of turbulent flux energy over land surfaces devoted to evaporation and transpiration (evapotranspiration). It has been used to characterize the energy partition over land surfaces and has potential for inferring daily energy balance information based on mid-day remote sensing measurements. The HAPEX-MOBILHY program's SAMER system provided surface energy balance data over a range of agricultural crops and soil types. The databases from this large-scale field experiment was analyzed for the purpose of studying the behavior and daylight stability of the evaporative fraction in both ideal and general meteorological conditions. Strong linear relations were found to exist between the mid-day evaporative fraction and the daylight mean evaporative fraction. Statistical tests however rejected the hypothesis that the two quantities were equal. The relations between the evaporative fraction and the surface soil moisture as well as soil moisture in the complete vegetation root zone were also explored.

  5. Stochastic linear programming models, theory, and computation

    CERN Document Server

    Kall, Peter

    2011-01-01

    This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...

  6. A computer program for two-particle generalized coefficients of fractional parentage

    Science.gov (United States)

    Deveikis, A.; Juodagalvis, A.

    2008-10-01

    We present a FORTRAN90 program GCFP for the calculation of the generalized coefficients of fractional parentage (generalized CFPs or GCFP). The approach is based on the observation that the multi-shell CFPs can be expressed in terms of single-shell CFPs, while the latter can be readily calculated employing a simple enumeration scheme of antisymmetric A-particle states and an efficient method of construction of the idempotent matrix eigenvectors. The program provides fast calculation of GCFPs for a given particle number and produces results possessing numerical uncertainties below the desired tolerance. A single j-shell is defined by four quantum numbers, (e,l,j,t). A supplemental C++ program parGCFP allows calculation to be done in batches and/or in parallel. Program summaryProgram title:GCFP, parGCFP Catalogue identifier: AEBI_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEBI_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 17 199 No. of bytes in distributed program, including test data, etc.: 88 658 Distribution format: tar.gz Programming language: FORTRAN 77/90 ( GCFP), C++ ( parGCFP) Computer: Any computer with suitable compilers. The program GCFP requires a FORTRAN 77/90 compiler. The auxiliary program parGCFP requires GNU-C++ compatible compiler, while its parallel version additionally requires MPI-1 standard libraries Operating system: Linux (Ubuntu, Scientific) (all programs), also checked on Windows XP ( GCFP, serial version of parGCFP) RAM: The memory demand depends on the computation and output mode. If this mode is not 4, the program GCFP demands the following amounts of memory on a computer with Linux operating system. It requires around 2 MB of RAM for the A=12 system at E⩽2. Computation of the A=50 particle system requires around 60 MB of

  7. Fitting program for linear regressions according to Mahon (1996)

    Energy Technology Data Exchange (ETDEWEB)

    2018-01-09

    This program takes the users' Input data and fits a linear regression to it using the prescription presented by Mahon (1996). Compared to the commonly used York fit, this method has the correct prescription for measurement error propagation. This software should facilitate the proper fitting of measurements with a simple Interface.

  8. Analysis of Students' Errors on Linear Programming at Secondary ...

    African Journals Online (AJOL)

    The purpose of this study was to identify secondary school students' errors on linear programming at 'O' level. It is based on the fact that students' errors inform teaching hence an essential tool for any serious mathematics teacher who intends to improve mathematics teaching. The study was guided by a descriptive survey ...

  9. Fractional charges

    International Nuclear Information System (INIS)

    Saminadayar, L.

    2001-01-01

    20 years ago fractional charges were imagined to explain values of conductivity in some materials. Recent experiments have proved the existence of charges whose value is the third of the electron charge. This article presents the experimental facts that have led theorists to predict the existence of fractional charges from the motion of quasi-particles in a linear chain of poly-acetylene to the quantum Hall effect. According to the latest theories, fractional charges are neither bosons nor fermions but anyons, they are submitted to an exclusive principle that is less stringent than that for fermions. (A.C.)

  10. Life cycle cost optimization of biofuel supply chains under uncertainties based on interval linear programming

    DEFF Research Database (Denmark)

    Ren, Jingzheng; Dong, Liang; Sun, Lu

    2015-01-01

    in this model, and the price of the resources, the yield of grain and the market demands were regarded as interval numbers instead of constants. An interval linear programming was developed, and a method for solving interval linear programming was presented. An illustrative case was studied by the proposed...

  11. Exact solutions to the time-fractional differential equations via local fractional derivatives

    Science.gov (United States)

    Guner, Ozkan; Bekir, Ahmet

    2018-01-01

    This article utilizes the local fractional derivative and the exp-function method to construct the exact solutions of nonlinear time-fractional differential equations (FDEs). For illustrating the validity of the method, it is applied to the time-fractional Camassa-Holm equation and the time-fractional-generalized fifth-order KdV equation. Moreover, the exact solutions are obtained for the equations which are formed by different parameter values related to the time-fractional-generalized fifth-order KdV equation. This method is an reliable and efficient mathematical tool for solving FDEs and it can be applied to other non-linear FDEs.

  12. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    KAUST Repository

    N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  13. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    KAUST Repository

    N'Doye, Ibrahima

    2015-07-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  14. A computer program for two-particle intrinsic coefficients of fractional parentage

    Science.gov (United States)

    Deveikis, A.

    2012-06-01

    A Fortran 90 program CESOS for the calculation of the two-particle intrinsic coefficients of fractional parentage for several j-shells with isospin and an arbitrary number of oscillator quanta (CESOs) is presented. The implemented procedure for CESOs calculation consistently follows the principles of antisymmetry and translational invariance. The approach is based on a simple enumeration scheme for antisymmetric many-particle states, efficient algorithms for calculation of the coefficients of fractional parentage for j-shells with isospin, and construction of the subspace of the center-of-mass Hamiltonian eigenvectors corresponding to the minimal eigenvalue equal to 3/2 (in ℏω). The program provides fast calculation of CESOs for a given particle number and produces results possessing small numerical uncertainties. The introduced CESOs may be used for calculation of expectation values of two-particle nuclear shell-model operators within the isospin formalism. Program summaryProgram title: CESOS Catalogue identifier: AELT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELT_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 10 932 No. of bytes in distributed program, including test data, etc.: 61 023 Distribution format: tar.gz Programming language: Fortran 90 Computer: Any computer with a Fortran 90 compiler Operating system: Windows XP, Linux RAM: The memory demand depends on the number of particles A and the excitation energy of the system E. Computation of the A=6 particle system with the total angular momentum J=0 and the total isospin T=1 requires around 4 kB of RAM at E=0,˜3 MB at E=3, and ˜172 MB at E=5. Classification: 17.18 Nature of problem: The code CESOS generates a list of two-particle intrinsic coefficients of fractional parentage for several

  15. Discounted semi-Markov decision processes : linear programming and policy iteration

    NARCIS (Netherlands)

    Wessels, J.; van Nunen, J.A.E.E.

    1975-01-01

    For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

  16. Discounted semi-Markov decision processes : linear programming and policy iteration

    NARCIS (Netherlands)

    Wessels, J.; van Nunen, J.A.E.E.

    1974-01-01

    For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal

  17. Radiation-induced lung damage in rats: The influence of fraction spacing on effect per fraction

    International Nuclear Information System (INIS)

    Haston, C.K.; Hill, R.P.; Newcomb, C.H.; Van Dyk, J.

    1994-01-01

    When the linear-quadratic model is used to predict fractionated treatments which are isoeffective, it is usually assumed that each (equal size) treatment fraction has an equal effect, independent of the time at which it was delivered during a course of treatment. Previous work has indicated that this assumption may not be valid in the context of radiation-induced lung damage in rats. Consequently the authors tested directly the validity of the assumption that each fraction has an equal effect, independent of the time it is delivered. An experiment was completed in which fractionated irradiation was given to whole thoraces of Sprague-Dawley rats. All treatment schedules consisted of eleven equal dose fractions in 36 days given as a split course, with some groups receiving the bulk of the doses early in the treatment schedule, before a 27-day gap, and others receiving most of the dose toward the end of the treatment schedule, after the time gap. To monitor the incidence of radiation-induced damage, breathing rate and lethality assays were used. The maximum differences in the LD 50 s and breathing rate ED 50 s for the different fractionation schedules were 4.0% and 7.7% respectively. The lethality data and breathing rate data were consistent with results expected from modelling using the linear-quadratic model with the inclusion of an overall time factor, but not the generalized linear-quadratic model which accounted for fraction spacing. For conventional daily fractionation, and within the range of experimental uncertainties, the results indicate that the effect of a treatment fraction does not depend on the time at which it is given (its position) in the treatment. The results indicate no need to extend isoeffect formulae to consider the effect of each fraction separately for radiation-induced lung damage. 21 refs., 6 figs., 3 tabs

  18. Interval linear programming model for long-term planning of vehicle recycling in the Republic of Serbia under uncertainty.

    Science.gov (United States)

    Simic, Vladimir; Dimitrijevic, Branka

    2015-02-01

    An interval linear programming approach is used to formulate and comprehensively test a model for optimal long-term planning of vehicle recycling in the Republic of Serbia. The proposed model is applied to a numerical case study: a 4-year planning horizon (2013-2016) is considered, three legislative cases and three scrap metal price trends are analysed, availability of final destinations for sorted waste flows is explored. Potential and applicability of the developed model are fully illustrated. Detailed insights on profitability and eco-efficiency of the projected contemporary equipped vehicle recycling factory are presented. The influences of the ordinance on the management of end-of-life vehicles in the Republic of Serbia on the vehicle hulks procuring, sorting generated material fractions, sorted waste allocation and sorted metals allocation decisions are thoroughly examined. The validity of the waste management strategy for the period 2010-2019 is tested. The formulated model can create optimal plans for procuring vehicle hulks, sorting generated material fractions, allocating sorted waste flows and allocating sorted metals. Obtained results are valuable for supporting the construction and/or modernisation process of a vehicle recycling system in the Republic of Serbia. © The Author(s) 2015.

  19. BEAMPATH: a program library for beam dynamics simulation in linear accelerators

    International Nuclear Information System (INIS)

    Batygin, Y.K.

    1992-01-01

    A structured programming technique was used to develop software for space charge dominated beams investigation in linear accelerators. The method includes hierarchical program design using program independent modules and a flexible combination of modules to provide a most effective version of structure for every specific case of simulation. A modular program BEAMPATH was developed for 2D and 3D particle-in-cell simulation of beam dynamics in a structure containing RF gaps, radio-frequency quadrupoles (RFQ), multipole lenses, waveguides, bending magnets and solenoids. (author) 5 refs.; 2 figs

  20. Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs

    International Nuclear Information System (INIS)

    Kiwiel, K. C.

    1998-01-01

    We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)

  1. A Partitioning and Bounded Variable Algorithm for Linear Programming

    Science.gov (United States)

    Sheskin, Theodore J.

    2006-01-01

    An interesting new partitioning and bounded variable algorithm (PBVA) is proposed for solving linear programming problems. The PBVA is a variant of the simplex algorithm which uses a modified form of the simplex method followed by the dual simplex method for bounded variables. In contrast to the two-phase method and the big M method, the PBVA does…

  2. Optimal traffic control in highway transportation networks using linear programming

    KAUST Repository

    Li, Yanning; Canepa, Edward S.; Claudel, Christian G.

    2014-01-01

    of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can

  3. Linear Programming Approaches for Power Savings in Software-defined Networks

    NARCIS (Netherlands)

    Moghaddam, F.A.; Grosso, P.

    2016-01-01

    Software-defined networks have been proposed as a viable solution to decrease the power consumption of the networking component in data center networks. Still the question remains on which scheduling algorithms are most suited to achieve this goal. We propose 4 different linear programming

  4. Method for solving fully fuzzy linear programming problems using deviation degree measure

    Institute of Scientific and Technical Information of China (English)

    Haifang Cheng; Weilai Huang; Jianhu Cai

    2013-01-01

    A new ful y fuzzy linear programming (FFLP) prob-lem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crispδ-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the δ-fuzzy optimal so-lution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the va-lues of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to il ustrate the proposed method.

  5. Nutrient density score of typical Indonesian foods and dietary formulation using linear programming.

    Science.gov (United States)

    Jati, Ignasius Radix A P; Vadivel, Vellingiri; Nöhr, Donatus; Biesalski, Hans Konrad

    2012-12-01

    The present research aimed to analyse the nutrient density (ND), nutrient adequacy score (NAS) and energy density (ED) of Indonesian foods and to formulate a balanced diet using linear programming. Data on typical Indonesian diets were obtained from the Indonesian Socio-Economic Survey 2008. ND was investigated for 122 Indonesian foods. NAS was calculated for single nutrients such as Fe, Zn and vitamin A. Correlation analysis was performed between ND and ED, as well as between monthly expenditure class and food consumption pattern in Indonesia. Linear programming calculations were performed using the software POM-QM for Windows version 3. Republic of Indonesia, 2008. Public households (n 68 800). Vegetables had the highest ND of the food groups, followed by animal-based foods, fruits and staple foods. Based on NAS, the top ten food items for each food group were identified. Most of the staple foods had high ED and contributed towards daily energy fulfillment, followed by animal-based foods, vegetables and fruits. Commodities with high ND tended to have low ED. Linear programming could be used to formulate a balanced diet. In contrast to staple foods, purchases of fruit, vegetables and animal-based foods increased with the rise of monthly expenditure. People should select food items based on ND and NAS to alleviate micronutrient deficiencies in Indonesia. Dietary formulation calculated using linear programming to achieve RDA levels for micronutrients could be recommended for different age groups of the Indonesian population.

  6. Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems

    Directory of Open Access Journals (Sweden)

    Leipo Liu

    2017-01-01

    Full Text Available The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS. Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.

  7. Measuring the Higgs branching fraction into two photons at future linear e+e- colliders

    International Nuclear Information System (INIS)

    Boos, E.; Schreiber, H.J.; Shanidze, R.

    2001-01-01

    We examine the prospects for a measurement of the branching fraction of the γγ decay mode of a Standard Model-like Higgs boson with a mass of 120 GeV/c 2 at the future TESLA linear e + e - collider, assuming an integrated luminosity of 1 ab -1 and centre-of-mass energies of 350 GeV and 500 GeV. A relative uncertainty on BF(H→γγ) of 16% can be achieved in unpolarised e + e - collisions at √(s) = 500 GeV, while for √(s) = 350 GeV the expected precision is slightly poorer. With appropriate initial state polarisations the uncertainty can be improved to 10%. If this measurement is combined with a measurement of the total Higgs width, a precision of 10% on the Higgs boson partial width for the γγ decay mode appears feasible. (orig.)

  8. A Novel Operational Matrix of Caputo Fractional Derivatives of Fibonacci Polynomials: Spectral Solutions of Fractional Differential Equations

    Directory of Open Access Journals (Sweden)

    Waleed M. Abd-Elhameed

    2016-09-01

    Full Text Available Herein, two numerical algorithms for solving some linear and nonlinear fractional-order differential equations are presented and analyzed. For this purpose, a novel operational matrix of fractional-order derivatives of Fibonacci polynomials was constructed and employed along with the application of the tau and collocation spectral methods. The convergence and error analysis of the suggested Fibonacci expansion were carefully investigated. Some numerical examples with comparisons are presented to ensure the efficiency, applicability and high accuracy of the proposed algorithms. Two accurate semi-analytic polynomial solutions for linear and nonlinear fractional differential equations are the result.

  9. Linear programming algorithms and applications

    CERN Document Server

    Vajda, S

    1981-01-01

    This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage­ ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...

  10. Efficient method for time-domain simulation of the linear feedback systems containing fractional order controllers.

    Science.gov (United States)

    Merrikh-Bayat, Farshad

    2011-04-01

    One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

  11. A mixed integer linear program for an integrated fishery | Hasan ...

    African Journals Online (AJOL)

    ... and labour allocation of quota based integrated fisheries. We demonstrate the workability of our model with a numerical example and sensitivity analysis based on data obtained from one of the major fisheries in New Zealand. Keywords: mixed integer linear program, fishing, trawler scheduling, processing, quotas ORiON: ...

  12. A linear programming approach for placement of applicants to academic programs.

    Science.gov (United States)

    Kassa, Biniyam Asmare

    2013-01-01

    This paper reports a linear programming approach for placement of applicants to study programs developed and implemented at the college of Business & Economics, Bahir Dar University, Bahir Dar, Ethiopia. The approach is estimated to significantly streamline the placement decision process at the college by reducing required man hour as well as the time it takes to announce placement decisions. Compared to the previous manual system where only one or two placement criteria were considered, the new approach allows the college's management to easily incorporate additional placement criteria, if needed. Comparison of our approach against manually constructed placement decisions based on actual data for the 2012/13 academic year suggested that about 93 percent of the placements from our model concur with the actual placement decisions. For the remaining 7 percent of placements, however, the actual placements made by the manual system display inconsistencies of decisions judged against the very criteria intended to guide placement decisions by the college's program management office. Overall, the new approach proves to be a significant improvement over the manual system in terms of efficiency of the placement process and the quality of placement decisions.

  13. adapta~k>n -11 of the surrogate memods for linear programming ...

    African Journals Online (AJOL)

    2005-08-02

    Aug 2, 2005 ... inequality problem is made uj~ of the primal and dual optimal solutions for the given primal ... KEYWORDS: Linear Programming, Duality Theory, Surrogate Methods. ..... replaces x and the process IS repeated with the new x.

  14. Influence of the void fraction in the linear reactivity model; Influencia de la fraccion de vacios en el modelo de reactividad lineal

    Energy Technology Data Exchange (ETDEWEB)

    Castillo, J.A.; Ramirez, J.R.; Alonso, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)]. e-mail: jacm@nuclear.inin.mx

    2003-07-01

    The linear reactivity model allows the multicycle analysis in pressurized water reactors in a simple and quick way. In the case of the Boiling water reactors the void fraction it varies axially from 0% of voids in the inferior part of the fuel assemblies until approximately 70% of voids to the exit of the same ones. Due to this it is very important the determination of the average void fraction during different stages of the reactor operation to predict the burnt one appropriately of the same ones to inclination of the pattern of linear reactivity. In this work a pursuit is made of the profile of power for different steps of burnt of a typical operation cycle of a Boiling water reactor. Starting from these profiles it builds an algorithm that allows to determine the voids profile and this way to obtain the average value of the same one. The results are compared against those reported by the CM-PRESTO code that uses another method to carry out this calculation. Finally, the range in which is the average value of the void fraction during a typical cycle is determined and an estimate of the impact that it would have the use of this value in the prediction of the reactivity produced by the fuel assemblies is made. (Author)

  15. Fractional approximations for linear first order differential equation with polynomial coefficients-application to E1(x) and Z(s)

    International Nuclear Information System (INIS)

    Martin, P.; Zamudio-Cristi, J.

    1982-01-01

    A method is described to obtain fractional approximations for linear first order differential equations with polynomial coefficients. This approximation can give good accuracy in a large region of the complex variable plane that may include all the real axis. The parameters of the approximation are solutions of algebraic equations obtained through the coefficients of the highest and lowest power of the variable after the sustitution of the fractional approximation in the differential equation. The method is more general than the asymptotical Pade method, and it is not required to determine the power series or asymptotical expansion. A simple approximation for the exponential integral is found, which give three exact digits for most of the real values of the variable. Approximations of higher accuracy and of the same degree than other authors are also obtained. (Author) [pt

  16. FGP Approach for Solving Multi-level Multi-objective Quadratic Fractional Programming Problem with Fuzzy parameters

    Directory of Open Access Journals (Sweden)

    m. s. osman

    2017-09-01

    Full Text Available In this paper, we consider fuzzy goal programming (FGP approach for solving multi-level multi-objective quadratic fractional programming (ML-MOQFP problem with fuzzy parameters in the constraints. Firstly, the concept of the ?-cut approach is applied to transform the set of fuzzy constraints into a common deterministic one. Then, the quadratic fractional objective functions in each level are transformed into quadratic objective functions based on a proposed transformation. Secondly, the FGP approach is utilized to obtain a compromise solution for the ML-MOQFP problem by minimizing the sum of the negative deviational variables. Finally, an illustrative numerical example is given to demonstrate the applicability and performance of the proposed approach.

  17. The use of linear programming in optimization of HDR implant dose distributions

    International Nuclear Information System (INIS)

    Jozsef, Gabor; Streeter, Oscar E.; Astrahan, Melvin A.

    2003-01-01

    The introduction of high dose rate brachytherapy enabled optimization of dose distributions to be used on a routine basis. The objective of optimization is to homogenize the dose distribution within the implant while simultaneously satisfying dose constraints on certain points. This is accomplished by varying the time the source dwells at different locations. As the dose at any point is a linear function of the dwell times, a linear programming approach seems to be a natural choice. The dose constraints are inherently linear inequalities. Homogeneity requirements are linearized by minimizing the maximum deviation of the doses at points inside the implant from a prescribed dose. The revised simplex method was applied for the solution of this linear programming problem. In the homogenization process the possible source locations were chosen as optimization points. To avoid the problem of the singular value of the dose at a source location from the source itself we define the 'self-contribution' as the dose at a small distance from the source. The effect of varying this distance is discussed. Test cases were optimized for planar, biplanar and cylindrical implants. A semi-irregular, fan-like implant with diverging needles was also investigated. Mean central dose calculation based on 3D Delaunay-triangulation of the source locations was used to evaluate the dose distributions. The optimization method resulted in homogeneous distributions (for brachytherapy). Additional dose constraints--when applied--were satisfied. The method is flexible enough to include other linear constraints such as the inclusion of the centroids of the Delaunay-triangulation for homogenization, or limiting the maximum allowable dwell time

  18. Calculated fraction of an incident current pulse that will be accelerated by an electron linear accelerator and comparisons with experimental data

    International Nuclear Information System (INIS)

    Alsmiller, R.G. Jr.; Alsmiller, F.S.; Lewis, T.A.

    1986-05-01

    In a series of previous papers, calculated results obtained using a one-dimensional ballistic model were presented to aid in the design of a prebuncher for the Oak Ridge Electron Linear Accelerator. As part of this work, a model was developed to provide limits on the fraction of an incident current pulse that would be accelerated by the existing accelerator. In this paper experimental data on this fraction are presented and the validity of the model developed previously is tested by comparing calculated and experimental data. Part of the experimental data is used to fix the physical parameters in the model and then good agreement between the calculated results and the rest of the experimental data is obtained

  19. Reduced-Size Integer Linear Programming Models for String Selection Problems: Application to the Farthest String Problem.

    Science.gov (United States)

    Zörnig, Peter

    2015-08-01

    We present integer programming models for some variants of the farthest string problem. The number of variables and constraints is substantially less than that of the integer linear programming models known in the literature. Moreover, the solution of the linear programming-relaxation contains only a small proportion of noninteger values, which considerably simplifies the rounding process. Numerical tests have shown excellent results, especially when a small set of long sequences is given.

  20. Cost Effectiveness of Iran National Plasma Contract Fractionation Program

    Directory of Open Access Journals (Sweden)

    Abdol Majid Cheraghali

    2012-10-01

    Full Text Available Plasma derived medicines (PDM including immunoglobulins, clotting factors and albumin are life saving medicines which due to their high costs are inaccessible for many patients living in developing countries. By contrary substantial volume of plasma as raw materials for production of these medicines are discarded worldwide. Good quality recovered plasma, as a result of separation of donated blood into its components, could be used for production of PDM. In 2011 Iranian donors donated about 2 million units of blood. A shift fromadministration of whole blood to components therapy has resulted in the generation of over 250,000 liters of surplus of recovered plasma. This created a good opportunity for Iran’s health care system to use this plasma for production of PDM. Therefore Iran national transfusion service has started a contract fractionation program for converting recovered plasma into PDM. This program not only provided essential PDM for Iran pharmaceutical market but also has created a direct saving of about 8.5 million Euros in 2011 for national health sector. In addition this program has drastically contributed to improvement of overall quality of working procedures and services provided by Iran national blood transfusion organization.

  1. LINTAB, Linear Interpolable Tables from any Continuous Variable Function

    International Nuclear Information System (INIS)

    1988-01-01

    1 - Description of program or function: LINTAB is designed to construct linearly interpolable tables from any function. The program will start from any function of a single continuous variable... FUNKY(X). By user input the function can be defined, (1) Over 1 to 100 X ranges. (2) Within each X range the function is defined by 0 to 50 constants. (3) At boundaries between X ranges the function may be continuous or discontinuous (depending on the constants used to define the function within each X range). 2 - Method of solution: LINTAB will construct a table of X and Y values where the tabulated (X,Y) pairs will be exactly equal to the function (Y=FUNKY(X)) and linear interpolation between the tabulated pairs will be within any user specified fractional uncertainty of the function for all values of X within the requested X range

  2. User's Guide to the Weighted-Multiple-Linear Regression Program (WREG version 1.0)

    Science.gov (United States)

    Eng, Ken; Chen, Yin-Yu; Kiang, Julie.E.

    2009-01-01

    Streamflow is not measured at every location in a stream network. Yet hydrologists, State and local agencies, and the general public still seek to know streamflow characteristics, such as mean annual flow or flood flows with different exceedance probabilities, at ungaged basins. The goals of this guide are to introduce and familiarize the user with the weighted multiple-linear regression (WREG) program, and to also provide the theoretical background for program features. The program is intended to be used to develop a regional estimation equation for streamflow characteristics that can be applied at an ungaged basin, or to improve the corresponding estimate at continuous-record streamflow gages with short records. The regional estimation equation results from a multiple-linear regression that relates the observable basin characteristics, such as drainage area, to streamflow characteristics.

  3. Contextual Fraction as a Measure of Contextuality

    Science.gov (United States)

    Abramsky, Samson; Barbosa, Rui Soares; Mansfield, Shane

    2017-08-01

    We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e., tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programing; it is monotonic with respect to the "free" operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement-based quantum computing.

  4. A Comparison of Linear and Systems Thinking Approaches for Program Evaluation Illustrated Using the Indiana Interdisciplinary GK-12

    Science.gov (United States)

    Dyehouse, Melissa; Bennett, Deborah; Harbor, Jon; Childress, Amy; Dark, Melissa

    2009-01-01

    Logic models are based on linear relationships between program resources, activities, and outcomes, and have been used widely to support both program development and evaluation. While useful in describing some programs, the linear nature of the logic model makes it difficult to capture the complex relationships within larger, multifaceted…

  5. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima

    2018-02-13

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  6. Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems

    KAUST Repository

    N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem

    2018-01-01

    In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.

  7. Linear programming based on neural networks for radiotherapy treatment planning

    International Nuclear Information System (INIS)

    Xingen Wu; Limin Luo

    2000-01-01

    In this paper, we propose a neural network model for linear programming that is designed to optimize radiotherapy treatment planning (RTP). This kind of neural network can be easily implemented by using a kind of 'neural' electronic system in order to obtain an optimization solution in real time. We first give an introduction to the RTP problem and construct a non-constraint objective function for the neural network model. We adopt a gradient algorithm to minimize the objective function and design the structure of the neural network for RTP. Compared to traditional linear programming methods, this neural network model can reduce the time needed for convergence, the size of problems (i.e., the number of variables to be searched) and the number of extra slack and surplus variables needed. We obtained a set of optimized beam weights that result in a better dose distribution as compared to that obtained using the simplex algorithm under the same initial condition. The example presented in this paper shows that this model is feasible in three-dimensional RTP. (author)

  8. Identification of fractional order systems using modulating functions method

    KAUST Repository

    Liu, Dayan

    2013-06-01

    The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.

  9. On the fractional calculus of Besicovitch function

    International Nuclear Information System (INIS)

    Liang Yongshun

    2009-01-01

    Relationship between fractional calculus and fractal functions has been explored. Based on prior investigations dealing with certain fractal functions, fractal dimensions including Hausdorff dimension, Box dimension, K-dimension and Packing dimension is shown to be a linear function of order of fractional calculus. Both Riemann-Liouville fractional calculus and Weyl-Marchaud fractional derivative of Besicovitch function have been discussed.

  10. Robust Control Design via Linear Programming

    Science.gov (United States)

    Keel, L. H.; Bhattacharyya, S. P.

    1998-01-01

    This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order. The closed loop specifications considered here are given in terms of a target performance vector representing a desired set of closed loop transfer functions connecting various signals. In general these point targets are unattainable with a fixed order controller. By enlarging the target from a fixed point set to an interval set the solvability conditions with a fixed order controller are relaxed and a solution is more easily enabled. Results from the parametric robust control literature can be used to design the interval target family so that the performance deterioration is acceptable, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications.

  11. A linear programming model of diet choice of free-living beavers

    NARCIS (Netherlands)

    Nolet, BA; VanderVeer, PJ; Evers, EGJ; Ottenheim, MM

    1995-01-01

    Linear programming has been remarkably successful in predicting the diet choice of generalist herbivores. We used this technique to test the diet choice of free-living beavers (Castor fiber) in the Biesbosch (The Netherlands) under different Foraging goals, i.e. maximization of intake of energy,

  12. Waste management under multiple complexities: Inexact piecewise-linearization-based fuzzy flexible programming

    International Nuclear Information System (INIS)

    Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen

    2012-01-01

    Highlights: ► Inexact piecewise-linearization-based fuzzy flexible programming is proposed. ► It’s the first application to waste management under multiple complexities. ► It tackles nonlinear economies-of-scale effects in interval-parameter constraints. ► It estimates costs more accurately than the linear-regression-based model. ► Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP’s advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP’s solutions demonstrate

  13. Introduction to linear programming: Coalitional game experiments

    Energy Technology Data Exchange (ETDEWEB)

    Lucas, W.

    1994-12-31

    Many solution notions in the multiperson cooperative games (in characteristic function form) make use of linear programming (LP). The popular concept of the {open_quotes}core{close_quotes} of a coalitional game is a special type of LP. It can be introduced in a very simple and quite exciting manner by means of a group experiment. A total of fifty dollars will be given to three randomly selected attendees who will take part in an experiment during this talk, presuming they behave in a Pareto optimal manner. Furthermore, the dual of the particular LP for the core gives rise to the idea of {open_quotes}balanced sets{close_quotes} which is an interesting combinatorial structure in its own right.

  14. The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

    Science.gov (United States)

    Pang, Haotian; Liu, Han; Vanderbei, Robert

    2014-02-01

    We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

  15. A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

    Science.gov (United States)

    Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

    2018-04-01

    In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

  16. Analytical scale purification of zirconia colloidal suspension using field programmed sedimentation field flow fractionation.

    Science.gov (United States)

    Van-Quynh, Alexandra; Blanchart, Philippe; Battu, Serge; Clédat, Dominique; Cardot, Philippe

    2006-03-03

    Sedimentation field flow fractionation was used to obtain purified fractions from a polydispersed zirconia colloidal suspension in the potential purpose of optical material hybrid coating. The zirconia particle size ranged from 50/70 nm to 1000 nm. It exhibited a log-Gaussian particle size distribution (in mass or volume) and a 115% polydispersity index (P.I.). Time dependent eluted fractions of the original zirconia colloidal suspension were collected. The particle size distribution of each fraction was determined with scanning electron microscopy and Coulter sub-micron particle sizer (CSPS). These orthogonal techniques generated similar data. From fraction average elution times and granulometry measurements, it was shown that zirconia colloids are eluted according to the Brownian elution mode. The four collected fractions have a Gaussian like distribution and respective average size and polydispersity index of 153 nm (P.I. = 34.7%); 188 nm (P.I. = 27.9%); 228 nm (P.I. = 22.6%), and 276 nm (P.I. = 22.3%). These data demonstrate the strong size selectivity of SdFFF operated with programmed field of exponential profile for sorting particles in the sub-micron range. Using this technique, the analytical production of zirconia of given average size and reduced polydispersity is possible.

  17. Computer Program For Linear Algebra

    Science.gov (United States)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  18. Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms

    Science.gov (United States)

    Hennelly, Bryan M.; Sheridan, John T.

    2005-05-01

    By use of matrix-based techniques it is shown how the space-bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadratic-phase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.

  19. Linear programming to build food-based dietary guidelines: Romanian food baskets

    DEFF Research Database (Denmark)

    Parlesak, Alexandr; Robertson, Aileen; Hondru, Gabriela

    approach using linear programming methodology to design national dietary recommendations which aim to prevent both NCDs and micronutrient deficiencies and still be affordable by low income groups. This new approach is applied within the context of food availability in Romania in 2014. Eating the same food...... every day is unrealistic and too monotonous to be maintained, so this novel approach is used to select a wide range of diverse foods that can be recommended for a period of up to, for example, one month. The following are the key findings of this report. • The simplest version of the Romanian food.......65 lei (~€ 4.46) for a day. • Key nutrients, primarily vitamin D, calcium, potassium and iron, were found to control the overall price. • The least expensive basket (one day’s rations) is monotonous and the linear programming approach is used to select a wide range of foods that can be recommended...

  20. Fuzzy linear programming based optimal fuel scheduling incorporating blending/transloading facilities

    Energy Technology Data Exchange (ETDEWEB)

    Djukanovic, M.; Babic, B.; Milosevic, B. [Electrical Engineering Inst. Nikola Tesla, Belgrade (Yugoslavia); Sobajic, D.J. [EPRI, Palo Alto, CA (United States). Power System Control; Pao, Y.H. [Case Western Reserve Univ., Cleveland, OH (United States)]|[AI WARE, Inc., Cleveland, OH (United States)

    1996-05-01

    In this paper the blending/transloading facilities are modeled using an interactive fuzzy linear programming (FLP), in order to allow the decision-maker to solve the problem of uncertainty of input information within the fuel scheduling optimization. An interactive decision-making process is formulated in which decision-maker can learn to recognize good solutions by considering all possibilities of fuzziness. The application of the fuzzy formulation is accompanied by a careful examination of the definition of fuzziness, appropriateness of the membership function and interpretation of results. The proposed concept provides a decision support system with integration-oriented features, whereby the decision-maker can learn to recognize the relative importance of factors in the specific domain of optimal fuel scheduling (OFS) problem. The formulation of a fuzzy linear programming problem to obtain a reasonable nonfuzzy solution under consideration of the ambiguity of parameters, represented by fuzzy numbers, is introduced. An additional advantage of the FLP formulation is its ability to deal with multi-objective problems.

  1. Fractional finite Fourier transform.

    Science.gov (United States)

    Khare, Kedar; George, Nicholas

    2004-07-01

    We show that a fractional version of the finite Fourier transform may be defined by using prolate spheroidal wave functions of order zero. The transform is linear and additive in its index and asymptotically goes over to Namias's definition of the fractional Fourier transform. As a special case of this definition, it is shown that the finite Fourier transform may be inverted by using information over a finite range of frequencies in Fourier space, the inversion being sensitive to noise. Numerical illustrations for both forward (fractional) and inverse finite transforms are provided.

  2. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Directory of Open Access Journals (Sweden)

    Mohammadtaghi Hamidi Beheshti

    2010-01-01

    Full Text Available We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  3. Robust Stabilization of Fractional-Order Systems with Interval Uncertainties via Fractional-Order Controllers

    Directory of Open Access Journals (Sweden)

    Sayyad Delshad Saleh

    2010-01-01

    Full Text Available Abstract We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.

  4. Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems

    Directory of Open Access Journals (Sweden)

    Xinbo Zhang

    2014-01-01

    Full Text Available A polymorphic uncertain linear programming (PULP model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.

  5. APPLYING ROBUST RANKING METHOD IN TWO PHASE FUZZY OPTIMIZATION LINEAR PROGRAMMING PROBLEMS (FOLPP

    Directory of Open Access Journals (Sweden)

    Monalisha Pattnaik

    2014-12-01

    Full Text Available Background: This paper explores the solutions to the fuzzy optimization linear program problems (FOLPP where some parameters are fuzzy numbers. In practice, there are many problems in which all decision parameters are fuzzy numbers, and such problems are usually solved by either probabilistic programming or multi-objective programming methods. Methods: In this paper, using the concept of comparison of fuzzy numbers, a very effective method is introduced for solving these problems. This paper extends linear programming based problem in fuzzy environment. With the problem assumptions, the optimal solution can still be theoretically solved using the two phase simplex based method in fuzzy environment. To handle the fuzzy decision variables can be initially generated and then solved and improved sequentially using the fuzzy decision approach by introducing robust ranking technique. Results and conclusions: The model is illustrated with an application and a post optimal analysis approach is obtained. The proposed procedure was programmed with MATLAB (R2009a version software for plotting the four dimensional slice diagram to the application. Finally, numerical example is presented to illustrate the effectiveness of the theoretical results, and to gain additional managerial insights. 

  6. Updating Linear Schedules with Lowest Cost: a Linear Programming Model

    Science.gov (United States)

    Biruk, Sławomir; Jaśkowski, Piotr; Czarnigowska, Agata

    2017-10-01

    Many civil engineering projects involve sets of tasks repeated in a predefined sequence in a number of work areas along a particular route. A useful graphical representation of schedules of such projects is time-distance diagrams that clearly show what process is conducted at a particular point of time and in particular location. With repetitive tasks, the quality of project performance is conditioned by the ability of the planner to optimize workflow by synchronizing the works and resources, which usually means that resources are planned to be continuously utilized. However, construction processes are prone to risks, and a fully synchronized schedule may expire if a disturbance (bad weather, machine failure etc.) affects even one task. In such cases, works need to be rescheduled, and another optimal schedule should be built for the changed circumstances. This typically means that, to meet the fixed completion date, durations of operations have to be reduced. A number of measures are possible to achieve such reduction: working overtime, employing more resources or relocating resources from less to more critical tasks, but they all come at a considerable cost and affect the whole project. The paper investigates the problem of selecting the measures that reduce durations of tasks of a linear project so that the cost of these measures is kept to the minimum and proposes an algorithm that could be applied to find optimal solutions as the need to reschedule arises. Considering that civil engineering projects, such as road building, usually involve less process types than construction projects, the complexity of scheduling problems is lower, and precise optimization algorithms can be applied. Therefore, the authors put forward a linear programming model of the problem and illustrate its principle of operation with an example.

  7. A new methodological development for solving linear bilevel integer programming problems in hybrid fuzzy environment

    Directory of Open Access Journals (Sweden)

    Animesh Biswas

    2016-04-01

    Full Text Available This paper deals with fuzzy goal programming approach to solve fuzzy linear bilevel integer programming problems with fuzzy probabilistic constraints following Pareto distribution and Frechet distribution. In the proposed approach a new chance constrained programming methodology is developed from the view point of managing those probabilistic constraints in a hybrid fuzzy environment. A method of defuzzification of fuzzy numbers using ?-cut has been adopted to reduce the problem into a linear bilevel integer programming problem. The individual optimal value of the objective of each DM is found in isolation to construct the fuzzy membership goals. Finally, fuzzy goal programming approach is used to achieve maximum degree of each of the membership goals by minimizing under deviational variables in the decision making environment. To demonstrate the efficiency of the proposed approach, a numerical example is provided.

  8. Generation of multi-wing chaotic attractor in fractional order system

    International Nuclear Information System (INIS)

    Zhang Chaoxia; Yu Simin

    2011-01-01

    Highlights: → We investigate a novel approach for generating multi-wing chaotic attractors. → We introduce a fundamental fractional differential nominal linear system. → A proper nonlinear state feedback controller is designed. → The controlled system can generate fractional-order multi-wing chaotic attractors. - Abstract: In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.

  9. Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming

    Science.gov (United States)

    Gurski, Katharine F.

    2009-01-01

    We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…

  10. Optimal local dimming for LED-backlit LCD displays via linear programming

    DEFF Research Database (Denmark)

    Shu, Xiao; Wu, Xiaolin; Forchhammer, Søren

    2012-01-01

    and the attenuations of LCD pixels. The objective is to minimize the distortion in luminance reproduction due to the leakage of LCD and the coarse granularity of the LED lights. The optimization problem is formulated as one of linear programming, and both exact and approximate algorithms are proposed. Simulation...

  11. Adaptive fractionation therapy: I. Basic concept and strategy

    International Nuclear Information System (INIS)

    Lu Weiguo; Chen Mingli; Chen Quan; Ruchala, Kenneth; Olivera, Gustavo

    2008-01-01

    Radiotherapy is fractionized to increase the therapeutic ratio. Fractionation in conventional treatment is determined as part of the prescription, and a fixed fraction size is used for the whole course of treatment. Due to patients' day-to-day variations on the relative distance between the tumor and the organs at risk (OAR), a better therapeutic ratio may be attained by using an adaptive fraction size. Intuitively, we want to use a larger fraction size when OAR and the tumor are far apart and a smaller fraction size when OAR and the tumor are close to each other. The concept and strategies of adaptive fractionation therapy (AFT) are introduced in this paper. AFT is an on-line adaptive technique that utilizes the variations of internal structures to get optimal OAR sparing. Changes of internal structures are classified as different configurations according to their feasibility to the radiation delivery. A priori knowledge is used to describe the probability distribution of these configurations. On-line processes include identifying the configuration via daily image guidance and optimizing the current fraction size. The optimization is modeled as a dynamic linear programming problem so that at the end of the treatment course, the tumor receives the same planned dose while OAR receives less dose than the regular fractionation delivery. Extensive simulations, which include thousands of treatment courses with each course consisting of 40 fractions, are used to test the efficiency and robustness of the presented technique. The gains of OAR sparing depend on the variations on configurations and the bounds of the fraction size. The larger the variations and the looser the bounds are, the larger the gains will be. Compared to the conventional fractionation technique with 2 Gy/fraction in 40 fractions, for a 20% variation on tumor-OAR configurations and [1 Gy, 3 Gy] fraction size bounds, the cumulative OAR dose with adaptive fractionation is 3-8 Gy, or 7-20% less than that

  12. On matrix fractional differential equations

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  13. Optimization of production planning in Czech agricultural co-operative via linear programming

    Directory of Open Access Journals (Sweden)

    Jitka Janová

    2009-01-01

    Full Text Available The production planning is one of the key managerial decisions in agricultural business, which must be done periodically every year. Correct decision must cover the agriculture demands of planting the crops such as crop rotation restrictions or water resource scarcity, while the decision maker aims to plan the crop design in most profitable way in sense of maximizing the total profit from the crop yield. This decision problem represents the optimization of crop design and can be treated by the me­thods of linear programming which begun to be extensively used in agriculture production planning in USA during 50’s. There is ongoing research of mathematical programming applications in agriculture worldwide, but the results are not easily transferable to other localities due to the specific local restrictions in each country. In Czech Republic the farmers use for production planning mainly their expert knowledge and past experience. However, the mathematical programming approach enables find the true optimal solution of the problem, which especially in the problems with a great number of constraints is not easy to find intuitively. One of the possible barriers for using the general decision support systems (which are based on mathematical programming methods for agriculture production planning in Czech Republic is its expensiveness. The small farmer can not afford to buy the expensive software or to employ a mathematical programming specialist. The aim of this paper is to present a user friendly linear programming model of the typical agricultural production planning problem in Czech Republic which can be solved via software tools commonly available in any farm (e.g. EXCEL. The linear programming model covering the restrictions on total costs, crop rotation, thresholds for the total area sowed by particular crops, total amount of manure and the need of feed crops is developed. The model is applied in real-world problem of Czech agriculture

  14. The Linear Programming to evaluate the performance of Oral Health in Primary Care.

    Science.gov (United States)

    Colussi, Claudia Flemming; Calvo, Maria Cristina Marino; Freitas, Sergio Fernando Torres de

    2013-01-01

    To show the use of Linear Programming to evaluate the performance of Oral Health in Primary Care. This study used data from 19 municipalities of Santa Catarina city that participated of the state evaluation in 2009 and have more than 50,000 habitants. A total of 40 indicators were evaluated, calculated using the Microsoft Excel 2007, and converted to the interval [0, 1] in ascending order (one indicating the best situation and zero indicating the worst situation). Applying the Linear Programming technique municipalities were assessed and compared among them according to performance curve named "quality estimated frontier". Municipalities included in the frontier were classified as excellent. Indicators were gathered, and became synthetic indicators. The majority of municipalities not included in the quality frontier (values different of 1.0) had lower values than 0.5, indicating poor performance. The model applied to the municipalities of Santa Catarina city assessed municipal management and local priorities rather than the goals imposed by pre-defined parameters. In the final analysis three municipalities were included in the "perceived quality frontier". The Linear Programming technique allowed to identify gaps that must be addressed by city managers to enhance actions taken. It also enabled to observe each municipal performance and compare results among similar municipalities.

  15. AN APPLICATION FOR EFFICIENT TELECOMMUNICATION NETWORKS PROVISIONING USING LINEAR PROGRAMMING

    Directory of Open Access Journals (Sweden)

    Maria Augusta Soares Machado

    2015-03-01

    Full Text Available This paper presents a practical proposition for the application of the Linear Programming quantitative method in order to assist planning and control of customer circuit delivery activities in telecommunications companies working with the corporative market. Based upon data provided for by a telecom company operating in Brazil, the Linear Programming method was employed for one of the classical problems of determining the optimum mix of production quantities for a set of five products of that company: Private Telephone Network, Internet Network, Intranet Network, Low Speed Data Network, and High Speed Data Network, in face of several limitations of the productive resources, seeking to maximize the company’s monthly revenue. By fitting the production data available into a primary model, observation was made as to what number of monthly activations for each product would be mostly optimized in order to achieve maximum revenues in the company. The final delivery of a complete network was not observed but the delivery of the circuits that make it up, and this was a limiting factor for the study herein, which, however, brings an innovative proposition for the planning of private telecommunications network provisioning.

  16. A Study of Joint Cost Inclusion in Linear Programming Optimization

    Directory of Open Access Journals (Sweden)

    P. Armaos

    2013-08-01

    Full Text Available The concept of Structural Optimization has been a topic or research over the past century. Linear Programming Optimization has proved being the most reliable method of structural optimization. Global advances in linear programming optimization have been recently powered by University of Sheffield researchers, to include joint cost, self-weight and buckling considerations. A joint cost inclusion scopes to reduce the number of joints existing in an optimized structural solution, transforming it to a practically viable solution. The topic of the current paper is to investigate the effects of joint cost inclusion, as this is currently implemented in the optimization code. An extended literature review on this subject was conducted prior to familiarization with small scale optimization software. Using IntelliFORM software, a structured series of problems were set and analyzed. The joint cost tests examined benchmark problems and their consequent changes in the member topology, as the design domain was expanding. The findings of the analyses were remarkable and are being commented further on. The distinct topologies of solutions created by optimization processes are also recognized. Finally an alternative strategy of penalizing joints is presented.

  17. Solving non-linear Horn clauses using a linear Horn clause solver

    DEFF Research Database (Denmark)

    Kafle, Bishoksan; Gallagher, John Patrick; Ganty, Pierre

    2016-01-01

    In this paper we show that checking satisfiability of a set of non-linear Horn clauses (also called a non-linear Horn clause program) can be achieved using a solver for linear Horn clauses. We achieve this by interleaving a program transformation with a satisfiability checker for linear Horn...... clauses (also called a solver for linear Horn clauses). The program transformation is based on the notion of tree dimension, which we apply to a set of non-linear clauses, yielding a set whose derivation trees have bounded dimension. Such a set of clauses can be linearised. The main algorithm...... dimension. We constructed a prototype implementation of this approach and performed some experiments on a set of verification problems, which shows some promise....

  18. Visual, Algebraic and Mixed Strategies in Visually Presented Linear Programming Problems.

    Science.gov (United States)

    Shama, Gilli; Dreyfus, Tommy

    1994-01-01

    Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…

  19. Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters

    Directory of Open Access Journals (Sweden)

    Zahra Shahraki

    2015-07-01

    Full Text Available This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.

  20. Broadband demonstrations of true-time delay using linear sideband chirped programming and optical coherent transients

    International Nuclear Information System (INIS)

    Reibel, R.R.; Barber, Z.W.; Fischer, J.A.; Tian, M.; Babbitt, W.R.

    2004-01-01

    Linear sideband chirped (LSC) programming is introduced as a means of configuring spatial-spectral holographic gratings for optical coherent transient processors. Similar to linear frequency chirped programming, LSC programming allows the use of broadband integrated electro-optic phase modulators to produce chirps instead of using elaborate broadband chirped lasers. This approach has several advantages including the ability to use a stabilized laser for the optical carrier as well as stable, reproducible chirped optical signals when the modulator is driven digitally. Using LSC programming, we experimentally demonstrate broadband true-time delay as a proof of principle for the optical control of phased array radars. Here both cw phase modulated and binary phase shift keyed probe signals are true-time delayed with bandwidths of 1 GHz and delay resolutions better than 60 ps

  1. Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers

    CERN Document Server

    Li, Deng-Feng

    2016-01-01

    This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .

  2. A versatile program for the calculation of linear accelerator room shielding.

    Science.gov (United States)

    Hassan, Zeinab El-Taher; Farag, Nehad M; Elshemey, Wael M

    2018-03-22

    This work aims at designing a computer program to calculate the necessary amount of shielding for a given or proposed linear accelerator room design in radiotherapy. The program (Shield Calculation in Radiotherapy, SCR) has been developed using Microsoft Visual Basic. It applies the treatment room shielding calculations of NCRP report no. 151 to calculate proper shielding thicknesses for a given linear accelerator treatment room design. The program is composed of six main user-friendly interfaces. The first enables the user to upload their choice of treatment room design and to measure the distances required for shielding calculations. The second interface enables the user to calculate the primary barrier thickness in case of three-dimensional conventional radiotherapy (3D-CRT), intensity modulated radiotherapy (IMRT) and total body irradiation (TBI). The third interface calculates the required secondary barrier thickness due to both scattered and leakage radiation. The fourth and fifth interfaces provide a means to calculate the photon dose equivalent for low and high energy radiation, respectively, in door and maze areas. The sixth interface enables the user to calculate the skyshine radiation for photons and neutrons. The SCR program has been successfully validated, precisely reproducing all of the calculated examples presented in NCRP report no. 151 in a simple and fast manner. Moreover, it easily performed the same calculations for a test design that was also calculated manually, and produced the same results. The program includes a new and important feature that is the ability to calculate required treatment room thickness in case of IMRT and TBI. It is characterised by simplicity, precision, data saving, printing and retrieval, in addition to providing a means for uploading and testing any proposed treatment room shielding design. The SCR program provides comprehensive, simple, fast and accurate room shielding calculations in radiotherapy.

  3. Wavelet-linear genetic programming: A new approach for modeling monthly streamflow

    Science.gov (United States)

    Ravansalar, Masoud; Rajaee, Taher; Kisi, Ozgur

    2017-06-01

    The streamflows are important and effective factors in stream ecosystems and its accurate prediction is an essential and important issue in water resources and environmental engineering systems. A hybrid wavelet-linear genetic programming (WLGP) model, which includes a discrete wavelet transform (DWT) and a linear genetic programming (LGP) to predict the monthly streamflow (Q) in two gauging stations, Pataveh and Shahmokhtar, on the Beshar River at the Yasuj, Iran were used in this study. In the proposed WLGP model, the wavelet analysis was linked to the LGP model where the original time series of streamflow were decomposed into the sub-time series comprising wavelet coefficients. The results were compared with the single LGP, artificial neural network (ANN), a hybrid wavelet-ANN (WANN) and Multi Linear Regression (MLR) models. The comparisons were done by some of the commonly utilized relevant physical statistics. The Nash coefficients (E) were found as 0.877 and 0.817 for the WLGP model, for the Pataveh and Shahmokhtar stations, respectively. The comparison of the results showed that the WLGP model could significantly increase the streamflow prediction accuracy in both stations. Since, the results demonstrate a closer approximation of the peak streamflow values by the WLGP model, this model could be utilized for the simulation of cumulative streamflow data prediction in one month ahead.

  4. The realization problem for positive and fractional systems

    CERN Document Server

    Kaczorek, Tadeusz

    2014-01-01

    This book addresses the realization problem of positive and fractional continuous-time and discrete-time linear systems. Roughly speaking the essence of the realization problem can be stated as follows: Find the matrices of the state space equations of linear systems for given their transfer matrices. This first book on this topic shows how many well-known classical approaches have been extended to the new classes of positive and fractional linear systems. The modified Gilbert method for multi-input multi-output linear systems, the method for determination of realizations in the controller canonical forms and in observer canonical forms are presented. The realization problem for linear systems described by differential operators, the realization problem in the Weierstrass canonical forms and of the descriptor linear systems for given Markov parameters are addressed. The book also presents a method for the determination of minimal realizations of descriptor linear systems and an extension for cone linear syste...

  5. Development of demand functions and their inclusion in linear programming forecasting models

    International Nuclear Information System (INIS)

    Chamberlin, J.H.

    1976-05-01

    The purpose of the paper is to present a method for including demand directly within a linear programming model, and to use this method to analyze the effect of the Liquid Metal Fast Breeder Reactor upon the nuclear energy system

  6. The application of the fall-vector method in decomposition schemes for the solution of integer linear programming problems

    International Nuclear Information System (INIS)

    Sergienko, I.V.; Golodnikov, A.N.

    1984-01-01

    This article applies the methods of decompositions, which are used to solve continuous linear problems, to integer and partially integer problems. The fall-vector method is used to solve the obtained coordinate problems. An algorithm of the fall-vector is described. The Kornai-Liptak decomposition principle is used to reduce the integer linear programming problem to integer linear programming problems of a smaller dimension and to a discrete coordinate problem with simple constraints

  7. Research and evaluation of the effectiveness of e-learning in the case of linear programming

    Directory of Open Access Journals (Sweden)

    Ljiljana Miletić

    2016-04-01

    Full Text Available The paper evaluates the effectiveness of the e-learning approach to linear programming. The goal was to investigate how proper use of information and communication technologies (ICT and interactive learning helps to improve high school students’ understanding, learning and retention of advanced non-curriculum material. The hypothesis was that ICT and e-learning is helpful in teaching linear programming methods. In the first phase of the research, a module of lessons for linear programming (LP was created using the software package Loomen Moodle and other interactive software packages such as Geogebra. In the second phase, the LP module was taught as a short course to two groups of high school students. These two groups of students were second-grade students in a Croatian high school. In Class 1, the module was taught using ICT and e-learning, while the module was taught using classical methods in Class 2. The action research methodology was an integral part in delivering the course to both student groups. The sample student groups were carefully selected to ensure that differences in background knowledge and learning potential were statistically negligible. Relevant data was collected while delivering the course. Statistical analysis of the collected data showed that the student group using the e-learning method produced better results than the group using a classical learning method. These findings support previous results on the effectiveness of e-learning, and also establish a specific approach to e-learning in linear programming.

  8. A Monte Carlo simulation study comparing linear regression, beta regression, variable-dispersion beta regression and fractional logit regression at recovering average difference measures in a two sample design.

    Science.gov (United States)

    Meaney, Christopher; Moineddin, Rahim

    2014-01-24

    In biomedical research, response variables are often encountered which have bounded support on the open unit interval--(0,1). Traditionally, researchers have attempted to estimate covariate effects on these types of response data using linear regression. Alternative modelling strategies may include: beta regression, variable-dispersion beta regression, and fractional logit regression models. This study employs a Monte Carlo simulation design to compare the statistical properties of the linear regression model to that of the more novel beta regression, variable-dispersion beta regression, and fractional logit regression models. In the Monte Carlo experiment we assume a simple two sample design. We assume observations are realizations of independent draws from their respective probability models. The randomly simulated draws from the various probability models are chosen to emulate average proportion/percentage/rate differences of pre-specified magnitudes. Following simulation of the experimental data we estimate average proportion/percentage/rate differences. We compare the estimators in terms of bias, variance, type-1 error and power. Estimates of Monte Carlo error associated with these quantities are provided. If response data are beta distributed with constant dispersion parameters across the two samples, then all models are unbiased and have reasonable type-1 error rates and power profiles. If the response data in the two samples have different dispersion parameters, then the simple beta regression model is biased. When the sample size is small (N0 = N1 = 25) linear regression has superior type-1 error rates compared to the other models. Small sample type-1 error rates can be improved in beta regression models using bias correction/reduction methods. In the power experiments, variable-dispersion beta regression and fractional logit regression models have slightly elevated power compared to linear regression models. Similar results were observed if the

  9. LIAR -- A new program for the modeling and simulation of linear accelerators with high gradients and small emittances

    International Nuclear Information System (INIS)

    Assmann, R.; Adolphsen, C.; Bane, K.; Raubenheimer, T.O.; Siemann, R.; Thompson, K.

    1996-09-01

    Linear accelerators are the central components of the proposed next generation of linear colliders. They need to provide acceleration of up to 750 GeV per beam while maintaining very small normalized emittances. Standard simulation programs, mainly developed for storage rings, do not meet the specific requirements for high energy linear accelerators. The authors present a new program LIAR (LInear Accelerator Research code) that includes wakefield effects, a 4D coupled beam description, specific optimization algorithms and other advanced features. Its modular structure allows to use and to extend it easily for different purposes. They present examples of simulations for SLC and NLC

  10. Optimization of radioactive waste management system by application of multiobjective linear programming

    International Nuclear Information System (INIS)

    Shimizu, Yoshiaki

    1981-01-01

    A mathematical procedure is proposed to make a radioactive waste management plan comprehensively. Since such planning is relevant to some different goals in management, decision making has to be formulated as a multiobjective optimization problem. A mathematical programming method was introduced to make a decision through an interactive manner which enables us to assess the preference of decision maker step by step among the conflicting objectives. The reference system taken as an example is the radioactive waste management system at the Research Reactor Institute of Kyoto University (KUR). Its linear model was built based on the experience in the actual management at KUR. The best-compromise model was then formulated as a multiobjective linear programming by the aid of the computational analysis through a conventional optimization. It was shown from the numerical results that the proposed approach could provide some useful informations to make an actual management plan. (author)

  11. Mixed integer linear programming model for dynamic supplier selection problem considering discounts

    Directory of Open Access Journals (Sweden)

    Adi Wicaksono Purnawan

    2018-01-01

    Full Text Available Supplier selection is one of the most important elements in supply chain management. This function involves evaluation of many factors such as, material costs, transportation costs, quality, delays, supplier capacity, storage capacity and others. Each of these factors varies with time, therefore, supplier identified for one period is not necessarily be same for the next period to supply the same product. So, mixed integer linear programming (MILP was developed to overcome the dynamic supplier selection problem (DSSP. In this paper, a mixed integer linear programming model is built to solve the lot-sizing problem with multiple suppliers, multiple periods, multiple products and quantity discounts. The buyer has to make a decision for some products which will be supplied by some suppliers for some periods cosidering by discount. To validate the MILP model with randomly generated data. The model is solved by Lingo 16.

  12. Mehar Methods for Fuzzy Optimal Solution and Sensitivity Analysis of Fuzzy Linear Programming with Symmetric Trapezoidal Fuzzy Numbers

    Directory of Open Access Journals (Sweden)

    Sukhpreet Kaur Sidhu

    2014-01-01

    Full Text Available The drawbacks of the existing methods to obtain the fuzzy optimal solution of such linear programming problems, in which coefficients of the constraints are represented by real numbers and all the other parameters as well as variables are represented by symmetric trapezoidal fuzzy numbers, are pointed out, and to resolve these drawbacks, a new method (named as Mehar method is proposed for the same linear programming problems. Also, with the help of proposed Mehar method, a new method, much easy as compared to the existing methods, is proposed to deal with the sensitivity analysis of the same type of linear programming problems.

  13. Sub-regional linear programming models in land use analysis: a case study of the Neguev settlement, Costa Rica.

    NARCIS (Netherlands)

    Schipper, R.A.; Stoorvogel, J.J.; Jansen, D.M.

    1995-01-01

    The paper deals with linear programming as a tool for land use analysis at the sub-regional level. A linear programming model of a case study area, the Neguev settlement in the Atlantic zone of Costa Rica, is presented. The matrix of the model includes five submatrices each encompassing a different

  14. Towards lexicographic multi-objective linear programming using grossone methodology

    Science.gov (United States)

    Cococcioni, Marco; Pappalardo, Massimo; Sergeyev, Yaroslav D.

    2016-10-01

    Lexicographic Multi-Objective Linear Programming (LMOLP) problems can be solved in two ways: preemptive and nonpreemptive. The preemptive approach requires the solution of a series of LP problems, with changing constraints (each time the next objective is added, a new constraint appears). The nonpreemptive approach is based on a scalarization of the multiple objectives into a single-objective linear function by a weighted combination of the given objectives. It requires the specification of a set of weights, which is not straightforward and can be time consuming. In this work we present both mathematical and software ingredients necessary to solve LMOLP problems using a recently introduced computational methodology (allowing one to work numerically with infinities and infinitesimals) based on the concept of grossone. The ultimate goal of such an attempt is an implementation of a simplex-like algorithm, able to solve the original LMOLP problem by solving only one single-objective problem and without the need to specify finite weights. The expected advantages are therefore obvious.

  15. A Homogeneous and Self-Dual Interior-Point Linear Programming Algorithm for Economic Model Predictive Control

    DEFF Research Database (Denmark)

    Sokoler, Leo Emil; Frison, Gianluca; Skajaa, Anders

    2015-01-01

    We develop an efficient homogeneous and self-dual interior-point method (IPM) for the linear programs arising in economic model predictive control of constrained linear systems with linear objective functions. The algorithm is based on a Riccati iteration procedure, which is adapted to the linear...... system of equations solved in homogeneous and self-dual IPMs. Fast convergence is further achieved using a warm-start strategy. We implement the algorithm in MATLAB and C. Its performance is tested using a conceptual power management case study. Closed loop simulations show that 1) the proposed algorithm...

  16. Ergodicity and Parameter Estimates for Infinite-Dimensional Fractional Ornstein-Uhlenbeck Process

    International Nuclear Information System (INIS)

    Maslowski, Bohdan; Pospisil, Jan

    2008-01-01

    Existence and ergodicity of a strictly stationary solution for linear stochastic evolution equations driven by cylindrical fractional Brownian motion are proved. Ergodic behavior of non-stationary infinite-dimensional fractional Ornstein-Uhlenbeck processes is also studied. Based on these results, strong consistency of suitably defined families of parameter estimators is shown. The general results are applied to linear parabolic and hyperbolic equations perturbed by a fractional noise

  17. Topics in computational linear optimization

    DEFF Research Database (Denmark)

    Hultberg, Tim Helge

    2000-01-01

    Linear optimization has been an active area of research ever since the pioneering work of G. Dantzig more than 50 years ago. This research has produced a long sequence of practical as well as theoretical improvements of the solution techniques avilable for solving linear optimization problems...... of high quality solvers and the use of algebraic modelling systems to handle the communication between the modeller and the solver. This dissertation features four topics in computational linear optimization: A) automatic reformulation of mixed 0/1 linear programs, B) direct solution of sparse unsymmetric...... systems of linear equations, C) reduction of linear programs and D) integration of algebraic modelling of linear optimization problems in C++. Each of these topics is treated in a separate paper included in this dissertation. The efficiency of solving mixed 0-1 linear programs by linear programming based...

  18. The effect of workload constraints in linear programming models for production planning

    NARCIS (Netherlands)

    Jansen, M.M.; Kok, de A.G.; Adan, I.J.B.F.

    2011-01-01

    Linear programming (LP) models for production planning incorporate a model of the manufacturing system that is necessarily deterministic. Although these deterministic models are the current state-of-the-art, it should be recognized that they are used in an environment that is inherently stochastic.

  19. Visualizing measurement for 3D smooth density distributions by means of linear programming

    International Nuclear Information System (INIS)

    Tayama, Norio; Yang, Xue-dong

    1994-01-01

    This paper is concerned with a theoretical possibility of a new visualizing measurement method based on an optimum 3D reconstruction from a few selected projections. A theory of optimum 3D reconstruction by a linear programming is discussed, utilizing a few projections for sampled 3D smooth-density-distribution model which satisfies the condition of the 3D sampling theorem. First by use of the sampling theorem, it is shown that we can set up simultaneous simple equations which corresponds to the case of the parallel beams. Then we solve the simultaneous simple equations by means of linear programming algorithm, and we can get an optimum 3D density distribution images with minimum error in the reconstruction. The results of computer simulation with the algorithm are presented. (author)

  20. linear-quadratic-linear model

    Directory of Open Access Journals (Sweden)

    Tanwiwat Jaikuna

    2017-02-01

    Full Text Available Purpose: To develop an in-house software program that is able to calculate and generate the biological dose distribution and biological dose volume histogram by physical dose conversion using the linear-quadratic-linear (LQL model. Material and methods : The Isobio software was developed using MATLAB version 2014b to calculate and generate the biological dose distribution and biological dose volume histograms. The physical dose from each voxel in treatment planning was extracted through Computational Environment for Radiotherapy Research (CERR, and the accuracy was verified by the differentiation between the dose volume histogram from CERR and the treatment planning system. An equivalent dose in 2 Gy fraction (EQD2 was calculated using biological effective dose (BED based on the LQL model. The software calculation and the manual calculation were compared for EQD2 verification with pair t-test statistical analysis using IBM SPSS Statistics version 22 (64-bit. Results: Two and three-dimensional biological dose distribution and biological dose volume histogram were displayed correctly by the Isobio software. Different physical doses were found between CERR and treatment planning system (TPS in Oncentra, with 3.33% in high-risk clinical target volume (HR-CTV determined by D90%, 0.56% in the bladder, 1.74% in the rectum when determined by D2cc, and less than 1% in Pinnacle. The difference in the EQD2 between the software calculation and the manual calculation was not significantly different with 0.00% at p-values 0.820, 0.095, and 0.593 for external beam radiation therapy (EBRT and 0.240, 0.320, and 0.849 for brachytherapy (BT in HR-CTV, bladder, and rectum, respectively. Conclusions : The Isobio software is a feasible tool to generate the biological dose distribution and biological dose volume histogram for treatment plan evaluation in both EBRT and BT.

  1. A scalable parallel algorithm for multiple objective linear programs

    Science.gov (United States)

    Wiecek, Malgorzata M.; Zhang, Hong

    1994-01-01

    This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.

  2. IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS

    Science.gov (United States)

    Fogle, F. R.

    1994-01-01

    IESIP, an Improved Exploratory Search Technique for Pure Integer Linear Programming Problems, addresses the problem of optimizing an objective function of one or more variables subject to a set of confining functions or constraints by a method called discrete optimization or integer programming. Integer programming is based on a specific form of the general linear programming problem in which all variables in the objective function and all variables in the constraints are integers. While more difficult, integer programming is required for accuracy when modeling systems with small numbers of components such as the distribution of goods, machine scheduling, and production scheduling. IESIP establishes a new methodology for solving pure integer programming problems by utilizing a modified version of the univariate exploratory move developed by Robert Hooke and T.A. Jeeves. IESIP also takes some of its technique from the greedy procedure and the idea of unit neighborhoods. A rounding scheme uses the continuous solution found by traditional methods (simplex or other suitable technique) and creates a feasible integer starting point. The Hook and Jeeves exploratory search is modified to accommodate integers and constraints and is then employed to determine an optimal integer solution from the feasible starting solution. The user-friendly IESIP allows for rapid solution of problems up to 10 variables in size (limited by DOS allocation). Sample problems compare IESIP solutions with the traditional branch-and-bound approach. IESIP is written in Borland's TURBO Pascal for IBM PC series computers and compatibles running DOS. Source code and an executable are provided. The main memory requirement for execution is 25K. This program is available on a 5.25 inch 360K MS DOS format diskette. IESIP was developed in 1990. IBM is a trademark of International Business Machines. TURBO Pascal is registered by Borland International.

  3. On Fractional Order Hybrid Differential Equations

    Directory of Open Access Journals (Sweden)

    Mohamed A. E. Herzallah

    2014-01-01

    Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.

  4. BASIC program to compute uranium density and void volume fraction in laboratory-scale uranium silicide aluminum dispersion plate-type fuel

    International Nuclear Information System (INIS)

    Ugajin, Mitsuhiro

    1991-05-01

    BASIC program simple and easy to operate has been developed to compute uranium density and void volume fraction for laboratory-scale uranium silicide aluminum dispersion plate-type fuel, so called miniplate. An example of the result of calculation is given in order to demonstrate how the calculated void fraction correlates with the microstructural distribution of the void in a miniplate prepared in our laboratory. The program is also able to constitute data base on important parameters for miniplates from experimentally-determined values of density, weight of each constituent and dimensions of miniplates. Utility programs pertinent to the development of the BASIC program are also given which run in the popular MS-DOS environment. All the source lists are attached and brief description for each program is made. (author)

  5. The synchronization of three fractional differential systems

    International Nuclear Information System (INIS)

    Li Changpin; Yan Jianping

    2007-01-01

    In this paper, a new method is proposed and applied to the synchronization of fractional differential systems (or 'differential systems with fractional orders'), where both drive and response systems have the same dimensionality and are coupled by the driving signal. The present technique is based on the stability criterion of linear fractional systems. This method is implemented in (chaos) synchronization of the fractional Lorenz system, Chen system and Chua circuit. Numerical simulations show the present synchronization method works well

  6. The fundamental solutions for fractional evolution equations of parabolic type

    Directory of Open Access Journals (Sweden)

    Mahmoud M. El-Borai

    2004-01-01

    Full Text Available The fundamental solutions for linear fractional evolution equations are obtained. The coefficients of these equations are a family of linear closed operators in the Banach space. Also, the continuous dependence of solutions on the initial conditions is studied. A mixed problem of general parabolic partial differential equations with fractional order is given as an application.

  7. Municipal solid waste management planning for Xiamen City, China: a stochastic fractional inventory-theory-based approach.

    Science.gov (United States)

    Chen, Xiujuan; Huang, Guohe; Zhao, Shan; Cheng, Guanhui; Wu, Yinghui; Zhu, Hua

    2017-11-01

    In this study, a stochastic fractional inventory-theory-based waste management planning (SFIWP) model was developed and applied for supporting long-term planning of the municipal solid waste (MSW) management in Xiamen City, the special economic zone of Fujian Province, China. In the SFIWP model, the techniques of inventory model, stochastic linear fractional programming, and mixed-integer linear programming were integrated in a framework. Issues of waste inventory in MSW management system were solved, and the system efficiency was maximized through considering maximum net-diverted wastes under various constraint-violation risks. Decision alternatives for waste allocation and capacity expansion were also provided for MSW management planning in Xiamen. The obtained results showed that about 4.24 × 10 6  t of waste would be diverted from landfills when p i is 0.01, which accounted for 93% of waste in Xiamen City, and the waste diversion per unit of cost would be 26.327 × 10 3  t per $10 6 . The capacities of MSW management facilities including incinerators, composting facility, and landfills would be expanded due to increasing waste generation rate.

  8. Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

    Energy Technology Data Exchange (ETDEWEB)

    Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)

    2014-06-19

    This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.

  9. Chromosome structures: reduction of certain problems with unequal gene content and gene paralogs to integer linear programming.

    Science.gov (United States)

    Lyubetsky, Vassily; Gershgorin, Roman; Gorbunov, Konstantin

    2017-12-06

    Chromosome structure is a very limited model of the genome including the information about its chromosomes such as their linear or circular organization, the order of genes on them, and the DNA strand encoding a gene. Gene lengths, nucleotide composition, and intergenic regions are ignored. Although highly incomplete, such structure can be used in many cases, e.g., to reconstruct phylogeny and evolutionary events, to identify gene synteny, regulatory elements and promoters (considering highly conserved elements), etc. Three problems are considered; all assume unequal gene content and the presence of gene paralogs. The distance problem is to determine the minimum number of operations required to transform one chromosome structure into another and the corresponding transformation itself including the identification of paralogs in two structures. We use the DCJ model which is one of the most studied combinatorial rearrangement models. Double-, sesqui-, and single-operations as well as deletion and insertion of a chromosome region are considered in the model; the single ones comprise cut and join. In the reconstruction problem, a phylogenetic tree with chromosome structures in the leaves is given. It is necessary to assign the structures to inner nodes of the tree to minimize the sum of distances between terminal structures of each edge and to identify the mutual paralogs in a fairly large set of structures. A linear algorithm is known for the distance problem without paralogs, while the presence of paralogs makes it NP-hard. If paralogs are allowed but the insertion and deletion operations are missing (and special constraints are imposed), the reduction of the distance problem to integer linear programming is known. Apparently, the reconstruction problem is NP-hard even in the absence of paralogs. The problem of contigs is to find the optimal arrangements for each given set of contigs, which also includes the mutual identification of paralogs. We proved that these

  10. How to Use Linear Programming for Information System Performances Optimization

    Directory of Open Access Journals (Sweden)

    Hell Marko

    2014-09-01

    Full Text Available Background: Organisations nowadays operate in a very dynamic environment, and therefore, their ability of continuously adjusting the strategic plan to the new conditions is a must for achieving their strategic objectives. BSC is a well-known methodology for measuring performances enabling organizations to learn how well they are doing. In this paper, “BSC for IS” will be proposed in order to measure the IS impact on the achievement of organizations’ business goals. Objectives: The objective of this paper is to present the original procedure which is used to enhance the BSC methodology in planning the optimal targets of IS performances value in order to maximize the organization's effectiveness. Methods/Approach: The method used in this paper is the quantitative methodology - linear programming. In the case study, linear programming is used for optimizing organization’s strategic performance. Results: Results are shown on the example of a case study national park. An optimal performance value for the strategic objective has been calculated, as well as an optimal performance value for each DO (derived objective. Results are calculated in Excel, using Solver Add-in. Conclusions: The presentation of methodology through the case study of a national park shows that this methodology, though it requires a high level of formalisation, provides a very transparent performance calculation.

  11. Fault detection and initial state verification by linear programming for a class of Petri nets

    Science.gov (United States)

    Rachell, Traxon; Meyer, David G.

    1992-01-01

    The authors present an algorithmic approach to determining when the marking of a LSMG (live safe marked graph) or a LSFC (live safe free choice) net is in the set of live safe markings M. Hence, once the marking of a net is determined to be in M, then if at some time thereafter the marking of this net is determined not to be in M, this indicates a fault. It is shown how linear programming can be used to determine if m is an element of M. The worst-case computational complexity of each algorithm is bounded by the number of linear programs necessary to compute.

  12. Optimal traffic control in highway transportation networks using linear programming

    KAUST Repository

    Li, Yanning

    2014-06-01

    This article presents a framework for the optimal control of boundary flows on transportation networks. The state of the system is modeled by a first order scalar conservation law (Lighthill-Whitham-Richards PDE). Based on an equivalent formulation of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can be extended to an arbitrary transportation network, preserving linear constraints. Unlike previously investigated transportation network control schemes, this framework leverages the intrinsic properties of the Halmilton-Jacobi equation, and does not require any discretization or boolean variables on the link. Hence this framework is very computational efficient and provides the globally optimal solution. The feasibility of this framework is illustrated by an on-ramp metering control example.

  13. Dose fractionated gamma knife radiosurgery for large arteriovenous malformations on daily or alternate day schedule outside the linear quadratic model: Proof of concept and early results. A substitute to volume fractionation.

    Science.gov (United States)

    Mukherjee, Kanchan Kumar; Kumar, Narendra; Tripathi, Manjul; Oinam, Arun S; Ahuja, Chirag K; Dhandapani, Sivashanmugam; Kapoor, Rakesh; Ghoshal, Sushmita; Kaur, Rupinder; Bhatt, Sandeep

    2017-01-01

    To evaluate the feasibility, safety and efficacy of dose fractionated gamma knife radiosurgery (DFGKRS) on a daily schedule beyond the linear quadratic (LQ) model, for large volume arteriovenous malformations (AVMs). Between 2012-16, 14 patients of large AVMs (median volume 26.5 cc) unsuitable for surgery or embolization were treated in 2-3 of DFGKRS sessions. The Leksell G frame was kept in situ during the whole procedure. 86% (n = 12) patients had radiologic evidence of bleed, and 43% (n = 6) had presented with a history of seizures. 57% (n = 8) patients received a daily treatment for 3 days and 43% (n = 6) were on an alternate day (2 fractions) regimen. The marginal dose was split into 2 or 3 fractions of the ideal prescription dose of a single fraction of 23-25 Gy. The median follow up period was 35.6 months (8-57 months). In the three-fraction scheme, the marginal dose ranged from 8.9-11.5 Gy, while in the two-fraction scheme, the marginal dose ranged from 11.3-15 Gy at 50% per fraction. Headache (43%, n = 6) was the most common early postoperative complication, which was controlled with short course steroids. Follow up evaluation of at least three years was achieved in seven patients, who have shown complete nidus obliteration in 43% patients while the obliteration has been in the range of 50-99% in rest of the patients. Overall, there was a 67.8% reduction in the AVM volume at 3 years. Nidus obliteration at 3 years showed a significant rank order correlation with the cumulative prescription dose (p 0.95, P value 0.01), with attainment of near-total (more than 95%) obliteration rates beyond 29 Gy of the cumulative prescription dose. No patient receiving a cumulative prescription dose of less than 31 Gy had any severe adverse reaction. In co-variate adjusted ordinal regression, only the cumulative prescription dose had a significant correlation with common terminology criteria for adverse events (CTCAE) severity (P value 0.04), independent of age, AVM volume

  14. Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

    OpenAIRE

    Aihong Ren

    2016-01-01

    This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solut...

  15. Optimization of fractional composition of the excipient in the elastomeric covering for asphalt highways

    Directory of Open Access Journals (Sweden)

    E. M. Nurullaev

    2013-04-01

    Full Text Available The computational method of optimum fractional composition of a dispersible filler of polymeric composite on the basis of three-dimensionally linked elastomer is developed according to non-linear programming. The coefficient of dynamic viscosity of polymeric suspension or the initial module of a viscoelasticity of the join solidification low-molecular rubbers with the final functional groups, filled by many fractional dioxide of silicon are considered as criteria of optimization. Influence of the limiting volume filling on energy of mechanical destruction was investigated. The elastomeric material is offered for use as a covering of asphalt highways in the form of a frost-proof waterproofing layer, which allowing multiply to increase operating properties.

  16. Chaos-based partial image encryption scheme based on linear fractional and lifting wavelet transforms

    Science.gov (United States)

    Belazi, Akram; Abd El-Latif, Ahmed A.; Diaconu, Adrian-Viorel; Rhouma, Rhouma; Belghith, Safya

    2017-01-01

    In this paper, a new chaos-based partial image encryption scheme based on Substitution-boxes (S-box) constructed by chaotic system and Linear Fractional Transform (LFT) is proposed. It encrypts only the requisite parts of the sensitive information in Lifting-Wavelet Transform (LWT) frequency domain based on hybrid of chaotic maps and a new S-box. In the proposed encryption scheme, the characteristics of confusion and diffusion are accomplished in three phases: block permutation, substitution, and diffusion. Then, we used dynamic keys instead of fixed keys used in other approaches, to control the encryption process and make any attack impossible. The new S-box was constructed by mixing of chaotic map and LFT to insure the high confidentiality in the inner encryption of the proposed approach. In addition, the hybrid compound of S-box and chaotic systems strengthened the whole encryption performance and enlarged the key space required to resist the brute force attacks. Extensive experiments were conducted to evaluate the security and efficiency of the proposed approach. In comparison with previous schemes, the proposed cryptosystem scheme showed high performances and great potential for prominent prevalence in cryptographic applications.

  17. A linear program for assessing the assignment and scheduling of radioactive wastes for disposal to sea

    International Nuclear Information System (INIS)

    Hutchinson, W.

    1983-04-01

    The report takes the form of a user guide to a computer program using linear programming techniques to aid the assignment and scheduling of radioactive wastes for disposal to sea. The program is aimed at the identification of 'optimum' amounts of each waste stream for disposal to sea without violating specific constraints values and/or fairness parameters. (author)

  18. An Interval-Parameter Fuzzy Linear Programming with Stochastic Vertices Model for Water Resources Management under Uncertainty

    Directory of Open Access Journals (Sweden)

    Yan Han

    2013-01-01

    Full Text Available An interval-parameter fuzzy linear programming with stochastic vertices (IFLPSV method is developed for water resources management under uncertainty by coupling interval-parameter fuzzy linear programming (IFLP with stochastic programming (SP. As an extension of existing interval parameter fuzzy linear programming, the developed IFLPSV approach has advantages in dealing with dual uncertainty optimization problems, which uncertainty presents as interval parameter with stochastic vertices in both of the objective functions and constraints. The developed IFLPSV method improves upon the IFLP method by allowing dual uncertainty parameters to be incorporated into the optimization processes. A hybrid intelligent algorithm based on genetic algorithm and artificial neural network is used to solve the developed model. The developed method is then applied to water resources allocation in Beijing city of China in 2020, where water resources shortage is a challenging issue. The results indicate that reasonable solutions have been obtained, which are helpful and useful for decision makers. Although the amount of water supply from Guanting and Miyun reservoirs is declining with rainfall reduction, water supply from the South-to-North Water Transfer project will have important impact on water supply structure of Beijing city, particularly in dry year and extraordinary dry year.

  19. A Unique Technique to get Kaprekar Iteration in Linear Programming Problem

    Science.gov (United States)

    Sumathi, P.; Preethy, V.

    2018-04-01

    This paper explores about a frivolous number popularly known as Kaprekar constant and Kaprekar numbers. A large number of courses and the different classroom capacities with difference in study periods make the assignment between classrooms and courses complicated. An approach of getting the minimum value of number of iterations to reach the Kaprekar constant for four digit numbers and maximum value is also obtained through linear programming techniques.

  20. LPmerge: an R package for merging genetic maps by linear programming.

    Science.gov (United States)

    Endelman, Jeffrey B; Plomion, Christophe

    2014-06-01

    Consensus genetic maps constructed from multiple populations are an important resource for both basic and applied research, including genome-wide association analysis, genome sequence assembly and studies of evolution. The LPmerge software uses linear programming to efficiently minimize the mean absolute error between the consensus map and the linkage maps from each population. This minimization is performed subject to linear inequality constraints that ensure the ordering of the markers in the linkage maps is preserved. When marker order is inconsistent between linkage maps, a minimum set of ordinal constraints is deleted to resolve the conflicts. LPmerge is on CRAN at http://cran.r-project.org/web/packages/LPmerge. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

  1. The MARX Modulator Development Program for the International Linear Collider

    International Nuclear Information System (INIS)

    Leyh, G.E.

    2006-01-01

    The International Linear Collider (ILC) Marx Modulator Development Program at SLAC is working towards developing a full-scale ILC Marx ''Reference Design'' modulator prototype, with the goal of significantly reducing the size and cost of the ILC modulator while improving overall modulator efficiency and availability. The ILC Reference Design prototype will provide a proof-of-concept model to industry in advance of Phase II SBIR funding, and also allow operation of the new 10MW L-Band Klystron prototypes immediately upon their arrival at SLAC

  2. Marginal cost of electricity conservation: an application of linear program

    International Nuclear Information System (INIS)

    Silveira, A.M. da; Hollanda, J.B. de

    1987-01-01

    This paper is addressed ti the planning of electricity industry when the use of energetically efficient appliances (conservation) is financed by the utilities. It is based on the Linear Programming Model proposed by Masse and Boiteaux for planning of conventional energy sources, where one unity of electricity (Kw/Kw h) saved is treated as if it were a generator of equivalent size. In spite of the formal simplicity of the models it can support interesting concessions on the subject of a electrical energy conservation policy. (author)

  3. Life cycle cost optimization of biofuel supply chains under uncertainties based on interval linear programming.

    Science.gov (United States)

    Ren, Jingzheng; Dong, Liang; Sun, Lu; Goodsite, Michael Evan; Tan, Shiyu; Dong, Lichun

    2015-01-01

    The aim of this work was to develop a model for optimizing the life cycle cost of biofuel supply chain under uncertainties. Multiple agriculture zones, multiple transportation modes for the transport of grain and biofuel, multiple biofuel plants, and multiple market centers were considered in this model, and the price of the resources, the yield of grain and the market demands were regarded as interval numbers instead of constants. An interval linear programming was developed, and a method for solving interval linear programming was presented. An illustrative case was studied by the proposed model, and the results showed that the proposed model is feasible for designing biofuel supply chain under uncertainties. Copyright © 2015 Elsevier Ltd. All rights reserved.

  4. A primal-dual exterior point algorithm for linear programming problems

    Directory of Open Access Journals (Sweden)

    Samaras Nikolaos

    2009-01-01

    Full Text Available The aim of this paper is to present a new simplex type algorithm for the Linear Programming Problem. The Primal - Dual method is a Simplex - type pivoting algorithm that generates two paths in order to converge to the optimal solution. The first path is primal feasible while the second one is dual feasible for the original problem. Specifically, we use a three-phase-implementation. The first two phases construct the required primal and dual feasible solutions, using the Primal Simplex algorithm. Finally, in the third phase the Primal - Dual algorithm is applied. Moreover, a computational study has been carried out, using randomly generated sparse optimal linear problems, to compare its computational efficiency with the Primal Simplex algorithm and also with MATLAB's Interior Point Method implementation. The algorithm appears to be very promising since it clearly shows its superiority to the Primal Simplex algorithm as well as its robustness over the IPM algorithm.

  5. Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming

    Directory of Open Access Journals (Sweden)

    Fusun Kucukbay

    2016-04-01

    Full Text Available Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP. Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.

  6. Optimal placement of capacitors in a radial network using conic and mixed integer linear programming

    Energy Technology Data Exchange (ETDEWEB)

    Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box: 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)

    2008-06-15

    This paper considers the problem of optimally placing fixed and switched type capacitors in a radial distribution network. The aim of this problem is to minimize the costs associated with capacitor banks, peak power, and energy losses whilst satisfying a pre-specified set of physical and technical constraints. The proposed solution is obtained using a two-phase approach. In phase-I, the problem is formulated as a conic program in which all nodes are candidates for placement of capacitor banks whose sizes are considered as continuous variables. A global solution of the phase-I problem is obtained using an interior-point based conic programming solver. Phase-II seeks a practical optimal solution by considering capacitor sizes as discrete variables. The problem in this phase is formulated as a mixed integer linear program based on minimizing the L1-norm of deviations from the phase-I state variable values. The solution to the phase-II problem is obtained using a mixed integer linear programming solver. The proposed method is validated via extensive comparisons with previously published results. (author)

  7. Different elution modes and field programming in gravitational field-flow fractionation IV. Field programming achieved with channels of non-constant cross-sections

    Czech Academy of Sciences Publication Activity Database

    Plocková, Jana; Matulík, František; Chmelík, Josef

    2002-01-01

    Roč. 955, č. 1 (2002), s. 95-103 ISSN 0021-9673 R&D Projects: GA AV ČR IAA4031805 Institutional research plan: CEZ:AV0Z4031919 Keywords : gravitational field-flow fractionation * field programming * hydrodynamic lift forces Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 3.098, year: 2002

  8. Fuzzy chance constrained linear programming model for scrap charge optimization in steel production

    DEFF Research Database (Denmark)

    Rong, Aiying; Lahdelma, Risto

    2008-01-01

    the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product...

  9. A new neural network model for solving random interval linear programming problems.

    Science.gov (United States)

    Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza

    2017-05-01

    This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.

  10. Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

    Directory of Open Access Journals (Sweden)

    Aihong Ren

    2016-01-01

    Full Text Available This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

  11. Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System

    Directory of Open Access Journals (Sweden)

    Zhenhua Hu

    2013-01-01

    Full Text Available We propose a new nonlinear economic system with fractional derivative. According to the Jumarie’s definition of fractional derivative, we obtain a discrete fractional nonlinear economic system. Three variables, the gross domestic production, inflation, and unemployment rate, are considered by this nonlinear system. Based on the concrete macroeconomic data of USA, the coefficients of this nonlinear system are estimated by the method of least squares. The application of discrete fractional economic model with linear and nonlinear structure is shown to illustrate the efficiency of modeling the macroeconomic data with discrete fractional dynamical system. The empirical study suggests that the nonlinear discrete fractional dynamical system can describe the actual economic data accurately and predict the future behavior more reasonably than the linear dynamic system. The method proposed in this paper can be applied to investigate other macroeconomic variables of more states.

  12. A penalization approach to linear programming duality with application to capacity constrained transport

    OpenAIRE

    Korman, Jonathan; McCann, Robert J.; Seis, Christian

    2013-01-01

    A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.

  13. Role of exponential type random invexities for asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming.

    Science.gov (United States)

    Verma, Ram U; Seol, Youngsoo

    2016-01-01

    First a new notion of the random exponential Hanson-Antczak type [Formula: see text]-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function [Formula: see text] of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. Furthermore, several sets of asymptotic sufficiency results in which various generalized exponential type [Formula: see text]-V-invexity assumptions are imposed on certain vector functions whose components are the individual as well as some combinations of the problem functions are examined and proved. To the best of our knowledge, all the established results on the semi-infinite aspects of the multi-objective fractional programming are new, which is a significantly new emerging field of the interdisciplinary research in nature. We also observed that the investigated results can be modified and applied to several special classes of nonlinear programming problems.

  14. An Interactive Method to Solve Infeasibility in Linear Programming Test Assembling Models

    Science.gov (United States)

    Huitzing, Hiddo A.

    2004-01-01

    In optimal assembly of tests from item banks, linear programming (LP) models have proved to be very useful. Assembly by hand has become nearly impossible, but these LP techniques are able to find the best solutions, given the demands and needs of the test to be assembled and the specifics of the item bank from which it is assembled. However,…

  15. Optimal blood glucose control in diabetes mellitus treatment using dynamic programming based on Ackerman’s linear model

    Science.gov (United States)

    Pradanti, Paskalia; Hartono

    2018-03-01

    Determination of insulin injection dose in diabetes mellitus treatment can be considered as an optimal control problem. This article is aimed to simulate optimal blood glucose control for patient with diabetes mellitus. The blood glucose regulation of diabetic patient is represented by Ackerman’s Linear Model. This problem is then solved using dynamic programming method. The desired blood glucose level is obtained by minimizing the performance index in Lagrange form. The results show that dynamic programming based on Ackerman’s Linear Model is quite good to solve the problem.

  16. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  17. Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Order Form

    Directory of Open Access Journals (Sweden)

    Sifeu Takougang Kingni

    2017-01-01

    Full Text Available A linear resistive-capacitive-inductance shunted junction (LRCLSJ model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.

  18. INTELLIGENT FRACTIONAL ORDER ITERATIVE LEARNING CONTROL USING FEEDBACK LINEARIZATION FOR A SINGLE-LINK ROBOT

    Directory of Open Access Journals (Sweden)

    Iman Ghasemi

    2017-05-01

    Full Text Available In this paper, iterative learning control (ILC is combined with an optimal fractional order derivative (BBO-Da-type ILC and optimal fractional and proportional-derivative (BBO-PDa-type ILC. In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where  to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both  and  learning law i.e. proportional , derivative  and  are optimized using Biogeography-Based optimization algorithm (BBO. Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC

  19. Linear Polarization Properties of Parsec-Scale AGN Jets

    Directory of Open Access Journals (Sweden)

    Alexander B. Pushkarev

    2017-12-01

    Full Text Available We used 15 GHz multi-epoch Very Long Baseline Array (VLBA polarization sensitive observations of 484 sources within a time interval 1996–2016 from the MOJAVE program, and also from the NRAO data archive. We have analyzed the linear polarization characteristics of the compact core features and regions downstream, and their changes along and across the parsec-scale active galactic nuclei (AGN jets. We detected a significant increase of fractional polarization with distance from the radio core along the jet as well as towards the jet edges. Compared to quasars, BL Lacs have a higher degree of polarization and exhibit more stable electric vector position angles (EVPAs in their core features and a better alignment of the EVPAs with the local jet direction. The latter is accompanied by a higher degree of linear polarization, suggesting that compact bright jet features might be strong transverse shocks, which enhance magnetic field regularity by compression.

  20. A comparison between linear and non-linear analysis of flexible pavements

    Energy Technology Data Exchange (ETDEWEB)

    Soleymani, H.R.; Berthelot, C.F.; Bergan, A.T. [Saskatchewan Univ., Saskatoon, SK (Canada). Dept. of Mechanical Engineering

    1995-12-31

    Computer pavement analysis programs, which are based on mathematical simulation models, were compared. The programs included in the study were: ELSYM5, an Elastic Linear (EL) pavement analysis program, MICH-PAVE, a Finite Element Non-Linear (FENL) and Finite Element Linear (FEL) pavement analysis program. To perform the analysis different tire pressures, pavement material properties and asphalt layer thicknesses were selected. Evaluation criteria used in the analysis were tensile strain in bottom of the asphalt layer, vertical compressive strain at the top of the subgrade and surface displacement. Results showed that FENL methods predicted more strain and surface deflection than the FEL and EL analysis methods. Analyzing pavements with FEL does not offer many advantages over the EL method. Differences in predicted strains between the three methods of analysis in some cases was found to be close to 100% It was suggested that these programs require more calibration and validation both theoretically and empirically to accurately correlate with field observations. 19 refs., 4 tabs., 9 figs.

  1. A novel approach based on preference-based index for interval bilevel linear programming problem

    OpenAIRE

    Aihong Ren; Yuping Wang; Xingsi Xue

    2017-01-01

    This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrain...

  2. Averaging and Linear Programming in Some Singularly Perturbed Problems of Optimal Control

    Energy Technology Data Exchange (ETDEWEB)

    Gaitsgory, Vladimir, E-mail: vladimir.gaitsgory@mq.edu.au [Macquarie University, Department of Mathematics (Australia); Rossomakhine, Sergey, E-mail: serguei.rossomakhine@flinders.edu.au [Flinders University, Flinders Mathematical Sciences Laboratory, School of Computer Science, Engineering and Mathematics (Australia)

    2015-04-15

    The paper aims at the development of an apparatus for analysis and construction of near optimal solutions of singularly perturbed (SP) optimal controls problems (that is, problems of optimal control of SP systems) considered on the infinite time horizon. We mostly focus on problems with time discounting criteria but a possibility of the extension of results to periodic optimization problems is discussed as well. Our consideration is based on earlier results on averaging of SP control systems and on linear programming formulations of optimal control problems. The idea that we exploit is to first asymptotically approximate a given problem of optimal control of the SP system by a certain averaged optimal control problem, then reformulate this averaged problem as an infinite-dimensional linear programming (LP) problem, and then approximate the latter by semi-infinite LP problems. We show that the optimal solution of these semi-infinite LP problems and their duals (that can be found with the help of a modification of an available LP software) allow one to construct near optimal controls of the SP system. We demonstrate the construction with two numerical examples.

  3. A non-differentiable solution for the local fractional telegraph equation

    Directory of Open Access Journals (Sweden)

    Li Jie

    2017-01-01

    Full Text Available In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

  4. Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

    Science.gov (United States)

    Oktem, Figen S; Ozaktas, Haldun M

    2010-08-01

    Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.

  5. Linear programming phase unwrapping for dual-wavelength digital holography.

    Science.gov (United States)

    Wang, Zhaomin; Jiao, Jiannan; Qu, Weijuan; Yang, Fang; Li, Hongru; Tian, Ailing; Asundi, Anand

    2017-01-20

    A linear programming phase unwrapping method in dual-wavelength digital holography is proposed and verified experimentally. The proposed method uses the square of height difference as a convergence standard and theoretically gives the boundary condition in a searching process. A simulation was performed by unwrapping step structures at different levels of Gaussian noise. As a result, our method is capable of recovering the discontinuities accurately. It is robust and straightforward. In the experiment, a microelectromechanical systems sample and a cylindrical lens were measured separately. The testing results were in good agreement with true values. Moreover, the proposed method is applicable not only in digital holography but also in other dual-wavelength interferometric techniques.

  6. Numerical solution of distributed order fractional differential equations

    Science.gov (United States)

    Katsikadelis, John T.

    2014-02-01

    In this paper a method for the numerical solution of distributed order FDEs (fractional differential equations) of a general form is presented. The method applies to both linear and nonlinear equations. The Caputo type fractional derivative is employed. The distributed order FDE is approximated with a multi-term FDE, which is then solved by adjusting appropriately the numerical method developed for multi-term FDEs by Katsikadelis. Several example equations are solved and the response of mechanical systems described by such equations is studied. The convergence and the accuracy of the method for linear and nonlinear equations are demonstrated through well corroborated numerical results.

  7. Different elution modes and field programming in gravitational field-flow fractionation. III. Field programming by flow-rate gradient generated by a programmable pump

    Czech Academy of Sciences Publication Activity Database

    Plocková, Jana; Chmelík, Josef

    2001-01-01

    Roč. 918, č. 2 (2001), s. 361-370 ISSN 0021-9673 R&D Projects: GA AV ČR IAA4031805 Institutional research plan: CEZ:AV0Z4031919 Keywords : field-flow fractionation * field programming * flow-rate gradients Subject RIV: CB - Analytical Chemistry, Separation Impact factor: 2.793, year: 2001

  8. The Value Proposition for Fractionated Space Architectures

    Science.gov (United States)

    2006-09-01

    fractionation “mass penalty” assumptions , the expected launch costs are nearly a factor of two lower for the fractionated system than for the monolith...humidity variations which may affect fire propagation speed. 23 The Capital Asset Pricing Model ( CAPM ...spacecraft, can be very significant. In any event, however, the assumption that spacecraft cost scales roughly linearly with its mass is an artifact of

  9. A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

    Science.gov (United States)

    Arneson, Heather M.; Dousse, Nicholas; Langbort, Cedric

    2014-01-01

    We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

  10. Fractional Consumption of Liquid Hydrogen and Liquid Oxygen During the Space Shuttle Program

    Science.gov (United States)

    Partridge, Jonathan K.

    2011-01-01

    The Space Shuttle uses the propellants, liquid hydrogen and liquid oxygen, to meet part of the propulsion requirements from ground to orbit. The Kennedy Space Center procured over 25 million kilograms of liquid hydrogen and over 250 million kilograms of liquid oxygen during the 3D-year Space Shuttle Program. Because of the cryogenic nature of the propellants, approximately 55% of the total purchased liquid hydrogen and 30% of the total purchased liquid oxygen were used in the Space Shuttle Main Engines. The balance of the propellants were vaporized during operations for various purposes. This paper dissects the total consumption of liqUid hydrogen and liqUid oxygen and determines the fraction attributable to each of the various processing and launch operations that occurred during the entire Space Shuttle Program at the Kennedy Space Center.

  11. Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming.

    Science.gov (United States)

    Maillot, Matthieu; Ferguson, Elaine L; Drewnowski, Adam; Darmon, Nicole

    2008-06-01

    Nutrient profiling ranks foods based on their nutrient content. They may help identify foods with a good nutritional quality for their price. This hypothesis was tested using diet modeling with linear programming. Analyses were undertaken using food intake data from the nationally representative French INCA (enquête Individuelle et Nationale sur les Consommations Alimentaires) survey and its associated food composition and price database. For each food, a nutrient profile score was defined as the ratio between the previously published nutrient density score (NDS) and the limited nutrient score (LIM); a nutritional quality for price indicator was developed and calculated from the relationship between its NDS:LIM and energy cost (in euro/100 kcal). We developed linear programming models to design diets that fulfilled increasing levels of nutritional constraints at a minimal cost. The median NDS:LIM values of foods selected in modeled diets increased as the levels of nutritional constraints increased (P = 0.005). In addition, the proportion of foods with a good nutritional quality for price indicator was higher (P linear programming and the nutrient profiling approaches indicates that nutrient profiling can help identify foods of good nutritional quality for their price. Linear programming is a useful tool for testing nutrient profiling systems and validating the concept of nutrient profiling.

  12. A recurrent neural network for solving bilevel linear programming problem.

    Science.gov (United States)

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian

    2014-04-01

    In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.

  13. Correction of heterogeneities in the issue compositions in the construction plans optimized in radiotherapy using linear programming

    International Nuclear Information System (INIS)

    Viana, Rodrigo Sartorelo S.; Lima, Ernesto A.B.F.; Florentino, Helenice de Oliveira; Fonseca, Paulo Roberto da; Homem, Thiago Pedro Donadon

    2009-01-01

    Linear programming models are widely found in the literature addressing various aspects involved in the creation of optimized planning for radiotherapy. However, most mathematical formulations does not incorporate certain factors that are of extreme importance for the formulation of a real planning like the attenuation of the beam of radiation and heterogeneity in the composition of tissue irradiated. In this context are proposed in this paper some modifications in the formulation of a linear programming problem with the objective of making the simulation closer to the real planning for radiotherapy and thus enable a more reliable and comprehensive planning requirements. (author)

  14. Generalized Fractional Derivative Anisotropic Viscoelastic Characterization

    Directory of Open Access Journals (Sweden)

    Harry H. Hilton

    2012-01-01

    Full Text Available Isotropic linear and nonlinear fractional derivative constitutive relations are formulated and examined in terms of many parameter generalized Kelvin models and are analytically extended to cover general anisotropic homogeneous or non-homogeneous as well as functionally graded viscoelastic material behavior. Equivalent integral constitutive relations, which are computationally more powerful, are derived from fractional differential ones and the associated anisotropic temperature-moisture-degree-of-cure shift functions and reduced times are established. Approximate Fourier transform inversions for fractional derivative relations are formulated and their accuracy is evaluated. The efficacy of integer and fractional derivative constitutive relations is compared and the preferential use of either characterization in analyzing isotropic and anisotropic real materials must be examined on a case-by-case basis. Approximate protocols for curve fitting analytical fractional derivative results to experimental data are formulated and evaluated.

  15. Identification of fractional order systems using modulating functions method

    KAUST Repository

    Liu, Dayan; Laleg-Kirati, Taous-Meriem; Gibaru, O.; Perruquetti, Wilfrid

    2013-01-01

    can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear

  16. Explicit/multi-parametric model predictive control (MPC) of linear discrete-time systems by dynamic and multi-parametric programming

    KAUST Repository

    Kouramas, K.I.; Faí sca, N.P.; Panos, C.; Pistikopoulos, E.N.

    2011-01-01

    This work presents a new algorithm for solving the explicit/multi- parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques

  17. A study of the use of linear programming techniques to improve the performance in design optimization problems

    Science.gov (United States)

    Young, Katherine C.; Sobieszczanski-Sobieski, Jaroslaw

    1988-01-01

    This project has two objectives. The first is to determine whether linear programming techniques can improve performance when handling design optimization problems with a large number of design variables and constraints relative to the feasible directions algorithm. The second purpose is to determine whether using the Kreisselmeier-Steinhauser (KS) function to replace the constraints with one constraint will reduce the cost of total optimization. Comparisons are made using solutions obtained with linear and non-linear methods. The results indicate that there is no cost saving using the linear method or in using the KS function to replace constraints.

  18. The fractional Fourier transform and applications

    Science.gov (United States)

    Bailey, David H.; Swarztrauber, Paul N.

    1991-01-01

    This paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity e exp -2(pi)i/n, the fractional Fourier transform is based on fractional roots of unity e exp -2(pi)i(alpha), where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with noninteger periodicities, performing high-resolution trigonometric interpolation, detecting lines in noisy images, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.

  19. Near-Regular Structure Discovery Using Linear Programming

    KAUST Repository

    Huang, Qixing

    2014-06-02

    Near-regular structures are common in manmade and natural objects. Algorithmic detection of such regularity greatly facilitates our understanding of shape structures, leads to compact encoding of input geometries, and enables efficient generation and manipulation of complex patterns on both acquired and synthesized objects. Such regularity manifests itself both in the repetition of certain geometric elements, as well as in the structured arrangement of the elements. We cast the regularity detection problem as an optimization and efficiently solve it using linear programming techniques. Our optimization has a discrete aspect, that is, the connectivity relationships among the elements, as well as a continuous aspect, namely the locations of the elements of interest. Both these aspects are captured by our near-regular structure extraction framework, which alternates between discrete and continuous optimizations. We demonstrate the effectiveness of our framework on a variety of problems including near-regular structure extraction, structure-preserving pattern manipulation, and markerless correspondence detection. Robustness results with respect to geometric and topological noise are presented on synthesized, real-world, and also benchmark datasets. © 2014 ACM.

  20. A linear programming approach to characterizing norm bounded uncertainty from experimental data

    Science.gov (United States)

    Scheid, R. E.; Bayard, D. S.; Yam, Y.

    1991-01-01

    The linear programming spectral overbounding and factorization (LPSOF) algorithm, an algorithm for finding a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified nonparametric function of frequency, is introduced. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).

  1. Mass Optimization of Battery/Supercapacitors Hybrid Systems Based on a Linear Programming Approach

    Science.gov (United States)

    Fleury, Benoit; Labbe, Julien

    2014-08-01

    The objective of this paper is to show that, on a specific launcher-type mission profile, a 40% gain of mass is expected using a battery/supercapacitors active hybridization instead of a single battery solution. This result is based on the use of a linear programming optimization approach to perform the mass optimization of the hybrid power supply solution.

  2. Fractional hereditariness of lipid membranes: Instabilities and linearized evolution.

    Science.gov (United States)

    Deseri, L; Pollaci, P; Zingales, M; Dayal, K

    2016-05-01

    In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler-Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving the Euler-Lagrange equation above exhibits time-decay and the large number of spatial oscillation slowly relaxes, thereby keeping the features of a long-tail type time-response. Copyright © 2015 Elsevier Ltd. All rights reserved.

  3. Nelson's syndrome: single centre experience using the linear accelerator (LINAC) for stereotactic radiosurgery and fractionated stereotactic radiotherapy.

    Science.gov (United States)

    Wilson, Peter J; Williams, Janet R; Smee, Robert I

    2014-09-01

    Nelson's syndrome is a unique clinical phenomenon of growth of a pituitary adenoma following bilateral adrenalectomies for the control of Cushing's disease. Primary management is surgical, with limited effective medical therapies available. We report our own institution's series of this pathology managed with radiation: prior to 1990, 12 patients were managed with conventional radiotherapy, and between 1990 and 2007, five patients underwent stereotactic radiosurgery (SRS) and two patients fractionated stereotactic radiotherapy (FSRT), both using the linear accelerator (LINAC). Tumour control was equivocal, with two of the five SRS patients having a reduction in tumour volume, one patient remaining unchanged, and two patients having an increase in volume. In the FSRT group, one patient had a decrease in tumour volume whilst the other had an increase in volume. Treatment related morbidity was low. Nelson's syndrome is a challenging clinical scenario, with a highly variable response to radiation in our series. Copyright © 2014 Elsevier Ltd. All rights reserved.

  4. Automated design and optimization of flexible booster autopilots via linear programming, volume 1

    Science.gov (United States)

    Hauser, F. D.

    1972-01-01

    A nonlinear programming technique was developed for the automated design and optimization of autopilots for large flexible launch vehicles. This technique, which resulted in the COEBRA program, uses the iterative application of linear programming. The method deals directly with the three main requirements of booster autopilot design: to provide (1) good response to guidance commands; (2) response to external disturbances (e.g. wind) to minimize structural bending moment loads and trajectory dispersions; and (3) stability with specified tolerances on the vehicle and flight control system parameters. The method is applicable to very high order systems (30th and greater per flight condition). Examples are provided that demonstrate the successful application of the employed algorithm to the design of autopilots for both single and multiple flight conditions.

  5. Mixed Integer Linear Programming model for Crude Palm Oil Supply Chain Planning

    Science.gov (United States)

    Sembiring, Pasukat; Mawengkang, Herman; Sadyadharma, Hendaru; Bu'ulolo, F.; Fajriana

    2018-01-01

    The production process of crude palm oil (CPO) can be defined as the milling process of raw materials, called fresh fruit bunch (FFB) into end products palm oil. The process usually through a series of steps producing and consuming intermediate products. The CPO milling industry considered in this paper does not have oil palm plantation, therefore the FFB are supplied by several public oil palm plantations. Due to the limited availability of FFB, then it is necessary to choose from which plantations would be appropriate. This paper proposes a mixed integer linear programming model the supply chain integrated problem, which include waste processing. The mathematical programming model is solved using neighborhood search approach.

  6. An improved multiple linear regression and data analysis computer program package

    Science.gov (United States)

    Sidik, S. M.

    1972-01-01

    NEWRAP, an improved version of a previous multiple linear regression program called RAPIER, CREDUC, and CRSPLT, allows for a complete regression analysis including cross plots of the independent and dependent variables, correlation coefficients, regression coefficients, analysis of variance tables, t-statistics and their probability levels, rejection of independent variables, plots of residuals against the independent and dependent variables, and a canonical reduction of quadratic response functions useful in optimum seeking experimentation. A major improvement over RAPIER is that all regression calculations are done in double precision arithmetic.

  7. Mixed-Integer-Linear-Programming-Based Energy Management System for Hybrid PV-Wind-Battery Microgrids

    DEFF Research Database (Denmark)

    Hernández, Adriana Carolina Luna; Aldana, Nelson Leonardo Diaz; Graells, Moises

    2017-01-01

    -side strategy, defined as a general mixed-integer linear programming by taking into account two stages for proper charging of the storage units. This model is considered as a deterministic problem that aims to minimize operating costs and promote self-consumption based on 24-hour ahead forecast data...

  8. Comparison of acrylamide intake from Western and guideline based diets using probabilistic techniques and linear programming.

    Science.gov (United States)

    Katz, Josh M; Winter, Carl K; Buttrey, Samuel E; Fadel, James G

    2012-03-01

    Western and guideline based diets were compared to determine if dietary improvements resulting from following dietary guidelines reduce acrylamide intake. Acrylamide forms in heat treated foods and is a human neurotoxin and animal carcinogen. Acrylamide intake from the Western diet was estimated with probabilistic techniques using teenage (13-19 years) National Health and Nutrition Examination Survey (NHANES) food consumption estimates combined with FDA data on the levels of acrylamide in a large number of foods. Guideline based diets were derived from NHANES data using linear programming techniques to comport to recommendations from the Dietary Guidelines for Americans, 2005. Whereas the guideline based diets were more properly balanced and rich in consumption of fruits, vegetables, and other dietary components than the Western diets, acrylamide intake (mean±SE) was significantly greater (Plinear programming and results demonstrate that linear programming techniques can be used to model specific diets for the assessment of toxicological and nutritional dietary components. Copyright © 2011 Elsevier Ltd. All rights reserved.

  9. On the singular perturbations for fractional differential equation.

    Science.gov (United States)

    Atangana, Abdon

    2014-01-01

    The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  10. Fraction magnitude understanding and its unique role in predicting general mathematics achievement at two early stages of fraction instruction.

    Science.gov (United States)

    Liu, Yingyi

    2017-09-08

    Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.

  11. Learning Bayesian network structure: towards the essential graph by integer linear programming tools

    Czech Academy of Sciences Publication Activity Database

    Studený, Milan; Haws, D.

    2014-01-01

    Roč. 55, č. 4 (2014), s. 1043-1071 ISSN 0888-613X R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : learning Bayesian network structure * integer linear programming * characteristic imset * essential graph Subject RIV: BA - General Mathematics Impact factor: 2.451, year: 2014 http://library.utia.cas.cz/separaty/2014/MTR/studeny-0427002.pdf

  12. Optimized remedial groundwater extraction using linear programming

    International Nuclear Information System (INIS)

    Quinn, J.J.

    1995-01-01

    Groundwater extraction systems are typically installed to remediate contaminant plumes or prevent further spread of contamination. These systems are expensive to install and maintain. A traditional approach to designing such a wellfield uses a series of trial-and-error simulations to test the effects of various well locations and pump rates. However, the optimal locations and pump rates of extraction wells are difficult to determine when objectives related to the site hydrogeology and potential pumping scheme are considered. This paper describes a case study of an application of linear programming theory to determine optimal well placement and pump rates. The objectives of the pumping scheme were to contain contaminant migration and reduce contaminant concentrations while minimizing the total amount of water pumped and treated. Past site activities at the area under study included disposal of contaminants in pits. Several groundwater plumes have been identified, and others may be present. The area of concern is bordered on three sides by a wetland, which receives a portion of its input budget as groundwater discharge from the pits. Optimization of the containment pumping scheme was intended to meet three goals: (1) prevent discharge of contaminated groundwater to the wetland, (2) minimize the total water pumped and treated (cost benefit), and (3) avoid dewatering of the wetland (cost and ecological benefits). Possible well locations were placed at known source areas. To constrain the problem, the optimization program was instructed to prevent any flow toward the wetland along a user-specified border. In this manner, the optimization routine selects well locations and pump rates so that a groundwater divide is produced along this boundary

  13. Distributed Sleep Scheduling in Wireless Sensor Networks via Fractional Domatic Partitioning

    Science.gov (United States)

    Schumacher, André; Haanpää, Harri

    We consider setting up sleep scheduling in sensor networks. We formulate the problem as an instance of the fractional domatic partition problem and obtain a distributed approximation algorithm by applying linear programming approximation techniques. Our algorithm is an application of the Garg-Könemann (GK) scheme that requires solving an instance of the minimum weight dominating set (MWDS) problem as a subroutine. Our two main contributions are a distributed implementation of the GK scheme for the sleep-scheduling problem and a novel asynchronous distributed algorithm for approximating MWDS based on a primal-dual analysis of Chvátal's set-cover algorithm. We evaluate our algorithm with ns2 simulations.

  14. Void fraction prediction in saturated flow boiling

    International Nuclear Information System (INIS)

    Francisco J Collado

    2005-01-01

    Full text of publication follows: An essential element in thermal-hydraulics is the accurate prediction of the vapor void fraction, or fraction of the flow cross-sectional area occupied by steam. Recently, the author has suggested to calculate void fraction working exclusively with thermodynamic properties. It is well known that the usual 'flow' quality, merely a mass flow rate ratio, is not at all a thermodynamic property because its expression in function of thermodynamic properties includes the slip ratio, which is a parameter of the process not a function of state. By the other hand, in the classic and well known expression of the void fraction - in function of the true mass fraction of vapor (also called 'static' quality), and the vapor and liquid densities - does not appear the slip ratio. Of course, this would suggest a direct procedure for calculating the void fraction, provided we had an accurate value of the true mass fraction of vapor, clearly from the heat balance. However the classic heat balance is usually stated in function of the 'flow' quality, what sounds really contradictory because this parameter, as we have noted above, is not at all a thermodynamic property. Then we should check against real data the actual relationship between the thermodynamic properties and the applied heat. For saturated flow boiling just from the inlet of the heated tube, and not having into account the kinetic and potential terms, the uniform applied heat per unit mass of inlet water and per unit length (in short, specific linear heat) should be closely related to a (constant) slope of the mixture enthalpy. In this work, we have checked the relation between the specific linear heat and the thermodynamic enthalpy of the liquid-vapor mixture using the actual mass fraction. This true mass fraction is calculated using the accurate measurements of the outlet void fraction taken during the Cambridge project by Knights and Thom in the sixties for vertical and horizontal

  15. A Method of Determination of an Acquisition Program in Order to Maximize the Total Utility Using Linear Programming in Integer Numbers

    Directory of Open Access Journals (Sweden)

    Alin Cristian Ioan

    2010-03-01

    Full Text Available This paper solves in a different way the problem of maximization of the total utility using the linear programming in integer numbers. The author uses the diofantic equations (equations in integers numbers and after a decomposing in different cases, he obtains the maximal utility.

  16. A Novel Linear Programming Formulation of Maximum Lifetime Routing Problem in Wireless Sensor Networks

    DEFF Research Database (Denmark)

    Cetin, Bilge Kartal; Prasad, Neeli R.; Prasad, Ramjee

    2011-01-01

    In wireless sensor networks, one of the key challenge is to achieve minimum energy consumption in order to maximize network lifetime. In fact, lifetime depends on many parameters: the topology of the sensor network, the data aggregation regime in the network, the channel access schemes, the routing...... protocols, and the energy model for transmission. In this paper, we tackle the routing challenge for maximum lifetime of the sensor network. We introduce a novel linear programming approach to the maximum lifetime routing problem. To the best of our knowledge, this is the first mathematical programming...

  17. Reduced differential transform method for partial differential equations within local fractional derivative operators

    Directory of Open Access Journals (Sweden)

    Hossein Jafari

    2016-04-01

    Full Text Available The non-differentiable solution of the linear and non-linear partial differential equations on Cantor sets is implemented in this article. The reduced differential transform method is considered in the local fractional operator sense. The four illustrative examples are given to show the efficiency and accuracy features of the presented technique to solve local fractional partial differential equations.

  18. Experience and development program for the I.V. Kurchatov Atomic Energy Institute electron linear accelerator

    International Nuclear Information System (INIS)

    Aref'ev, A.V.; Blokhov, M.V.; Gerasimov, V.F.

    1981-01-01

    A program of physical investigations and the corresponding requirements to accelerated beam parameters are discussed in brief. The state and working capacity of separate units and the accelerator as a whole for the 8-year operating period are analyzed. The aim and principal program points of linear electron accelerator modernization are defined. The program of accelerator modernization assumes: electron beam energy increase up to 100-120 MeV; mounting of three additional accelerating sections; clystron efficiency increase; development of a highly reliable modulator; stabilized power supply sources; a system of synchronous start-up; a focusing system; a beam separation system and etc [ru

  19. Linear and kernel methods for multivariate change detection

    DEFF Research Database (Denmark)

    Canty, Morton J.; Nielsen, Allan Aasbjerg

    2012-01-01

    ), as well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images, both linear and kernel-based (nonlinear), may further enhance change signals relative to no-change background. IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric...... normalization, and kernel PCA/MAF/MNF transformations are presented that function as transparent and fully integrated extensions of the ENVI remote sensing image analysis environment. The train/test approach to kernel PCA is evaluated against a Hebbian learning procedure. Matlab code is also available...... that allows fast data exploration and experimentation with smaller datasets. New, multiresolution versions of IR-MAD that accelerate convergence and that further reduce no-change background noise are introduced. Computationally expensive matrix diagonalization and kernel image projections are programmed...

  20. A Mixed Integer Linear Programming Model for the North Atlantic Aircraft Trajectory Planning

    OpenAIRE

    Sbihi , Mohammed; Rodionova , Olga; Delahaye , Daniel; Mongeau , Marcel

    2015-01-01

    International audience; This paper discusses the trajectory planning problem for ights in the North Atlantic oceanic airspace (NAT). We develop a mathematical optimization framework in view of better utilizing available capacity by re-routing aircraft. The model is constructed by discretizing the problem parameters. A Mixed integer linear program (MILP) is proposed. Based on the MILP a heuristic to solve real-size instances is also introduced

  1. What linear programming contributes: world food programme experience with the "cost of the diet" tool.

    Science.gov (United States)

    Frega, Romeo; Lanfranco, Jose Guerra; De Greve, Sam; Bernardini, Sara; Geniez, Perrine; Grede, Nils; Bloem, Martin; de Pee, Saskia

    2012-09-01

    Linear programming has been used for analyzing children's complementary feeding diets, for optimizing nutrient adequacy of dietary recommendations for a population, and for estimating the economic value of fortified foods. To describe and apply a linear programming tool ("Cost of the Diet") with data from Mozambique to determine what could be cost-effective fortification strategies. Based on locally assessed average household dietary needs, seasonal market prices of available food products, and food composition data, the tool estimates the lowest-cost diet that meets almost all nutrient needs. The results were compared with expenditure data from Mozambique to establish the affordability of this diet by quintiles of the population. Three different applications were illustrated: identifying likely "limiting nutrients," comparing cost effectiveness of different fortification interventions at the household level, and assessing economic access to nutritious foods. The analysis identified iron, vitamin B2, and pantothenic acid as "limiting nutrients." Under the Mozambique conditions, vegetable oil was estimated as a more cost-efficient vehicle for vitamin A fortification than sugar; maize flour may also be an effective vehicle to provide other constraining micronutrients. Multiple micronutrient fortification of maize flour could reduce the cost of the "lowest-cost nutritious diet" by 18%, but even this diet can be afforded by only 20% of the Mozambican population. Within the context of fortification, linear programming can be a useful tool for identifying likely nutrient inadequacies, for comparing fortification options in terms of cost effectiveness, and for illustrating the potential benefit of fortification for improving household access to a nutritious diet.

  2. On some new properties of fractional derivatives with Mittag-Leffler kernel

    Science.gov (United States)

    Baleanu, Dumitru; Fernandez, Arran

    2018-06-01

    We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes. We also prove existence and uniqueness results for certain families of linear and nonlinear fractional ODEs defined using this fractional derivative. We consider the possibility of a semigroup property for these derivatives, and establish extensions of the product rule and chain rule, with an application to fractional mechanics.

  3. MODLP program description: A program for solving linear optimal hydraulic control of groundwater contamination based on MODFLOW simulation. Version 1.0

    International Nuclear Information System (INIS)

    Ahlfeld, D.P.; Dougherty, D.E.

    1994-11-01

    MODLP is a computational tool that may help design capture zones for controlling the movement of contaminated groundwater. It creates and solves linear optimization programs that contain constraints on hydraulic head or head differences in a groundwater system. The groundwater domain is represented by USGS MODFLOW groundwater flow simulation model. This document describes the general structure of the computer program, MODLP, the types of constraints that may be imposed, detailed input instructions, interpretation of the output, and the interaction with the MODFLOW simulation kernel

  4. On the Singular Perturbations for Fractional Differential Equation

    Directory of Open Access Journals (Sweden)

    Abdon Atangana

    2014-01-01

    Full Text Available The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

  5. An SDP Approach for Multiperiod Mixed 0–1 Linear Programming Models with Stochastic Dominance Constraints for Risk Management

    DEFF Research Database (Denmark)

    Escudero, Laureano F.; Monge, Juan Francisco; Morales, Dolores Romero

    2015-01-01

    In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multist...

  6. EABOT - Energetic analysis as a basis for robust optimization of trigeneration systems by linear programming

    International Nuclear Information System (INIS)

    Piacentino, A.; Cardona, F.

    2008-01-01

    The optimization of synthesis, design and operation in trigeneration systems for building applications is a quite complex task, due to the high number of decision variables, the presence of irregular heat, cooling and electric load profiles and the variable electricity price. Consequently, computer-aided techniques are usually adopted to achieve the optimal solution, based either on iterative techniques, linear or non-linear programming or evolutionary search. Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, assuming stochastic behaviour for energy loads and prices. This paper is based on the assumption that margins for improvements in the optimization of trigeneration systems still exist, which require an in-depth understanding of plant's energetic behaviour. Robustness in the optimization of trigeneration systems has more to do with a 'correct and comprehensive' than with an 'efficient' modelling, being larger efforts required to energy specialists rather than to experts in efficient algorithms. With reference to a mixed integer linear programming model implemented in MatLab for a trigeneration system including a pressurized (medium temperature) heat storage, the relevant contribute of thermoeconomics and energo-environmental analysis in the phase of mathematical modelling and code testing are shown

  7. A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

    Science.gov (United States)

    Ebrahimnejad, Ali

    2015-08-01

    There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

  8. STICAP: A linear circuit analysis program with stiff systems capability. Volume 1: Theory manual. [network analysis

    Science.gov (United States)

    Cooke, C. H.

    1975-01-01

    STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.

  9. A Genetic-Algorithms-Based Approach for Programming Linear and Quadratic Optimization Problems with Uncertainty

    Directory of Open Access Journals (Sweden)

    Weihua Jin

    2013-01-01

    Full Text Available This paper proposes a genetic-algorithms-based approach as an all-purpose problem-solving method for operation programming problems under uncertainty. The proposed method was applied for management of a municipal solid waste treatment system. Compared to the traditional interactive binary analysis, this approach has fewer limitations and is able to reduce the complexity in solving the inexact linear programming problems and inexact quadratic programming problems. The implementation of this approach was performed using the Genetic Algorithm Solver of MATLAB (trademark of MathWorks. The paper explains the genetic-algorithms-based method and presents details on the computation procedures for each type of inexact operation programming problems. A comparison of the results generated by the proposed method based on genetic algorithms with those produced by the traditional interactive binary analysis method is also presented.

  10. Regularization by fractional filter methods and data smoothing

    International Nuclear Information System (INIS)

    Klann, E; Ramlau, R

    2008-01-01

    This paper is concerned with the regularization of linear ill-posed problems by a combination of data smoothing and fractional filter methods. For the data smoothing, a wavelet shrinkage denoising is applied to the noisy data with known error level δ. For the reconstruction, an approximation to the solution of the operator equation is computed from the data estimate by fractional filter methods. These fractional methods are based on the classical Tikhonov and Landweber method, but avoid, at least partially, the well-known drawback of oversmoothing. Convergence rates as well as numerical examples are presented

  11. Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems

    Directory of Open Access Journals (Sweden)

    Rafał Stanisławski

    2016-01-01

    Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.

  12. Cushing's disease: a single centre's experience using the linear accelerator (LINAC) for stereotactic radiosurgery and fractionated stereotactic radiotherapy.

    Science.gov (United States)

    Wilson, P J; Williams, J R; Smee, R I

    2014-01-01

    Cushing's disease is hypercortisolaemia secondary to an adrenocorticotrophic hormone secreting pituitary adenoma. Primary management is almost always surgical, with limited effective medical interventions available. Adjuvant therapy in the form of radiation is gaining popularity, with the bulk of the literature related to the Gamma Knife. We present the results from our own institution using the linear accelerator (LINAC) since 1990. Thirty-six patients who underwent stereotactic radiosurgery (SRS), one patient who underwent fractionated stereotactic radiotherapy (FSRT) and for the purposes of comparison, 13 patients who had undergone conventional radiotherapy prior to 1990, were included in the analysis. Serum cortisol levels improved in nine of 36 (25%) SRS patients and 24 hour urinary free cortisol levels improved in 13 of 36 patients (36.1%). Tumour volume control was excellent in the SRS group with deterioration in only one patient (3%). The patient who underwent FSRT had a highly aggressive tumour refractory to radiation. Published by Elsevier Ltd.

  13. Dose optimization based on linear programming implemented in a system for treatment planning in Monte Carlo

    International Nuclear Information System (INIS)

    Ureba, A.; Palma, B. A.; Leal, A.

    2011-01-01

    Develop a more efficient method of optimization in relation to time, based on linear programming designed to implement a multi objective penalty function which also permits a simultaneous solution integrated boost situations considering two white volumes simultaneously.

  14. GIS Application to Define Biomass Collection Points as Sources for Linear Programming of Delivery Networks

    NARCIS (Netherlands)

    Velazquez-Marti, B.; Annevelink, E.

    2009-01-01

    Much bio-energy can be obtained from wood pruning operations in forests and fruit orchards. Several spatial studies have been carried out for biomass surveys, and many linear programming models have been developed to model the logistics of bio-energy chains. These models can assist in determining

  15. Stress-constrained truss topology optimization problems that can be solved by linear programming

    DEFF Research Database (Denmark)

    Stolpe, Mathias; Svanberg, Krister

    2004-01-01

    We consider the problem of simultaneously selecting the material and determining the area of each bar in a truss structure in such a way that the cost of the structure is minimized subject to stress constraints under a single load condition. We show that such problems can be solved by linear...... programming to give the global optimum, and that two different materials are always sufficient in an optimal structure....

  16. A computer tool for daily application of the linear quadratic model

    International Nuclear Information System (INIS)

    Macias Jaen, J.; Galan Montenegro, P.; Bodineau Gil, C.; Wals Zurita, A.; Serradilla Gil, A.M.

    2001-01-01

    The aim of this paper is to indicate the relevance of the criteria A.S.A.R.A. (As Short As Reasonably Achievable) in the optimization of a fractionated radiotherapy schedule and the presentation of a Windows computer program as an easy tool in order to: Evaluate the Biological Equivalent Dose (BED) in a fractionated schedule; Make comparison between different treatments; Compensate a treatment when a delay has been happened with a version of the Linear Quadratic model that has into account the factor of accelerated repopulation. Conclusions: Delays in the normal radiotherapy schedule are items that have to be controlled as much as possible because it is able to be a very important parameter in order to release a good application of treatment, principally when the tumour is fast growing. It is necessary to evaluate them. ASARA criteria is useful to indicate the relevance of this aspect. Also, computer tools like this one could help us in order to achieve this. (author)

  17. Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

    Science.gov (United States)

    Guo, Sangang

    2017-09-01

    There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

  18. Problem Based Learning Technique and Its Effect on Acquisition of Linear Programming Skills by Secondary School Students in Kenya

    Science.gov (United States)

    Nakhanu, Shikuku Beatrice; Musasia, Amadalo Maurice

    2015-01-01

    The topic Linear Programming is included in the compulsory Kenyan secondary school mathematics curriculum at form four. The topic provides skills for determining best outcomes in a given mathematical model involving some linear relationship. This technique has found application in business, economics as well as various engineering fields. Yet many…

  19. Solution of Fractional Partial Differential Equations in Fluid Mechanics by Extension of Some Iterative Method

    Directory of Open Access Journals (Sweden)

    A. A. Hemeda

    2013-01-01

    Full Text Available An extension of the so-called new iterative method (NIM has been used to handle linear and nonlinear fractional partial differential equations. The main property of the method lies in its flexibility and ability to solve nonlinear equations accurately and conveniently. Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with those obtained by both Adomian decomposition method (ADM and the variational iteration method (VIM reveals that the NIM is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar linear and nonlinear problems in fractional calculus.

  20. Study on Fuzzy Adaptive Fractional Order PIλDμ Control for Maglev Guiding System

    Science.gov (United States)

    Hu, Qing; Hu, Yuwei

    The mathematical model of the linear elevator maglev guiding system is analyzed in this paper. For the linear elevator needs strong stability and robustness to run, the integer order PID was expanded to the fractional order, in order to improve the steady state precision, rapidity and robustness of the system, enhance the accuracy of the parameter in fractional order PIλDμ controller, the fuzzy control is combined with the fractional order PIλDμ control, using the fuzzy logic achieves the parameters online adjustment. The simulations reveal that the system has faster response speed, higher tracking precision, and has stronger robustness to the disturbance.

  1. Fractionating power and outlet stream polydispersity in asymmetrical flow field-flow fractionation. Part I: isocratic operation.

    Science.gov (United States)

    Williams, P Stephen

    2016-05-01

    Asymmetrical flow field-flow fractionation (As-FlFFF) has become the most commonly used of the field-flow fractionation techniques. However, because of the interdependence of the channel flow and the cross flow through the accumulation wall, it is the most difficult of the techniques to optimize, particularly for programmed cross flow operation. For the analysis of polydisperse samples, the optimization should ideally be guided by the predicted fractionating power. Many experimentalists, however, neglect fractionating power and rely on light scattering detection simply to confirm apparent selectivity across the breadth of the eluted peak. The size information returned by the light scattering software is assumed to dispense with any reliance on theory to predict retention, and any departure of theoretical predictions from experimental observations is therefore considered of no importance. Separation depends on efficiency as well as selectivity, however, and efficiency can be a strong function of retention. The fractionation of a polydisperse sample by field-flow fractionation never provides a perfectly separated series of monodisperse fractions at the channel outlet. The outlet stream has some residual polydispersity, and it will be shown in this manuscript that the residual polydispersity is inversely related to the fractionating power. Due to the strong dependence of light scattering intensity and its angular distribution on the size of the scattering species, the outlet polydispersity must be minimized if reliable size data are to be obtained from the light scattering detector signal. It is shown that light scattering detection should be used with careful control of fractionating power to obtain optimized analysis of polydisperse samples. Part I is concerned with isocratic operation of As-FlFFF, and part II with programmed operation.

  2. Solutions to estimation problems for scalar hamilton-jacobi equations using linear programming

    KAUST Repository

    Claudel, Christian G.; Chamoin, Timothee; Bayen, Alexandre M.

    2014-01-01

    This brief presents new convex formulations for solving estimation problems in systems modeled by scalar Hamilton-Jacobi (HJ) equations. Using a semi-analytic formula, we show that the constraints resulting from a HJ equation are convex, and can be written as a set of linear inequalities. We use this fact to pose various (and seemingly unrelated) estimation problems related to traffic flow-engineering as a set of linear programs. In particular, we solve data assimilation and data reconciliation problems for estimating the state of a system when the model and measurement constraints are incompatible. We also solve traffic estimation problems, such as travel time estimation or density estimation. For all these problems, a numerical implementation is performed using experimental data from the Mobile Century experiment. In the context of reproducible research, the code and data used to compute the results presented in this brief have been posted online and are accessible to regenerate the results. © 2013 IEEE.

  3. Optimisation of substrate blends in anaerobic co-digestion using adaptive linear programming.

    Science.gov (United States)

    García-Gen, Santiago; Rodríguez, Jorge; Lema, Juan M

    2014-12-01

    Anaerobic co-digestion of multiple substrates has the potential to enhance biogas productivity by making use of the complementary characteristics of different substrates. A blending strategy based on a linear programming optimisation method is proposed aiming at maximising COD conversion into methane, but simultaneously maintaining a digestate and biogas quality. The method incorporates experimental and heuristic information to define the objective function and the linear restrictions. The active constraints are continuously adapted (by relaxing the restriction boundaries) such that further optimisations in terms of methane productivity can be achieved. The feasibility of the blends calculated with this methodology was previously tested and accurately predicted with an ADM1-based co-digestion model. This was validated in a continuously operated pilot plant, treating for several months different mixtures of glycerine, gelatine and pig manure at organic loading rates from 1.50 to 4.93 gCOD/Ld and hydraulic retention times between 32 and 40 days at mesophilic conditions. Copyright © 2014 Elsevier Ltd. All rights reserved.

  4. The overlap Dirac operator as a continued fraction

    International Nuclear Information System (INIS)

    Wenger, U.; Deutsches Elektronen-Synchrotron

    2004-03-01

    We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method and nested conjugate gradient procedures are avoided. We point out that the five dimensional linear system can be made well conditioned using equivalence transformations on the continued fractions. (orig.)

  5. Chaos synchronization of the fractional-order Chen's system

    International Nuclear Information System (INIS)

    Zhu Hao; Zhou Shangbo; He Zhongshi

    2009-01-01

    In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to check the chaos synchronization of fractional systems with incommensurate order. Chaos synchronization is studied by utilizing the Pecora-Carroll (PC) method and the coupling method. The necessary condition can also be used as a tool to confirm results of a numerical simulation. Numerical simulation results show the effectiveness of the necessary condition.

  6. Stationarity-conservation laws for fractional differential equations with variable coefficients

    International Nuclear Information System (INIS)

    Klimek, Malgorzata

    2002-01-01

    In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)

  7. Stationarity-conservation laws for fractional differential equations with variable coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Klimek, Malgorzata [Institute of Mathematics and Computer Science, Technical University of Czestochowa, Czestochowa (Poland)

    2002-08-09

    In this paper, we study linear fractional differential equations with variable coefficients. It is shown that, by assuming some conditions for the coefficients, the stationarity-conservation laws can be derived. The area where these are valid is restricted by the asymptotic properties of solutions of the respective equation. Applications of the proposed procedure include the fractional Fokker-Planck equation in (1+1)- and (d+1)-dimensional space and the fractional Klein-Kramers equation. (author)

  8. Storage and distribution/Linear programming for storage operations

    Energy Technology Data Exchange (ETDEWEB)

    Coleman, D

    1978-07-15

    The techniques of linear programing to solve storage problems as applied in a tank farm tie-in with refinery throughput operation include: (1) the time-phased model which works on storage and refinery operations input parameters, e.g., production, distribution, cracking, etc., and is capable of representing product stockpiling in slack periods to meet future peak demands, and investigating alternative strategies such as exchange deals and purchase and leasing of additional storage, and (2) the Monte Carlo simulation method, which inputs parameters, e.g., arrival of crude products at refinery, tankage size, likely demand for products, etc., as probability distributions rather than single values, and is capable of showing the average utilization of facilities, potential bottlenecks, investment required to achieve an increase in utilization, and to enable the user to predict total investment, cash flow, and profit emanating from the original financing decision. The increasing use of computer techniques to solve refinery and storage problems is attributed to potential savings resulting from more effective planning, reduced computer costs, ease of access and more usable software. Diagrams.

  9. Local beam angle optimization with linear programming and gradient search

    International Nuclear Information System (INIS)

    Craft, David

    2007-01-01

    The optimization of beam angles in IMRT planning is still an open problem, with literature focusing on heuristic strategies and exhaustive searches on discrete angle grids. We show how a beam angle set can be locally refined in a continuous manner using gradient-based optimization in the beam angle space. The gradient is derived using linear programming duality theory. Applying this local search to 100 random initial angle sets of a phantom pancreatic case demonstrates the method, and highlights the many-local-minima aspect of the BAO problem. Due to this function structure, we recommend a search strategy of a thorough global search followed by local refinement at promising beam angle sets. Extensions to nonlinear IMRT formulations are discussed. (note)

  10. A novel linear programming approach to fluence map optimization for intensity modulated radiation therapy treatment planning

    International Nuclear Information System (INIS)

    Romeijn, H Edwin; Ahuja, Ravindra K; Dempsey, James F; Kumar, Arvind; Li, Jonathan G

    2003-01-01

    We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (>95%), target homogeneity (<10% overdosing and <7% underdosing) and organ sparing using at least one of the two models

  11. Chance-constrained/stochastic linear programming model for acid rain abatement. I. Complete colinearity and noncolinearity

    Energy Technology Data Exchange (ETDEWEB)

    Ellis, J H; McBean, E A; Farquhar, G J

    1985-01-01

    A Linear Programming model is presented for development of acid rain abatement strategies in eastern North America. For a system comprised of 235 large controllable point sources and 83 uncontrolled area sources, it determines the least-cost method of reducing SO/sub 2/ emissions to satisfy maximum wet sulfur deposition limits at 20 sensitive receptor locations. In this paper, the purely deterministic model is extended to a probabilistic form by incorporating the effects of meteorologic variability on the long-range pollutant transport processes. These processes are represented by source-receptor-specific transfer coefficients. Experiments for quantifying the spatial variability of transfer coefficients showed their distributions to be approximately lognormal with logarithmic standard deviations consistently about unity. Three methods of incorporating second-moment random variable uncertainty into the deterministic LP framework are described: Two-Stage Programming Under Uncertainty, Chance-Constrained Programming and Stochastic Linear Programming. A composite CCP-SLP model is developed which embodies the two-dimensional characteristics of transfer coefficient uncertainty. Two probabilistic formulations are described involving complete colinearity and complete noncolinearity for the transfer coefficient covariance-correlation structure. The completely colinear and noncolinear formulations are considered extreme bounds in a meteorologic sense and yield abatement strategies of largely didactic value. Such strategies can be characterized as having excessive costs and undesirable deposition results in the completely colinear case and absence of a clearly defined system risk level (other than expected-value) in the noncolinear formulation.

  12. Controlling general projective synchronization of fractional order Rossler systems

    International Nuclear Information System (INIS)

    Shao Shiquan

    2009-01-01

    This paper proposed a method to achieve general projective synchronization of two fractional order Rossler systems. First, we construct the fractional order Rossler system's corresponding approximation integer order system. Then, a control method based on a partially linear decomposition and negative feedback of state errors was utilized on the integer order system. Numerical simulations show the effectiveness of the proposed method.

  13. Split diversity in constrained conservation prioritization using integer linear programming.

    Science.gov (United States)

    Chernomor, Olga; Minh, Bui Quang; Forest, Félix; Klaere, Steffen; Ingram, Travis; Henzinger, Monika; von Haeseler, Arndt

    2015-01-01

    Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization.Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator-prey interactions between the species in a community to define viability constraints.Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure.We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda.

  14. Flexible solution of linear program with an application to decommissioning planning of nuclear reactor

    International Nuclear Information System (INIS)

    Shimizu, Yoshiaki

    1988-01-01

    Due to the simplicity and effectiveness, linear program has been popular in the actual optimization in various fields. In the previous study, the uncertainty involved in the model at the different stage of optimization was dealt with by post-optimizing analysis. But it often becomes insufficient to make a decision how to deal with an uncertain system especially suffering large parameter deviation. Recently in the field of processing systems, it is desired to obtain a flexible solution which can present the counterplan to a deviating system from a practical viewpoint. The scope of this preliminary note presents how to apply a methodology development to obtain the flexible solution of a linear program. For this purpose, a simple example associated with nuclear reactor decommissioning is shown. The problem to maximize a system performance given as an objective function under the constraint of the static behavior of the system is considered, and the flexible solution is determined. In Japan, the decommissioning of commercial nuclear power plants will being in near future, and the study using the retired research reactor JPDR is in progress. The planning of decontamination and the reuse of wastes is taken as the example. (Kako, I.)

  15. A linear goal programming model for urban energy-economy-environment interaction

    Energy Technology Data Exchange (ETDEWEB)

    Kambo, N.S.; Handa, B.R. (Indian Inst. of Tech., New Delhi (India). Dept. of Mathematics); Bose, R.K. (Tata Energy Research Inst., New Delhi (India))

    1991-01-01

    This paper provides a comprehensive and systematic analysis of energy and pollution problems interconnected with the economic structure, by using a multi-objective sectoral end-use model for addressing regional energy policy issues. The multi-objective model proposed for the study is a 'linear goal programming (LGP)' technique of analysing a 'reference energy system (RES)' in a framework within which alternative policies and technical strategies may be evaluated. The model so developed has further been tested for the city of Delhi (India) for the period 1985 - 86, and a scenario analysis has been carried out by assuming different policy options. (orig./BWJ).

  16. Linking linear programming and spatial simulation models to predict landscape effects of forest management alternatives

    Science.gov (United States)

    Eric J. Gustafson; L. Jay Roberts; Larry A. Leefers

    2006-01-01

    Forest management planners require analytical tools to assess the effects of alternative strategies on the sometimes disparate benefits from forests such as timber production and wildlife habitat. We assessed the spatial patterns of alternative management strategies by linking two models that were developed for different purposes. We used a linear programming model (...

  17. Detection of fractional solitons in quantum spin Hall systems

    Science.gov (United States)

    Fleckenstein, C.; Traverso Ziani, N.; Trauzettel, B.

    2018-03-01

    We propose two experimental setups that allow for the implementation and the detection of fractional solitons of the Goldstone-Wilczek type. The first setup is based on two magnetic barriers at the edge of a quantum spin Hall system for generating the fractional soliton. If then a quantum point contact is created with the other edge, the linear conductance shows evidence of the fractional soliton. The second setup consists of a single magnetic barrier covering both edges and implementing a long quantum point contact. In this case, the fractional soliton can unambiguously be detected as a dip in the conductance without the need to control the magnetization of the barrier.

  18. Finite element method for time-space-fractional Schrodinger equation

    Directory of Open Access Journals (Sweden)

    Xiaogang Zhu

    2017-07-01

    Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.

  19. Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative

    Directory of Open Access Journals (Sweden)

    Yongjun Shen

    2014-01-01

    Full Text Available The subharmonic resonance of van der Pol (VDP oscillator with fractional-order derivative is studied by the averaging method. At first, the first-order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC and equivalent linear stiffness coefficient (ELSC for subharmonic resonance are established, and the effects of the fractional-order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR is also obtained. At last, the comparisons of the fractional-order and the traditional integer-order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.

  20. Chaos in the fractional order Chen system and its control

    International Nuclear Information System (INIS)

    Li Chunguang; Chen Guanrong

    2004-01-01

    In this letter, we study the chaotic behaviors in the fractional order Chen system. We found that chaos exists in the fractional order Chen system with order less than 3. The lowest order we found to have chaos in this system is 2.1. Linear feedback control of chaos in this system is also studied

  1. Solution of Moving Boundary Space-Time Fractional Burger’s Equation

    Directory of Open Access Journals (Sweden)

    E. A.-B. Abdel-Salam

    2014-01-01

    Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.

  2. A Global Optimization Algorithm for Sum of Linear Ratios Problem

    OpenAIRE

    Yuelin Gao; Siqiao Jin

    2013-01-01

    We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the c...

  3. CiOpt: a program for optimization of the frequency response of linear circuits

    OpenAIRE

    Miró Sans, Joan Maria; Palà Schönwälder, Pere

    1991-01-01

    An interactive personal-computer program for optimizing the frequency response of linear lumped circuits (CiOpt) is presented. CiOpt has proved to be an efficient tool in improving designs where the inclusion of more accurate device models distorts the desired frequency response, as well as in device modeling. The outputs of CiOpt are the element values which best match the obtained and the desired frequency response. The optimization algorithms used (the Fletcher-Powell and Newton's methods,...

  4. Fuzzy solution of the linear programming problem with interval coefficients in the constraints

    OpenAIRE

    Dorota Kuchta

    2005-01-01

    A fuzzy concept of solving the linear programming problem with interval coefficients is proposed. For each optimism level of the decision maker (where the optimism concerns the certainty that no errors have been committed in the estimation of the interval coefficients and the belief that optimistic realisations of the interval coefficients will occur) another interval solution of the problem will be generated and the decision maker will be able to choose the final solution having a complete v...

  5. Intervals between multiple fractions per day

    International Nuclear Information System (INIS)

    Fowler, J.F.

    1988-01-01

    Assuming the linear quadratic model for dose-response curves enables the proportion of repairable damage to be calculated for any size of dose per fraction. It is given by the beta (dose squared) term, and represents a larger proportion of the total damage for larger doses per fraction, but also for late-reacting than for early-reacting tissues. For example at 2 Gy per fraction, repairable damage could represent nearly half the total damage in late-reacting tissues but only one fifth in early-reacting tissues. Even if repair occurs at the same rate in both tissues, it will obviously take longer for 50% of the damage to fade to an undetectable level (3 or 5%) than for 20% to do so. This means that late reactions require longer intervals than early reactions when multiple fraction per day radiotherapy is planned, even if the half-lives of repair are not different. (orig.)

  6. Generalized Functions for the Fractional Calculus

    Science.gov (United States)

    Lorenzo, Carl F.; Hartley, Tom T.

    1999-01-01

    Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function F(sub q)[a,t] of Hartley & Lorenzo (1998). These functions provided direct solution and important understanding for the fundamental linear fractional order differential equation and for the related initial value problem (Hartley and Lorenzo, 1999). This paper examines related functions and their Laplace transforms. Presented for consideration are two generalized functions, the R-function and the G-function, useful in analysis and as a basis for computation in the fractional calculus. The R-function is unique in that it contains all of the derivatives and integrals of the F-function. The R-function also returns itself on qth order differ-integration. An example application of the R-function is provided. A further generalization of the R-function, called the G-function brings in the effects of repeated and partially repeated fractional poles.

  7. Fuzzy risk explicit interval linear programming model for end-of-life vehicle recycling planning in the EU.

    Science.gov (United States)

    Simic, Vladimir

    2015-01-01

    End-of-life vehicles (ELVs) are vehicles that have reached the end of their useful lives and are no longer registered or licensed for use. The ELV recycling problem has become very serious in the last decade and more and more efforts are made in order to reduce the impact of ELVs on the environment. This paper proposes the fuzzy risk explicit interval linear programming model for ELV recycling planning in the EU. It has advantages in reflecting uncertainties presented in terms of intervals in the ELV recycling systems and fuzziness in decision makers' preferences. The formulated model has been applied to a numerical study in which different decision maker types and several ELV types under two EU ELV Directive legislative cases were examined. This study is conducted in order to examine the influences of the decision maker type, the α-cut level, the EU ELV Directive and the ELV type on decisions about vehicle hulks procuring, storing unprocessed hulks, sorting generated material fractions, allocating sorted waste flows and allocating sorted metals. Decision maker type can influence quantity of vehicle hulks kept in storages. The EU ELV Directive and decision maker type have no influence on which vehicle hulk type is kept in the storage. Vehicle hulk type, the EU ELV Directive and decision maker type do not influence the creation of metal allocation plans, since each isolated metal has its regular destination. The valid EU ELV Directive eco-efficiency quotas can be reached even when advanced thermal treatment plants are excluded from the ELV recycling process. The introduction of the stringent eco-efficiency quotas will significantly reduce the quantities of land-filled waste fractions regardless of the type of decision makers who will manage vehicle recycling system. In order to reach these stringent quotas, significant quantities of sorted waste need to be processed in advanced thermal treatment plants. Proposed model can serve as the support for the European

  8. Eigenfunction expansion for fractional Brownian motions

    International Nuclear Information System (INIS)

    Maccone, C.

    1981-01-01

    The fractional Brownian motions, a class of nonstationary stochastic processes defined as the Riemann-Liouville fractional integral/derivative of the Brownian motion, are studied. It is shown that these processes can be regarded as the output of a suitable linear system of which the input is the white noise. Their autocorrelation is then derived with a study of their standard-deviation curves. Their power spectra are found by resorting to the nonstationary spectral theory. And finally their eigenfunction expansion (Karhunen-Loeve expansion) is obtained: the eigenfunctions are proved to be suitable Bessel functions and the eigenvalues zeros of the Bessel functions. (author)

  9. Function projective lag synchronization of fractional-order chaotic systems

    International Nuclear Information System (INIS)

    Wang Sha; Yu Yong-Guang; Wang Hu; Rahmani Ahmed

    2014-01-01

    Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme. (general)

  10. Aether: leveraging linear programming for optimal cloud computing in genomics.

    Science.gov (United States)

    Luber, Jacob M; Tierney, Braden T; Cofer, Evan M; Patel, Chirag J; Kostic, Aleksandar D

    2018-05-01

    Across biology, we are seeing rapid developments in scale of data production without a corresponding increase in data analysis capabilities. Here, we present Aether (http://aether.kosticlab.org), an intuitive, easy-to-use, cost-effective and scalable framework that uses linear programming to optimally bid on and deploy combinations of underutilized cloud computing resources. Our approach simultaneously minimizes the cost of data analysis and provides an easy transition from users' existing HPC pipelines. Data utilized are available at https://pubs.broadinstitute.org/diabimmune and with EBI SRA accession ERP005989. Source code is available at (https://github.com/kosticlab/aether). Examples, documentation and a tutorial are available at http://aether.kosticlab.org. chirag_patel@hms.harvard.edu or aleksandar.kostic@joslin.harvard.edu. Supplementary data are available at Bioinformatics online.

  11. Microgrid Reliability Modeling and Battery Scheduling Using Stochastic Linear Programming

    Energy Technology Data Exchange (ETDEWEB)

    Cardoso, Goncalo; Stadler, Michael; Siddiqui, Afzal; Marnay, Chris; DeForest, Nicholas; Barbosa-Povoa, Ana; Ferrao, Paulo

    2013-05-23

    This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6percent.

  12. Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems

    Directory of Open Access Journals (Sweden)

    Cuimei Jiang

    2015-07-01

    Full Text Available Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.

  13. A non-linear regression analysis program for describing electrophysiological data with multiple functions using Microsoft Excel.

    Science.gov (United States)

    Brown, Angus M

    2006-04-01

    The objective of this present study was to demonstrate a method for fitting complex electrophysiological data with multiple functions using the SOLVER add-in of the ubiquitous spreadsheet Microsoft Excel. SOLVER minimizes the difference between the sum of the squares of the data to be fit and the function(s) describing the data using an iterative generalized reduced gradient method. While it is a straightforward procedure to fit data with linear functions, and we have previously demonstrated a method of non-linear regression analysis of experimental data based upon a single function, it is more complex to fit data with multiple functions, usually requiring specialized expensive computer software. In this paper we describe an easily understood program for fitting experimentally acquired data, in this case the stimulus-evoked compound action potential from the mouse optic nerve, with multiple Gaussian functions. The program is flexible and can be applied to describe data with a wide variety of user-input functions.

  14. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems

    Science.gov (United States)

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.

  15. Statistical mechanical analysis of linear programming relaxation for combinatorial optimization problems.

    Science.gov (United States)

    Takabe, Satoshi; Hukushima, Koji

    2016-05-01

    Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.

  16. Fitting boxes to Manhattan scenes using linear integer programming

    KAUST Repository

    Li, Minglei

    2016-02-19

    We propose an approach for automatic generation of building models by assembling a set of boxes using a Manhattan-world assumption. The method first aligns the point cloud with a per-building local coordinate system, and then fits axis-aligned planes to the point cloud through an iterative regularization process. The refined planes partition the space of the data into a series of compact cubic cells (candidate boxes) spanning the entire 3D space of the input data. We then choose to approximate the target building by the assembly of a subset of these candidate boxes using a binary linear programming formulation. The objective function is designed to maximize the point cloud coverage and the compactness of the final model. Finally, all selected boxes are merged into a lightweight polygonal mesh model, which is suitable for interactive visualization of large scale urban scenes. Experimental results and a comparison with state-of-the-art methods demonstrate the effectiveness of the proposed framework.

  17. An Improved Heaviside Approach to Partial Fraction Expansion and Its Applications

    Science.gov (United States)

    Man, Yiu-Kwong

    2009-01-01

    In this note, we present an improved Heaviside approach to compute the partial fraction expansions of proper rational functions. This method uses synthetic divisions to determine the unknown partial fraction coefficients successively, without the need to use differentiation or to solve a system of linear equations. Examples of its applications in…

  18. PAPR reduction in FBMC using an ACE-based linear programming optimization

    Science.gov (United States)

    van der Neut, Nuan; Maharaj, Bodhaswar TJ; de Lange, Frederick; González, Gustavo J.; Gregorio, Fernando; Cousseau, Juan

    2014-12-01

    This paper presents four novel techniques for peak-to-average power ratio (PAPR) reduction in filter bank multicarrier (FBMC) modulation systems. The approach extends on current PAPR reduction active constellation extension (ACE) methods, as used in orthogonal frequency division multiplexing (OFDM), to an FBMC implementation as the main contribution. The four techniques introduced can be split up into two: linear programming optimization ACE-based techniques and smart gradient-project (SGP) ACE techniques. The linear programming (LP)-based techniques compensate for the symbol overlaps by utilizing a frame-based approach and provide a theoretical upper bound on achievable performance for the overlapping ACE techniques. The overlapping ACE techniques on the other hand can handle symbol by symbol processing. Furthermore, as a result of FBMC properties, the proposed techniques do not require side information transmission. The PAPR performance of the techniques is shown to match, or in some cases improve, on current PAPR techniques for FBMC. Initial analysis of the computational complexity of the SGP techniques indicates that the complexity issues with PAPR reduction in FBMC implementations can be addressed. The out-of-band interference introduced by the techniques is investigated. As a result, it is shown that the interference can be compensated for, whilst still maintaining decent PAPR performance. Additional results are also provided by means of a study of the PAPR reduction of the proposed techniques at a fixed clipping probability. The bit error rate (BER) degradation is investigated to ensure that the trade-off in terms of BER degradation is not too severe. As illustrated by exhaustive simulations, the SGP ACE-based technique proposed are ideal candidates for practical implementation in systems employing the low-complexity polyphase implementation of FBMC modulators. The methods are shown to offer significant PAPR reduction and increase the feasibility of FBMC as

  19. Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

    Directory of Open Access Journals (Sweden)

    Olaniyi Samuel Iyiola

    2014-09-01

    Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

  20. Reactor Network Synthesis Using Coupled Genetic Algorithm with the Quasi-linear Programming Method

    OpenAIRE

    Soltani, H.; Shafiei, S.; Edraki, J.

    2016-01-01

    This research is an attempt to develop a new procedure for the synthesis of reactor networks (RNs) using a genetic algorithm (GA) coupled with the quasi-linear programming (LP) method. The GA is used to produce structural configuration, whereas continuous variables are handled using a quasi-LP formulation for finding the best objective function. Quasi-LP consists of LP together with a search loop to find the best reactor conversions (xi), as well as split and recycle ratios (yi). Quasi-LP rep...

  1. Robust Fuzzy Control for Fractional-Order Uncertain Hydroturbine Regulating System with Random Disturbances

    OpenAIRE

    Fengjiao Wu; Guitao Zhang; Zhengzhong Wang

    2016-01-01

    The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. ...

  2. Finite-time stability of discrete fractional delay systems: Gronwall inequality and stability criterion

    Science.gov (United States)

    Wu, Guo-Cheng; Baleanu, Dumitru; Zeng, Sheng-Da

    2018-04-01

    This study investigates finite-time stability of Caputo delta fractional difference equations. A generalized Gronwall inequality is given on a finite time domain. A finite-time stability criterion is proposed for fractional differential equations. Then the idea is extended to the discrete fractional case. A linear fractional difference equation with constant delays is considered and finite-time stable conditions are provided. One example is numerically illustrated to support the theoretical result.

  3. Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems

    Directory of Open Access Journals (Sweden)

    Bambang Riyanto

    2005-11-01

    Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.

  4. A Mixed-Integer Linear Programming approach to wind farm layout and inter-array cable routing

    DEFF Research Database (Denmark)

    Fischetti, Martina; Leth, John-Josef; Borchersen, Anders Bech

    2015-01-01

    A Mixed-Integer Linear Programming (MILP) approach is proposed to optimize the turbine allocation and inter-array offshore cable routing. The two problems are considered with a two steps strategy, solving the layout problem first and then the cable problem. We give an introduction to both problems...... and present the MILP models we developed to solve them. To deal with interference in the onshore cases, we propose an adaptation of the standard Jensen’s model, suitable for 3D cases. A simple Stochastic Programming variant of our model allows us to consider different wind scenarios in the optimization...

  5. A Mixed Integer Linear Programming Approach to Electrical Stimulation Optimization Problems.

    Science.gov (United States)

    Abouelseoud, Gehan; Abouelseoud, Yasmine; Shoukry, Amin; Ismail, Nour; Mekky, Jaidaa

    2018-02-01

    Electrical stimulation optimization is a challenging problem. Even when a single region is targeted for excitation, the problem remains a constrained multi-objective optimization problem. The constrained nature of the problem results from safety concerns while its multi-objectives originate from the requirement that non-targeted regions should remain unaffected. In this paper, we propose a mixed integer linear programming formulation that can successfully address the challenges facing this problem. Moreover, the proposed framework can conclusively check the feasibility of the stimulation goals. This helps researchers to avoid wasting time trying to achieve goals that are impossible under a chosen stimulation setup. The superiority of the proposed framework over alternative methods is demonstrated through simulation examples.

  6. Array processors based on Gaussian fraction-free method

    Energy Technology Data Exchange (ETDEWEB)

    Peng, S; Sedukhin, S [Aizu Univ., Aizuwakamatsu, Fukushima (Japan); Sedukhin, I

    1998-03-01

    The design of algorithmic array processors for solving linear systems of equations using fraction-free Gaussian elimination method is presented. The design is based on a formal approach which constructs a family of planar array processors systematically. These array processors are synthesized and analyzed. It is shown that some array processors are optimal in the framework of linear allocation of computations and in terms of number of processing elements and computing time. (author)

  7. R-Function Relationships for Application in the Fractional Calculus

    Science.gov (United States)

    Lorenzo, Carl F.; Hartley, Tom T.

    2000-01-01

    The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

  8. The use of linear programming to determine whether a formulated complementary food product can ensure adequate nutrients for 6- to 11-month-old Cambodian infants

    DEFF Research Database (Denmark)

    Skau, Jutta Kloppenborg Heick; Bunthang, Touch; Chamnan, Chhoun

    2014-01-01

    A new software tool, Optifood, developed by the WHO and based on linear programming (LP) analysis, has been developed to formulate food-based recommendations.......A new software tool, Optifood, developed by the WHO and based on linear programming (LP) analysis, has been developed to formulate food-based recommendations....

  9. The linear canonical transformation : definition and properties

    NARCIS (Netherlands)

    Bastiaans, Martin J.; Alieva, Tatiana; Healy, J.J.; Kutay, M.A.; Ozaktas, H.M.; Sheridan, J.T.

    2016-01-01

    In this chapter we introduce the class of linear canonical transformations, which includes as particular cases the Fourier transformation (and its generalization: the fractional Fourier transformation), the Fresnel transformation, and magnifier, rotation and shearing operations. The basic properties

  10. Bubble-Induced Color Doppler Feedback for Histotripsy Tissue Fractionation.

    Science.gov (United States)

    Miller, Ryan M; Zhang, Xi; Maxwell, Adam D; Cain, Charles A; Xu, Zhen

    2016-03-01

    Histotripsy therapy produces cavitating bubble clouds to increasingly fractionate and eventually liquefy tissue using high-intensity ultrasound pulses. Following cavitation generated by each pulse, coherent motion of the cavitation residual nuclei can be detected using metrics formed from ultrasound color Doppler acquisitions. In this paper, three experiments were performed to investigate the characteristics of this motion as real-time feedback on histotripsy tissue fractionation. In the first experiment, bubble-induced color Doppler (BCD) and particle image velocimetry (PIV) analysis monitored the residual cavitation nuclei in the treatment region in an agarose tissue phantom treated with two-cycle histotripsy pulses at [Formula: see text] using a 500-kHz transducer. Both BCD and PIV results showed brief chaotic motion of the residual nuclei followed by coherent motion first moving away from the transducer and then rebounding back. Velocity measurements from both PIV and BCD agreed well, showing a monotonic increase in rebound time up to a saturation point for increased therapy dose. In a second experiment, a thin layer of red blood cells (RBC) was added to the phantom to allow quantification of the fractionation of the RBC layer to compare with BCD metrics. A strong linear correlation was observed between the fractionation level and the time to BCD peak rebound velocity over histotripsy treatment. Finally, the correlation between BCD feedback and histotripsy tissue fractionation was validated in ex vivo porcine liver evaluated histologically. BCD metrics showed strong linear correlation with fractionation progression, suggesting that BCD provides useful quantitative real-time feedback on histotripsy treatment progression.

  11. What next in fractionated radiotherapy

    International Nuclear Information System (INIS)

    Fowler, J.F.

    1984-01-01

    Trends in models for predicting the total dose required to produce tolerable normal-tissue injury can be seen by the progression from the ''cube root law'', through Strandqvist's slope of 0.22, to NSD, TDF and CRE which have separate time and fraction number exponents, to even better approximations now available. The dose-response formulae that can be used to define the effect of fraction size (and number) include (1) the linear quadratic (LQ) model (2) the two-component (TC) multi-target model and (3) repair-misrepair models. The LQ model offers considerable convenience, requires only two parameters to be determined, and emphasizes the difference between late and early normal-tissue dependence on dose per fraction first shown by exponents greater than the NSD slope of 0.24. Exponents of overall time, e.g. Tsup(0.11), yield the wrong shape of time curve, suggesting that most proliferating occurs early, although it really occurs after a delay depending on the turnover time of the tissue. Improved clinical results are being sought by hyperfractionation, accelerated fractionation, or continuous low dose rate irradiation as in interstitial implants. (U.K.)

  12. A Global Optimization Algorithm for Sum of Linear Ratios Problem

    Directory of Open Access Journals (Sweden)

    Yuelin Gao

    2013-01-01

    Full Text Available We equivalently transform the sum of linear ratios programming problem into bilinear programming problem, then by using the linear characteristics of convex envelope and concave envelope of double variables product function, linear relaxation programming of the bilinear programming problem is given, which can determine the lower bound of the optimal value of original problem. Therefore, a branch and bound algorithm for solving sum of linear ratios programming problem is put forward, and the convergence of the algorithm is proved. Numerical experiments are reported to show the effectiveness of the proposed algorithm.

  13. CONTRIBUTION OF A LINEAR PROGRAMMING VBA MODULE TO STUDENTS PEFORMANCE

    Directory of Open Access Journals (Sweden)

    KUČÍRKOVÁ Lenka

    2010-12-01

    Full Text Available This paper deals with the application of freeware modules as a teaching support of Operations Research methods at the Department of Systems Engineering, Czech university of Life Sciences (CULS Prague. In particular, we concentrated on a linear programming module and measured the impact on student performance. The motivation for this evaluation is based on a current development of a new module that focuses on Traveling Salesman Problem. First, we explain the current situation both worldwide and in the Czech Republic and the CULS Prague. Subsequently, we describe the content of students’ exams and statistical methods applied to the evaluation. Finally, we analyze and generalize the obtained results. The students exams have show a positive impact of the modules. Further, our analysis has proven that this impact is statistically significant. The findings motivate us to made new modules for other methods.

  14. Construction of Healthy and Palatable Diet for Low Socioeconomic Female Adults using Linear Programming

    OpenAIRE

    Roslee Rajikan; Nurul Izza Ahmad Zaidi; Siti Masitah Elias; Suzana Shahar; Zahara Abd Manaf; Noor Aini Md Yusoff

    2017-01-01

    Differences in socioeconomic profile may influences healthy food choices, particularly among individuals with low socioeconomic status. Thus, high-energy dense foods become the preferences compared to high nutritional content foods due to their cheaper price. The present study aims to develop healthy and palatable diet at the minimum cost based on Malaysian Dietary Guidelines 2010 and Recommended Nutrient Intake 2005 via linear programming. A total of 96 female adults from low socioeconomic f...

  15. A novel approach based on preference-based index for interval bilevel linear programming problem.

    Science.gov (United States)

    Ren, Aihong; Wang, Yuping; Xue, Xingsi

    2017-01-01

    This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation [Formula: see text]. Furthermore, the concept of a preference δ -optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

  16. A novel approach based on preference-based index for interval bilevel linear programming problem

    Directory of Open Access Journals (Sweden)

    Aihong Ren

    2017-05-01

    Full Text Available Abstract This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation ⪯ m w $\\preceq_{mw}$ . Furthermore, the concept of a preference δ-optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach.

  17. Possibility/Necessity-Based Probabilistic Expectation Models for Linear Programming Problems with Discrete Fuzzy Random Variables

    Directory of Open Access Journals (Sweden)

    Hideki Katagiri

    2017-10-01

    Full Text Available This paper considers linear programming problems (LPPs where the objective functions involve discrete fuzzy random variables (fuzzy set-valued discrete random variables. New decision making models, which are useful in fuzzy stochastic environments, are proposed based on both possibility theory and probability theory. In multi-objective cases, Pareto optimal solutions of the proposed models are newly defined. Computational algorithms for obtaining the Pareto optimal solutions of the proposed models are provided. It is shown that problems involving discrete fuzzy random variables can be transformed into deterministic nonlinear mathematical programming problems which can be solved through a conventional mathematical programming solver under practically reasonable assumptions. A numerical example of agriculture production problems is given to demonstrate the applicability of the proposed models to real-world problems in fuzzy stochastic environments.

  18. Inverse synchronization of coupled fractional-order systems through ...

    Indian Academy of Sciences (India)

    netic waves [8], boundary layer effects in ducts [9], dielectric polarization [10], and ... fractional-order systems [27–34] due to its potential applications in secure ..... Now, according to the stability theorem of linear FDEs [61], we can derive the ...

  19. SU-E-T-480: Radiobiological Dose Comparison of Single Fraction SRS, Multi-Fraction SRT and Multi-Stage SRS of Large Target Volumes Using the Linear-Quadratic Formula

    International Nuclear Information System (INIS)

    Ding, C; Hrycushko, B; Jiang, S; Meyer, J; Timmerman, R

    2014-01-01

    Purpose: To compare the radiobiological effect on large tumors and surrounding normal tissues from single fraction SRS, multi-fractionated SRT, and multi-staged SRS treatment. Methods: An anthropomorphic head phantom with a centrally located large volume target (18.2 cm 3 ) was scanned using a 16 slice large bore CT simulator. Scans were imported to the Multiplan treatment planning system where a total prescription dose of 20Gy was used for a single, three staged and three fractionated treatment. Cyber Knife treatment plans were inversely optimized for the target volume to achieve at least 95% coverage of the prescription dose. For the multistage plan, the target was segmented into three subtargets having similar volume and shape. Staged plans for individual subtargets were generated based on a planning technique where the beam MUs of the original plan on the total target volume are changed by weighting the MUs based on projected beam lengths within each subtarget. Dose matrices for each plan were export in DICOM format and used to calculate equivalent dose distributions in 2Gy fractions using an alpha beta ratio of 10 for the target and 3 for normal tissue. Results: Singe fraction SRS, multi-stage plan and multi-fractionated SRT plans had an average 2Gy dose equivalent to the target of 62.89Gy, 37.91Gy and 33.68Gy, respectively. The normal tissue within 12Gy physical dose region had an average 2Gy dose equivalent of 29.55Gy, 16.08Gy and 13.93Gy, respectively. Conclusion: The single fraction SRS plan had the largest predicted biological effect for the target and the surrounding normal tissue. The multi-stage treatment provided for a more potent biologically effect on target compared to the multi-fraction SRT treatments with less biological normal tissue than single-fraction SRS treatment

  20. Relationship between keff and the fraction of critical mass

    International Nuclear Information System (INIS)

    O'Dell, R.D.; Parsons, D.K.

    1997-01-01

    It is not universally understood that k eff and fractional critical mass are related in a non linear fashion. For example, a neutronic system with a k eff = 0. 95 is NOT at 95% of its critical mass. What is striking is just how non-linear the relationship between k eff and critical mass really is. This relationship is investigated and documented below for both unfavorable (i.e., very reactive) and favorable (less reactive) geometries. The implications of this non-linearity for criticality safety regulation will also be discussed

  1. New Approach for the Analysis of Damped Vibrations of Fractional Oscillators

    Directory of Open Access Journals (Sweden)

    Yuriy A. Rossikhin

    2009-01-01

    Full Text Available The dynamic behavior of linear and nonlinear mechanical oscillators with constitutive equations involving fractional derivatives defined as a fractional power of the operator of conventional time-derivative is considered. Such a definition of the fractional derivative enables one to analyse approximately vibratory regimes of the oscillator without considering the drift of its position of equilibrium. The assumption of small fractional derivative terms allows one to use the method of multiple time scales whereby a comparative analysis of the solutions obtained for different orders of low-level fractional derivatives and nonlinear elastic terms is possible to be carried out. The interrelationship of the fractional parameter (order of the fractional operator and nonlinearity manifests itself in full measure when orders of the small fractional derivative term and of the cubic nonlinearity entering in the oscillator's constitutive equation coincide.

  2. The dependence of radiation response on the dose per fraction

    International Nuclear Information System (INIS)

    Joiner, M.C.

    1989-01-01

    The linear-quadratic (LQ) model explains the dependence of total dose in a fractionated course on the dose per fraction, in a very wide range of tumour and normal tissue studies, providing the dose per fraction remains above 2 Gy. In the range 2-1 Gy per fraction, some experimental studies show less increase in total dose than predicted by LQ; a probable explanation is incomplete repair between fractions given 2 seen between 1 and 0.1 Gy per fraction. This cannot be explained by incomplete repair; a modified LQ model where α decreases sharply with increasing dose per fraction in the range 0-1 Gy fits these data. The basic LQ model describes data from neutron fractionation studies, so the relationship between relative biological effectiveness (RBE) and X-ray dose per fraction can be expressed in terms of LQ parameters and fitted directly to RBE data. Results from different experiments, different assays and both top-up and full-course fractionation techniques, can all be included in one analysis. (author)

  3. Mechanistic formulation of a lineal-quadratic-linear (LQL) model: Split-dose experiments and exponentially decaying sources

    International Nuclear Information System (INIS)

    Guerrero, Mariana; Carlone, Marco

    2010-01-01

    Purpose: In recent years, several models were proposed that modify the standard linear-quadratic (LQ) model to make the predicted survival curve linear at high doses. Most of these models are purely phenomenological and can only be applied in the particular case of acute doses per fraction. The authors consider a mechanistic formulation of a linear-quadratic-linear (LQL) model in the case of split-dose experiments and exponentially decaying sources. This model provides a comprehensive description of radiation response for arbitrary dose rate and fractionation with only one additional parameter. Methods: The authors use a compartmental formulation of the LQL model from the literature. They analytically solve the model's differential equations for the case of a split-dose experiment and for an exponentially decaying source. They compare the solutions of the survival fraction with the standard LQ equations and with the lethal-potentially lethal (LPL) model. Results: In the case of the split-dose experiment, the LQL model predicts a recovery ratio as a function of dose per fraction that deviates from the square law of the standard LQ. The survival fraction as a function of time between fractions follows a similar exponential law as the LQ but adds a multiplicative factor to the LQ parameter β. The LQL solution for the split-dose experiment is very close to the LPL prediction. For the decaying source, the differences between the LQL and the LQ solutions are negligible when the half-life of the source is much larger than the characteristic repair time, which is the clinically relevant case. Conclusions: The compartmental formulation of the LQL model can be used for arbitrary dose rates and provides a comprehensive description of dose response. When the survival fraction for acute doses is linear for high dose, a deviation of the square law formula of the recovery ratio for split doses is also predicted.

  4. The distribution and seasonal variations of diffuse fraction

    International Nuclear Information System (INIS)

    Anane-Fenin, K.

    1989-06-01

    A moving average approach is used to develop linear and polynomial regression models for the diffuse fraction averaged over 10, 15, 20 and 30 days. The correlations do not appear to be influenced by climate conditions or altitude. It is noted that the correlations vary with season. The time-dependent variations of the diffuse fraction correlations are examined by studying the residual differences between the measured diffuse fraction and those calculated from the over-all best-fit correlation. The residuals exhibit no pronounced pattern leading to the conclusion that the observed seasonal variation is caused by air mass and water vapour and that atmospheric turbidity plays little or no part. (author). 14 refs, 9 figs, 8 tabs

  5. Fractional Order PIλDμ Control for Maglev Guiding System

    Science.gov (United States)

    Hu, Qing; Hu, Yuwei

    To effectively suppress the external disturbances and parameter perturbation problem of the maglev guiding system, and improve speed and robustness, the electromagnetic guiding system is exactly linearized using state feedback method, Fractional calculus theory is introduced, the order of integer order PID control was extended to the field of fractional, then fractional order PIλDμ Controller was presented, Due to the extra two adjustable parameters compared with traditional PID controller, fractional order PIλDμ controllers were expected to show better control performance. The results of the computer simulation show that the proposed controller suppresses the external disturbances and parameter perturbation of the system effectively; the system response speed was increased; at the same time, it had flexible structure and stronger robustness.

  6. On using the linear-quadratic model in daily clinical practice

    International Nuclear Information System (INIS)

    Yaes, R.J.; Patel, P.; Maruyama, Y.

    1991-01-01

    To facilitate its use in the clinic, Barendsen's formulation of the Linear-Quadratic (LQ) model is modified by expressing isoeffect doses in terms of the Standard Effective Dose, Ds, the isoeffective dose for the standard fractionation schedule of 2 Gy fractions given once per day, 5 days per week. For any arbitrary fractionation schedule, where total dose D is given in N fractions of size d in a total time T, the corresponding Standard Effective Dose, Ds, will be proportional to the total dose D and the proportionality constant will be called the Standard Relative Effectiveness, SRE, to distinguish it from Barendsen's Relative Effectiveness, RE. Thus, Ds = SRE.D. The constant SRE depends on the parameters of the fractionation schedule, and on the tumor or normal tissue being irradiated. For the simple LQ model with no time dependence, which is applicable to late reacting tissue, SRE = [(d + delta)/(2 + delta)], where d is the fraction size and delta = alpha/beta is the alpha/beta ratio for the tissue of interest, with both d and delta expressed in units of Gy. Application of this method to the Linear Quadratic model with a time dependence, the LQ + time model, and to low dose rate brachytherapy will be discussed. To clarify the method of calculation, and to demonstrate its simplicity, examples from the clinical literature will be used

  7. INFORMATION SECURITY RISKS OPTIMIZATION IN CLOUDY SERVICES ON THE BASIS OF LINEAR PROGRAMMING

    Directory of Open Access Journals (Sweden)

    I. A. Zikratov

    2013-01-01

    Full Text Available The paper discusses theoretical aspects of secure cloud services creation for information processing of various confidentiality degrees. A new approach to the reasoning of information security composition in distributed computing structures is suggested, presenting the problem of risk assessment as an extreme problem of decisionmaking. Linear programming method application is proved to minimize the risk of information security for given performance security in compliance with the economic balance for the maintenance of security facilities and cost of services. An example is given to illustrate the obtained theoretical results.

  8. Comparison between linear quadratic and early time dose models

    International Nuclear Information System (INIS)

    Chougule, A.A.; Supe, S.J.

    1993-01-01

    During the 70s, much interest was focused on fractionation in radiotherapy with the aim of improving tumor control rate without producing unacceptable normal tissue damage. To compare the radiobiological effectiveness of various fractionation schedules, empirical formulae such as Nominal Standard Dose, Time Dose Factor, Cumulative Radiation Effect and Tumour Significant Dose, were introduced and were used despite many shortcomings. It has been claimed that a recent linear quadratic model is able to predict the radiobiological responses of tumours as well as normal tissues more accurately. We compared Time Dose Factor and Tumour Significant Dose models with the linear quadratic model for tumour regression in patients with carcinomas of the cervix. It was observed that the prediction of tumour regression estimated by the Tumour Significant Dose and Time Dose factor concepts varied by 1.6% from that of the linear quadratic model prediction. In view of the lack of knowledge of the precise values of the parameters of the linear quadratic model, it should be applied with caution. One can continue to use the Time Dose Factor concept which has been in use for more than a decade as its results are within ±2% as compared to that predicted by the linear quadratic model. (author). 11 refs., 3 figs., 4 tabs

  9. Integrating Linear Programming and Analytical Hierarchical ...

    African Journals Online (AJOL)

    Study area is about 28000 ha of Keleibar- Chai Watershed, located in eastern Azerbaijan, Iran. Socio-economic information collected through a two-stage survey of 19 villages, including 300 samples. Thematic maps also have summarized Ecological factors, including physical and economic data. A comprehensive Linear ...

  10. New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

    Science.gov (United States)

    Toufik, Mekkaoui; Atangana, Abdon

    2017-10-01

    Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

  11. Linear programming model for solution of matrix game with payoffs trapezoidal intuitionistic fuzzy number

    Directory of Open Access Journals (Sweden)

    Darunee Hunwisai

    2017-01-01

    Full Text Available In this work, we considered two-person zero-sum games with fuzzy payoffs and matrix games with payoffs of trapezoidal intuitionistic fuzzy numbers (TrIFNs. The concepts of TrIFNs and their arithmetic operations were used. The cut-set based method for matrix game with payoffs of TrIFNs was also considered. Compute the interval-type value of any alfa-constrategies by simplex method for linear programming. The proposed method is illustrated with a numerical example.

  12. The evaluation of multi-element personal dosemeters using the linear programming method

    International Nuclear Information System (INIS)

    Kragh, P.; Ambrosi, P.; Boehm, J.; Hilgers, G.

    1996-01-01

    Multi-element dosemeters are frequently used in individual monitoring. Each element can be regarded as an individual dosemeter with its own individual dose measurement value. In general, the individual dose values of one dosemeter vary according to the exposure conditions, i. e. the energy and angle of incidence of the radiation. The (final) dose measurement value of the personal dosemeter is calculated from the individual dose values by means of an evaluation algorithm. The best possible dose value, i.e. that of the smallest systematic (type B) uncertainty if the exposure conditions are changed in the dosemeter's rated range of use, is obtained by the method of linear programming. (author)

  13. Fractional Bhatnagar-Gross-Krook kinetic equation

    Science.gov (United States)

    Goychuk, Igor

    2017-11-01

    The linear Boltzmann equation (LBE) approach is generalized to describe fractional superdiffusive transport of the Lévy walk type in external force fields. The time distribution between scattering events is assumed to have a finite mean value and infinite variance. It is completely characterized by the two scattering rates, one fractional and a normal one, which defines also the mean scattering rate. We formulate a general fractional LBE approach and exemplify it with a particularly simple case of the Bohm and Gross scattering integral leading to a fractional generalization of the Bhatnagar, Gross and Krook (BGK) kinetic equation. Here, at each scattering event the particle velocity is completely randomized and takes a value from equilibrium Maxwell distribution at a given fixed temperature. We show that the retardation effects are indispensable even in the limit of infinite mean scattering rate and argue that this novel fractional kinetic equation provides a viable alternative to the fractional Kramers-Fokker-Planck (KFP) equation by Barkai and Silbey and its generalization by Friedrich et al. based on the picture of divergent mean time between scattering events. The case of divergent mean time is also discussed at length and compared with the earlier results obtained within the fractional KFP. Also a phenomenological fractional BGK equation without retardation effects is proposed in the limit of infinite scattering rates. It cannot be, however, rigorously derived from a scattering model, being rather clever postulated. It this respect, this retardationless equation is similar to the fractional KFP by Barkai and Silbey. However, it corresponds to the opposite, much more physical limit and, therefore, also presents a viable alternative.

  14. Analisis Peramalan Penjualan dan Penggunaan Metode Linear Programming dan Decision Tree Guna Mengoptimalkan Keuntungan pada PT Primajaya Pantes Garment

    Directory of Open Access Journals (Sweden)

    Inti Sariani Jianta Djie

    2013-09-01

    Full Text Available Primajaya Pantes Garment is a company that runs its business in garment sector. However, due to various numbers of requests each month, the company is difficult to determine the amount of production per month that is appropriate to maximize profits. The purpose of this study is to determine the appropriate forecasting method that can be used as a reference to determine the amount of production in the next period and to find a combination of products to maximize profits. Research used forecasting methods, including naive method, moving averages, weighted moving averages, exponential smoothing, exponential smoothing with trend, and linear regression. In addition, this study also used Linear Programming method with Simplex method to determine the best combination of products for the company and to choose a decision using a decision tree to determine which alternative should be done by the company. Results of this study found that the linear regression method is the most appropriate method in determining the forecast demand in the next period. While in the Linear Programming method, constraints used were the constraints of raw materials, labor hours, and limited demand for the product. The result of the decision tree is to increase production capacity.

  15. A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

    Directory of Open Access Journals (Sweden)

    F. Ghomanjani

    2016-10-01

    Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

  16. Network synchronization in a population of star-coupled fractional nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Wang Junwei, E-mail: wangjunweilj@yahoo.com.c [School of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006 (China); Zhang Yanbin [School of Computer Science, Hangzhou Dianzi University, Hangzhou 310018 (China)

    2010-03-29

    The topic of fractional calculus is enjoying growing interest among mathematicians, physicists and engineers in recent years. For complex network consisting of more than two fractional-order systems, however, it is difficult to establish its synchronization behavior. In this Letter, we study the synchronized motions in a star network of coupled fractional-order systems in which the major element is coupled to each of the noninteracting individual elements. On the basis of the stability theory of linear fractional-order differential equations, we derive a sufficient condition for the stability of the synchronization behavior in such a network. Furthermore, we verify our theoretical results by numerical simulations of star-coupled network with fractional-order chaotic nodes.

  17. A new analysis of the Fornberg-Whitham equation pertaining to a fractional derivative with Mittag-Leffler-type kernel

    Science.gov (United States)

    Kumar, Devendra; Singh, Jagdev; Baleanu, Dumitru

    2018-02-01

    The mathematical model of breaking of non-linear dispersive water waves with memory effect is very important in mathematical physics. In the present article, we examine a novel fractional extension of the non-linear Fornberg-Whitham equation occurring in wave breaking. We consider the most recent theory of differentiation involving the non-singular kernel based on the extended Mittag-Leffler-type function to modify the Fornberg-Whitham equation. We examine the existence of the solution of the non-linear Fornberg-Whitham equation of fractional order. Further, we show the uniqueness of the solution. We obtain the numerical solution of the new arbitrary order model of the non-linear Fornberg-Whitham equation with the aid of the Laplace decomposition technique. The numerical outcomes are displayed in the form of graphs and tables. The results indicate that the Laplace decomposition algorithm is a very user-friendly and reliable scheme for handling such type of non-linear problems of fractional order.

  18. Approximating high-dimensional dynamics by barycentric coordinates with linear programming

    Energy Technology Data Exchange (ETDEWEB)

    Hirata, Yoshito, E-mail: yoshito@sat.t.u-tokyo.ac.jp; Aihara, Kazuyuki; Suzuki, Hideyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan); Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); CREST, JST, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan); Shiro, Masanori [Department of Mathematical Informatics, The University of Tokyo, Bunkyo-ku, Tokyo 113-8656 (Japan); Mathematical Neuroinformatics Group, Advanced Industrial Science and Technology, Tsukuba, Ibaraki 305-8568 (Japan); Takahashi, Nozomu; Mas, Paloma [Center for Research in Agricultural Genomics (CRAG), Consorci CSIC-IRTA-UAB-UB, Barcelona 08193 (Spain)

    2015-01-15

    The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

  19. Approximating high-dimensional dynamics by barycentric coordinates with linear programming.

    Science.gov (United States)

    Hirata, Yoshito; Shiro, Masanori; Takahashi, Nozomu; Aihara, Kazuyuki; Suzuki, Hideyuki; Mas, Paloma

    2015-01-01

    The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data.

  20. Approximating high-dimensional dynamics by barycentric coordinates with linear programming

    International Nuclear Information System (INIS)

    Hirata, Yoshito; Aihara, Kazuyuki; Suzuki, Hideyuki; Shiro, Masanori; Takahashi, Nozomu; Mas, Paloma

    2015-01-01

    The increasing development of novel methods and techniques facilitates the measurement of high-dimensional time series but challenges our ability for accurate modeling and predictions. The use of a general mathematical model requires the inclusion of many parameters, which are difficult to be fitted for relatively short high-dimensional time series observed. Here, we propose a novel method to accurately model a high-dimensional time series. Our method extends the barycentric coordinates to high-dimensional phase space by employing linear programming, and allowing the approximation errors explicitly. The extension helps to produce free-running time-series predictions that preserve typical topological, dynamical, and/or geometric characteristics of the underlying attractors more accurately than the radial basis function model that is widely used. The method can be broadly applied, from helping to improve weather forecasting, to creating electronic instruments that sound more natural, and to comprehensively understanding complex biological data