Relaxation and decomposition methods for mixed integer nonlinear programming
Nowak, Ivo; Bank, RE
2005-01-01
This book presents a comprehensive description of efficient methods for solving nonconvex mixed integer nonlinear programs, including several numerical and theoretical results, which are presented here for the first time. It contains many illustrations and an up-to-date bibliography. Because on the emphasis on practical methods, as well as the introduction into the basic theory, the book is accessible to a wide audience. It can be used both as a research and as a graduate text.
AN ALGORITHM FOR FINDING GLOBAL MINIMUM OF NONLINEAR INTEGER PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Wei-wenTian; Lian-shengZhang
2004-01-01
A filled function is proposed by R.Ge[2] for finding a global minimizer of a function of several continuous variables. In [4], an approach for finding a global integer minimizer of nonlinear flmction using the above filled function is given. Meanwhile a major obstacle is met: if ρ > 0 is small, and ‖xI- xI* is large, where xI - an integer point, xI* - a current local integer minimizer, then the value of the filled function almost equals zero. Thus it is difficult to recognize the size of the value of the filled flmction and can not to find the global integer minimizer of nonlinear function. In this paper, two new filled functions are proposed for finding global integer minimizer of nonlinear flmction, the new filled function improves some properties of the filled function proposed by R. Ge [2]. Some numerical results are given, which indicate the new filled function (4.1) to find global integer minimizer of nonlinear function is efficient.
Approximating electrical distribution networks via mixed-integer nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Lakhera, Sanyogita [Citibank, New York City, NY (United States); Shanbhag, Uday V. [Department of Industrial and Enterprise Systems Engineering at the University of Illinois at Urbana-Champaign, 117 Transportation Building, 104 S. Mathews Ave., Urbana, IL 61801 (United States); McInerney, Michael K. [Construction Engineering Research Laboratory (CERL) (United States)
2011-02-15
Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an approximate electrical load distribution over a network of a prespecificed discretization. Together with partial information about existing substations, we determine the optimal placement of electrical substations to sustain such a load that minimizes the cost of capital and losses. This requires solving large-scale quadratic programs with discrete variables for which we present a novel penalization-smoothing scheme. The choice of locations allows one to determine the optimal flows in this network, as required by physical requirements which provide us with an approximation of the distribution network. Furthermore, the scheme allows for approximating systems in the presence of no-go areas, such as lakes and fields. We examine the performance of our algorithm on the solution of a set of location problems and observe that the scheme is capable of solving large-scale instances, well beyond the realm of existing mixed-integer nonlinear programming solvers. We conclude with a case study in which a stage-wise extension of this scheme is developed to reflect the temporal evolution of load. (author)
An Approximate Algorithm for a Class of Nonlinear Bilevel Integer Programming
Institute of Scientific and Technical Information of China (English)
LI Lei; TENG Chun-xian; TIAN Guang-yue
2002-01-01
The algorithm for a class of nonlinear bilevel integer programming is discussed in this paper. It is based on the theory and algorithm for nonlinear integer programming. The continuity methods for integer programming are studied in this paper. After simulated annealing algorithm is applied to the upper-level programming problem and the thought of filled function method for continuous global optimization is applied to the corresponding lower-level programming, an approximate algorithm is established. The satisfactory algorithm is elaborated in the following example.
Conforti, Michele; Zambelli, Giacomo
2014-01-01
This book is an elegant and rigorous presentation of integer programming, exposing the subject’s mathematical depth and broad applicability. Special attention is given to the theory behind the algorithms used in state-of-the-art solvers. An abundance of concrete examples and exercises of both theoretical and real-world interest explore the wide range of applications and ramifications of the theory. Each chapter is accompanied by an expertly informed guide to the literature and special topics, rounding out the reader’s understanding and serving as a gateway to deeper study. Key topics include: formulations polyhedral theory cutting planes decomposition enumeration semidefinite relaxations Written by renowned experts in integer programming and combinatorial optimization, Integer Programming is destined to become an essential text in the field.
A One-parameter Filled Function Method for Nonlinear Integer Programming
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
This paper gives a new definition of the filled function for nonlinear integer programming problem. A filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed filled function and the method using this filled function to solve nonlinear integer programming problem are also discussed. Numerical results indicate the efficiency and reliability of the proposed filled function algorithm.
One-parameter quasi-filled function algorithm for nonlinear integer programming
Institute of Scientific and Technical Information of China (English)
SHANG You-lin; HAN Bo-shun
2005-01-01
A definition of the quasi-filled function for nonlinear integer programming problem is given in this paper. A quasi-filled function satisfying our definition is presented. This function contains only one parameter. The properties of the proposed quasi-filled function and the method using this quasi-filled function to solve nonlinear integer programming problem are also discussed in this paper. Numerical results indicated the efficiency and reliability of the proposed quasi-filled function algorithm.
Two-parameters quasi-filled function algorithm for nonlinear integer programming
Institute of Scientific and Technical Information of China (English)
WANG Wei-xiang; SHANG You-lin; ZHANG Lian-sheng
2006-01-01
A quasi-filled function for nonlinear integer programming problem is given in this paper. This function contains two parameters which are easily to be chosen. Theoretical properties of the proposed quasi-filled function are investigated. Moreover,we also propose a new solution algorithm using this quasi-filled function to solve nonlinear integer programming problem in this paper. The examples with 2 to 6 variables are tested and computational results indicated the efficiency and reliability of the proposed quasi-filled function algorithm.
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
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...... of selected units by 23%, while for a non-linear approach the increase can be higher than 39%. The results indicate a higher coherence between the two latter approaches, and that the MLP (mixed integer programming) optimisation is most appropriate from a viewpoint of accuracy and runtime. © 2014 Elsevier Ltd...
Greenberg, Harold
1971-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Energy Technology Data Exchange (ETDEWEB)
Linderoth, Jeff T. [University of Wisconsin-Madison; Luedtke, James R. [University of Wisconsin-Madison
2013-05-30
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Problems involving both discrete and nonlinear components are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems. This research project added to the understanding of this area by making a number of fundamental advances. First, the work demonstrated many novel, strong, tractable relaxations designed to deal with non-convexities arising in mathematical formulation. Second, the research implemented the ideas in software that is available to the public. Finally, the work demonstrated the importance of these ideas on practical applications and disseminated the work through scholarly journals, survey publications, and conference presentations.
Designing A Nonlinear Integer Programming Model For A Cross-Dock By A Genetic Algorithm
Bahareh Vaisi; Reza Tavakkoli-Moghaddam
2015-01-01
Abstract This paper presents a non-linear integer programming model for a cross-dock problem that considers the total transportation cost of inbound and outbound trucks from an origin to a destination and the total cost of assigning strip and stack doors to trucks based on their number of trips and the distance between doors in cross-dock. In previous studies these two cost-based problems are modeled separately however it is more realistic and practical to use both of them as an integrated cr...
Domínguez, Luis F.
2012-06-25
An algorithm for the solution of convex multiparametric mixed-integer nonlinear programming problems arising in process engineering problems under uncertainty is introduced. The proposed algorithm iterates between a multiparametric nonlinear programming subproblem and a mixed-integer nonlinear programming subproblem to provide a series of parametric upper and lower bounds. The primal subproblem is formulated by fixing the integer variables and solved through a series of multiparametric quadratic programming (mp-QP) problems based on quadratic approximations of the objective function, while the deterministic master subproblem is formulated so as to provide feasible integer solutions for the next primal subproblem. To reduce the computational effort when infeasibilities are encountered at the vertices of the critical regions (CRs) generated by the primal subproblem, a simplicial approximation approach is used to obtain CRs that are feasible at each of their vertices. The algorithm terminates when there does not exist an integer solution that is better than the one previously used by the primal problem. Through a series of examples, the proposed algorithm is compared with a multiparametric mixed-integer outer approximation (mp-MIOA) algorithm to demonstrate its computational advantages. © 2012 American Institute of Chemical Engineers (AIChE).
Exact Penalty Function and Asymptotic Strong Nonlinear Duality in Integer Programming
Institute of Scientific and Technical Information of China (English)
Fu-sheng Bai; Z.Y.Wu; L.S. Zhang
2004-01-01
In this paper, a logarithmic-exponential penalty function with two parameters for integer programmingis discussed. We obtain the exact penalty properties and then establish the asymptotic strong nonlinear duality in the corresponding logarithmic-exponential dual formulation by using the obtained exact penalty properties.The discussion is based on the logarithmic-exponential nonlinear dual formulation proposed in [6].
On the solution of mixed-integer nonlinear programming models for computer aided molecular design.
Ostrovsky, Guennadi M; Achenie, Luke E K; Sinha, Manish
2002-11-01
This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branchingfunctions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing.
Automatic design of synthetic gene circuits through mixed integer non-linear programming.
Huynh, Linh; Kececioglu, John; Köppe, Matthias; Tagkopoulos, Ilias
2012-01-01
Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits.
Designing A Nonlinear Integer Programming Model For A Cross-Dock By A Genetic Algorithm
Directory of Open Access Journals (Sweden)
Bahareh Vaisi
2015-03-01
Full Text Available Abstract This paper presents a non-linear integer programming model for a cross-dock problem that considers the total transportation cost of inbound and outbound trucks from an origin to a destination and the total cost of assigning strip and stack doors to trucks based on their number of trips and the distance between doors in cross-dock. In previous studies these two cost-based problems are modeled separately however it is more realistic and practical to use both of them as an integrated cross-docking model. Additionally this model is solved for a randomly generated numerical example with three suppliers and two customers by the use of a genetic algorithm. By comparing two different parameter levels i.e. low and high numbers of populations the optimum solution is obtained considering a high level population size. A number of strip and stack doors are equal to a number of inbound and outbound trucks in the same sequence as 4 and 6 respectively. Finally the conclusion is presented.
Yin, Sisi; Nishi, Tatsushi
2014-11-01
Quantity discount policy is decision-making for trade-off prices between suppliers and manufacturers while production is changeable due to demand fluctuations in a real market. In this paper, quantity discount models which consider selection of contract suppliers, production quantity and inventory simultaneously are addressed. The supply chain planning problem with quantity discounts under demand uncertainty is formulated as a mixed-integer nonlinear programming problem (MINLP) with integral terms. We apply an outer-approximation method to solve MINLP problems. In order to improve the efficiency of the proposed method, the problem is reformulated as a stochastic model replacing the integral terms by using a normalisation technique. We present numerical examples to demonstrate the efficiency of the proposed method.
Institute of Scientific and Technical Information of China (English)
Meysam Kamalinejad; Majid Amidpour; S.M. Mousavi Naeynian
2015-01-01
Liquefied natural gas (LNG) is the most economical way of transporting natural gas (NG) over long distances. Liq-uefaction of NG using vapor compression refrigeration system requires high operating and capital cost. Due to lack of systematic design methods for multistage refrigeration cycles, conventional approaches to determine op-timal cycle are largely trial-and-error. In this paper a novel mixed integer non-linear programming (MINLP) model is introduced to select optimal synthesis of refrigeration systems to reduce both operating and capital costs of an LNG plant. Better conceptual understanding of design improvement is illustrated on composite curve (CC) and exergetic grand composite curve (EGCC) of pinch analysis diagrams. In this method a superstruc-ture representation of complex refrigeration system is developed to select and optimize key decision variables in refrigeration cycles (i.e. partition temperature, compression configuration, refrigeration features, refrigerant flow rate and economic trade-off). Based on this method a program (LNG-Pro) is developed which integrates VBA, Refprop and Excel MINLP Solver to automate the methodology. Design procedure is applied on a sample LNG plant to illustrate advantages of using this method which shows a 3.3% reduction in total shaft work consumption.
Directory of Open Access Journals (Sweden)
Mohammad Ali Afshari
2012-10-01
Full Text Available The aim of this paper is to present mathematical models optimizing all materials flows in supply chain. In this research a fuzzy multi-objective nonlinear mixed- integer programming model with piecewise linear membership function is applied to design a multi echelon supply chain network (SCN by considering total transportation costs and capacities of all echelons with fuzzy objectives. The model that is proposed in this study has 4 fuzzy functions. The first function is minimizing the total transportation costs between all echelons (suppliers, factories, distribution centers (DCs and customers. The second one is minimizing holding and ordering cost on DCs. The third objective is minimizing the unnecessary and unused capacity of factories and DCs via decreasing variance of transported amounts between echelons. The forth is minimizing the number of total vehicles that ship the materials and products along with SCN. For solving such a problem, as nodes increases in SCN, the traditional method does not have ability to solve large scale problem. So, we applied a Meta heuristic method called Genetic Algorithm. The numerical example is real world applied and compared the results with each other demonstrate the feasibility of applying the proposed model to given problem, and also its advantages are discussed.
Domínguez, Luis F.
2010-12-01
This work introduces two algorithms for the solution of pure integer and mixed-integer bilevel programming problems by multiparametric programming techniques. The first algorithm addresses the integer case of the bilevel programming problem where integer variables of the outer optimization problem appear in linear or polynomial form in the inner problem. The algorithm employs global optimization techniques to convexify nonlinear terms generated by a reformulation linearization technique (RLT). A continuous multiparametric programming algorithm is then used to solve the reformulated convex inner problem. The second algorithm addresses the mixed-integer case of the bilevel programming problem where integer and continuous variables of the outer problem appear in linear or polynomial forms in the inner problem. The algorithm relies on the use of global multiparametric mixed-integer programming techniques at the inner optimization level. In both algorithms, the multiparametric solutions obtained are embedded in the outer problem to form a set of single-level (M)(I)(N)LP problems - which are then solved to global optimality using standard fixed-point (global) optimization methods. Numerical examples drawn from the open literature are presented to illustrate the proposed algorithms. © 2010 Elsevier Ltd.
Uilhoorn, F. E.
2016-10-01
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.
Integer programming theory, applications, and computations
Taha, Hamdy A
1975-01-01
Integer Programming: Theory, Applications, and Computations provides information pertinent to the theory, applications, and computations of integer programming. This book presents the computational advantages of the various techniques of integer programming.Organized into eight chapters, this book begins with an overview of the general categorization of integer applications and explains the three fundamental techniques of integer programming. This text then explores the concept of implicit enumeration, which is general in a sense that it is applicable to any well-defined binary program. Other
Directory of Open Access Journals (Sweden)
Samira Salahi
2016-08-01
Full Text Available Reduction of fossil resources, increasing the production of greenhouse gas emissions and demand growth lead to greater use of distributed energy resources in power system especially in distribution networks. Integrating these resources in order to supply local loads creates a new concept called micro-grid. Optimal operation of micro-grid in the specific time period is one of the most important problems of them. In this paper, the operation problem of micro-grids is modeled considering the economical, technical and environmental issues, as well as uncertainties related to loads, wind speed and solar radiation. The resulting model is a Mixed-Integer Non-Linear Programming (MINLP. To demonstrate the effectiveness of the proposed model, Bisheh village in Iran is considered as a case study. The results showed that considering load curtailment costs, the power losses of the main grid, the penalties of pollutant gasses emissions and the elimination of energy subsides will tremendous impacts on the operation of microgrids. Article History: Received March 12, 2016; Received in revised form June 20, 2016; Accepted July 2nd 2016; Available online How to Cite This Article: Salahi, S., and Bahramara, S. (2016 Modeling Operation Problem of Micro-grids Considering Economical, Technical and Environmental issues as Mixed-Integer Non-Linear Programming. Int. Journal of Renewable Energy Development, 5(2, 139-149. http://dx.doi.org/10.14710/ijred.5.2.139-149
Applied Integer Programming Modeling and Solution
Chen, Der-San; Dang, Yu
2011-01-01
An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and
Winebrake, James J; Corbett, James J; Wang, Chengfeng; Farrell, Alexander E; Woods, Pippa
2005-04-01
Emissions from passenger ferries operating in urban harbors may contribute significantly to emissions inventories and commuter exposure to air pollution. In particular, ferries are problematic because of high emissions of oxides of nitrogen (NOx) and particulate matter (PM) from primarily unregulated diesel engines. This paper explores technical solutions to reduce pollution from passenger ferries operating in the New York-New Jersey Harbor. The paper discusses and demonstrates a mixed-integer, non-linear programming model used to identify optimal control strategies for meeting NOx and PM reduction targets for 45 privately owned commuter ferries in the harbor. Results from the model can be used by policy-makers to craft programs aimed at achieving least-cost reduction targets.
Stochastic Programming with Simple Integer Recourse
Louveaux, François V.; van der Vlerk, Maarten H.
1993-01-01
Stochastic integer programs are notoriously difficult. Very few properties are known and solution algorithms are very scarce. In this paper, we introduce the class of stochastic programs with simple integer recourse, a natural extension of the simple recourse case extensively studied in stochastic c
Integer Programming Models for Computational Biology Problems
Institute of Scientific and Technical Information of China (English)
Giuseppe Lancia
2004-01-01
The recent years have seen an impressive increase in the use of Integer Programming models for the solution of optimization problems originating in Molecular Biology. In this survey, some of the most successful Integer Programming approaches are described, while a broad overview of application areas being is given in modern Computational Molecular Biology.
El-Qulity, Said Ali; Mohamed, Ali Wagdy
2016-01-01
This paper proposes a nonlinear integer goal programming model (NIGPM) for solving the general problem of admission capacity planning in a country as a whole. The work aims to satisfy most of the required key objectives of a country related to the enrollment problem for higher education. The system general outlines are developed along with the solution methodology for application to the time horizon in a given plan. The up-to-date data for Saudi Arabia is used as a case study and a novel evolutionary algorithm based on modified differential evolution (DE) algorithm is used to solve the complexity of the NIGPM generated for different goal priorities. The experimental results presented in this paper show their effectiveness in solving the admission capacity for higher education in terms of final solution quality and robustness.
Method for solving a convex integer programming problem
Stefanov, Stefan M.
2003-01-01
We consider a convex integer program which is a nonlinear version of the assignment problem. This problem is reformulated as an equivalent problem. An algorithm for solving the original problem is suggested which is based on solving the simple assignment problem via some of known algorithms.
Ko, Andi Setiady; Chang, Ni-Bin
2008-07-01
Energy supply and use is of fundamental importance to society. Although the interactions between energy and environment were originally local in character, they have now widened to cover regional and global issues, such as acid rain and the greenhouse effect. It is for this reason that there is a need for covering the direct and indirect economic and environmental impacts of energy acquisition, transport, production and use. In this paper, particular attention is directed to ways of resolving conflict between economic and environmental goals by encouraging a power plant to consider co-firing biomass and refuse-derived fuel (RDF) with coal simultaneously. It aims at reducing the emission level of sulfur dioxide (SO(2)) in an uncertain environment, using the power plant in Michigan City, Indiana as an example. To assess the uncertainty by a comparative way both deterministic and grey nonlinear mixed integer programming (MIP) models were developed to minimize the net operating cost with respect to possible fuel combinations. It aims at generating the optimal portfolio of alternative fuels while maintaining the same electricity generation simultaneously. To ease the solution procedure stepwise relaxation algorithm was developed for solving the grey nonlinear MIP model. Breakeven alternative fuel value can be identified in the post-optimization stage for decision-making. Research findings show that the inclusion of RDF does not exhibit comparative advantage in terms of the net cost, albeit relatively lower air pollution impact. Yet it can be sustained by a charge system, subsidy program, or emission credit as the price of coal increases over time.
Linear and integer programming made easy
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...
Integer programming techniques for educational timetabling
DEFF Research Database (Denmark)
Fonseca, George H.G.; Santos, Haroldo G.; Carrano, Eduardo G.
2017-01-01
in recent studies in the field. This work presents new cuts and reformulations for the existing integer programming model for XHSTT. The proposed cuts improved hugely the linear relaxation of the formulation, leading to an average gap reduction of 32%. Applied to XHSTT-2014 instance set, the alternative...
Optimized Waterspace Management and Scheduling Using Mixed-Integer Linear Programming
2016-01-01
TECHNICAL REPORT NSWC PCD TR 2015-003 OPTIMIZED WATERSPACE MANAGEMENT AND SCHEDULING USING MIXED-INTEGER LINEAR PROGRAMMING...constraints required for the mathematical formulation of the MCM scheduling problem pertaining to the survey constraints and logistics management . The...Floudas, Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications, Oxford University Press, 1995. [10] M. J. Bays, A. Shende, D. J
Logic integer programming models for signaling networks.
Haus, Utz-Uwe; Niermann, Kathrin; Truemper, Klaus; Weismantel, Robert
2009-05-01
We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this, we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in molecular biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.
Solving Integer Programming by Evolutionary Soft Agent
Institute of Scientific and Technical Information of China (English)
Yin Jian
2003-01-01
Many practical problems in commerce and industry involve finding the best way to allocate scarce resources a mong competing activities. This paper focuses on the problem of integer programming, and describes an evolutionary soft agent model to solve it. In proposed model, agent is composed of three components: goal, environment and behavior. Experirnental shows thne model has the characters of parallel computing and goal driving.
Network interdiction and stochastic integer programming
2003-01-01
On March 15, 2002 we held a workshop on network interdiction and the more general problem of stochastic mixed integer programming at the University of California, Davis. Jesús De Loera and I co-chaired the event, which included presentations of on-going research and discussion. At the workshop, we decided to produce a volume of timely work on the topics. This volume is the result. Each chapter represents state-of-the-art research and all of them were refereed by leading investigators in the respective fields. Problems - sociated with protecting and attacking computer, transportation, and social networks gain importance as the world becomes more dep- dent on interconnected systems. Optimization models that address the stochastic nature of these problems are an important part of the research agenda. This work relies on recent efforts to provide methods for - dressing stochastic mixed integer programs. The book is organized with interdiction papers first and the stochastic programming papers in the second part....
Bivium as a Mixed Integer Programming Problem
DEFF Research Database (Denmark)
Borghoff, Julia; Knudsen, Lars Ramkilde; Stolpe, Mathias
2009-01-01
Trivium is a stream cipher proposed for the eSTREAM project. Raddum introduced some reduced versions of Trivium, named Bivium A and Bivium B. In this article we present a numerical attack on the Biviums. The main idea is to transform the problem of solving a sparse system of quadratic equations...... over $GF(2)$ into a combinatorial optimization problem. We convert the Boolean equation system into an equation system over $\\mathbb{R}$ and formulate the problem of finding a $0$-$1$-valued solution for the system as a mixed-integer programming problem. This enables us to make use of several...... algorithms in the field of combinatorial optimization in order to find a solution for the problem and recover the initial state of Bivium. In particular this gives us an attack on Bivium B in estimated time complexity of $2^{63.7}$ seconds. But this kind of attack is also applicable to other cryptographic...
Ensemble segmentation using efficient integer linear programming.
Alush, Amir; Goldberger, Jacob
2012-10-01
We present a method for combining several segmentations of an image into a single one that in some sense is the average segmentation in order to achieve a more reliable and accurate segmentation result. The goal is to find a point in the "space of segmentations" which is close to all the individual segmentations. We present an algorithm for segmentation averaging. The image is first oversegmented into superpixels. Next, each segmentation is projected onto the superpixel map. An instance of the EM algorithm combined with integer linear programming is applied on the set of binary merging decisions of neighboring superpixels to obtain the average segmentation. Apart from segmentation averaging, the algorithm also reports the reliability of each segmentation. The performance of the proposed algorithm is demonstrated on manually annotated images from the Berkeley segmentation data set and on the results of automatic segmentation algorithms.
Institute of Scientific and Technical Information of China (English)
袁晓; 利洁婷; 王世其
2011-01-01
本文针对某公司电力容量扩展问题，采用一元线性回归模型拟合未来10年的需求量，再建立0—1非线性整数规划模型，并将该模型的0—1变量连续化处理，采用遗传算法中的GENOCOP算法求解。%In this paper,the next 10- year demand of a company for power capacity is fitted by monadic linear regression model. A model for 0 - 1 nonlinear integer programming is built, and the 0 - 1 variables of the model are disposed continuously. It is solved by the GENOCOP algorithm of genetic algorithm.
A Composite Algorithm for Mixed Integer Constrained Nonlinear Optimization.
1980-01-01
algorithm (FLEX) developed by Paviani and Himmelblau [53] is a direct search algorithm for constrained, nonlinear problems. It uses a variation on the...given in an appendix to Himmelblau [32]. Two changes were made to the program as listed in the rcference. Between card number 1340 and 1350 the...1972, pp. 293-308 (32] Himmelblau , D. M., Applied Nonlinear Programming, McGraw-Hill, 1972 (33] Himmelblau , D. M., "A Uniform Evaluation of Unconstrained
Linear and integer programming theory and practice
Sierksma, Gerard
2001-01-01
Linear optimisation; basic concepts; Dantzig's simplex method; duality and optimality; sensitivity analysis; karmarkar's interior path method; integer linear optimisation; linear network models; computational complexity issues; model building, case studies, and advanced techniques; solutions to selected exercises. Appendices: linear algebra; convexity; graph theory; optimisation theory; computer package INTPM.
Short Rational Generating Functions For Multiobjective Linear Integer Programming
Blanco, Victor
2007-01-01
This paper presents an algorithm for solving multiobjective integer programming problems. The algorithm uses Barvinok's rational functions of the polytope that defines the feasible region and provides as output the entire set of nondominated solutions for the problem. Theoretical complexity results on the algorithm are provided in the paper and an implementation of the algorithm shows that it is useful for solving multiobjective integer linear programs.
Institute of Scientific and Technical Information of China (English)
Jia Li-Xin; Dai Hao; Hui Meng
2010-01-01
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems.Based on Lyapunov stability theory and numerical differentiation，a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems.Numerical simulation results are presented to illustrate the effectiveness of this method.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower's functions are separable with respect to the follower's variables, and the other is that the follower's functions are convex if the follower's variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader's variable x, it is proved that the optimal solution y of the follower's mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower's programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter A, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
Mixed Integer Programming and Heuristic Scheduling for Space Communication
Lee, Charles H.; Cheung, Kar-Ming
2013-01-01
Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.
Integer Programming Model for Maximum Clique in Graph
Institute of Scientific and Technical Information of China (English)
YUAN Xi-bo; YANG You; ZENG Xin-hai
2005-01-01
The maximum clique or maximum independent set of graph is a classical problem in graph theory. Combined with Boolean algebra and integer programming, two integer programming models for maximum clique problem,which improve the old results were designed in this paper. Then, the programming model for maximum independent set is a corollary of the main results. These two models can be easily applied to computer algorithm and software, and suitable for graphs of any scale. Finally the models are presented as Lingo algorithms, verified and compared by several examples.
A new heuristic algorithm for general integer linear programming problems
Institute of Scientific and Technical Information of China (English)
GAO Pei-wang; CAI Ying
2006-01-01
A new heuristic algorithm is proposed for solving general integer linear programming problems.In the algorithm,the objective function hyperplane is used as a cutting plane,and then by introducing a special set of assistant sets,an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane.A simple numerical example shows that the algorithm is efficient for some problems,and therefore,of practical interest.
Designing fractional factorial split-plot experiments using integer programming
DEFF Research Database (Denmark)
Capehart, Shay R.; Keha, Ahmet; Kulahci, Murat
2011-01-01
factorial (FF) design, with the restricted randomisation structure to account for the whole plots and subplots. We discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions...
Designing fractional factorial split-plot experiments using integer programming
DEFF Research Database (Denmark)
Capehart, Shay R.; Keha, Ahmet; Kulahci, Murat
2011-01-01
factorial (FF) design, with the restricted randomisation structure to account for the whole plots and subplots. We discuss the formulation of FFSP designs using integer programming (IP) to achieve various design criteria. We specifically look at the maximum number of clear two-factor interactions...
Currency Arbitrage Detection Using a Binary Integer Programming Model
Soon, Wanmei; Ye, Heng-Qing
2011-01-01
In this article, we examine the use of a new binary integer programming (BIP) model to detect arbitrage opportunities in currency exchanges. This model showcases an excellent application of mathematics to the real world. The concepts involved are easily accessible to undergraduate students with basic knowledge in Operations Research. Through this…
Solving linear integer programming problems by a novel neural model.
Cavalieri, S
1999-02-01
The paper deals with integer linear programming problems. As is well known, these are extremely complex problems, even when the number of integer variables is quite low. Literature provides examples of various methods to solve such problems, some of which are of a heuristic nature. This paper proposes an alternative strategy based on the Hopfield neural network. The advantage of the strategy essentially lies in the fact that hardware implementation of the neural model allows for the time required to obtain a solution so as not depend on the size of the problem to be solved. The paper presents a particular class of integer linear programming problems, including well-known problems such as the Travelling Salesman Problem and the Set Covering Problem. After a brief description of this class of problems, it is demonstrated that the original Hopfield model is incapable of supplying valid solutions. This is attributed to the presence of constant bias currents in the dynamic of the neural model. A demonstration of this is given and then a novel neural model is presented which continues to be based on the same architecture as the Hopfield model, but introduces modifications thanks to which the integer linear programming problems presented can be solved. Some numerical examples and concluding remarks highlight the solving capacity of the novel neural model.
Investigating Integer Restrictions in Linear Programming
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…
Investigating Integer Restrictions in Linear Programming
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…
Shoemaker, Christine; Wan, Ying
2016-04-01
Optimization of nonlinear water resources management issues which have a mixture of fixed (e.g. construction cost for a well) and variable (e.g. cost per gallon of water pumped) costs has been not well addressed because prior algorithms for the resulting nonlinear mixed integer problems have required many groundwater simulations (with different configurations of decision variable), especially when the solution space is multimodal. In particular heuristic methods like genetic algorithms have often been used in the water resources area, but they require so many groundwater simulations that only small systems have been solved. Hence there is a need to have a method that reduces the number of expensive groundwater simulations. A recently published algorithm for nonlinear mixed integer programming using surrogates was shown in this study to greatly reduce the computational effort for obtaining accurate answers to problems involving fixed costs for well construction as well as variable costs for pumping because of a substantial reduction in the number of groundwater simulations required to obtain an accurate answer. Results are presented for a US EPA hazardous waste site. The nonlinear mixed integer surrogate algorithm is general and can be used on other problems arising in hydrology with open source codes in Matlab and python ("pySOT" in Bitbucket).
Extracting vascular networks under physiological constraints via integer programming.
Rempfler, Markus; Schneider, Matthias; Ielacqua, Giovanna D; Xiao, Xianghui; Stock, Stuart R; Klohs, Jan; Székely, Gábor; Andres, Bjoern; Menze, Bjoern H
2014-01-01
We introduce an integer programming-based approach to vessel network extraction that enforces global physiological constraints on the vessel structure and learn this prior from a high-resolution reference network. The method accounts for both image evidence and geometric relationships between vessels by formulating and solving an integer programming problem. Starting from an over-connected network, it is pruning vessel stumps and spurious connections by evaluating bifurcation angle and connectivity of the graph. We utilize a high-resolution micro computed tomography (μCT) dataset of a cerebrovascular corrosion cast to obtain a reference network, perform experiments on micro magnetic resonance angiography (μMRA) images of mouse brains and discuss properties of the networks obtained under different tracking and pruning approaches.
A fuzzy mixed integer programming for marketing planning
Directory of Open Access Journals (Sweden)
Abolfazl Danaei
2014-03-01
Full Text Available One of the primary concerns to market a product is to find appropriate channel to target customers. The recent advances on information technology have created new products with tremendous opportunities. This paper presents a mixed integer programming technique based on McCarthy's 4PS to locate suitable billboards for marketing newly introduced IPHONE product. The paper considers two types of information including age and income and tries to find the best places such that potential consumers aged 25-35 with high income visit the billboards and the cost of advertisement is minimized. The model is formulated in terms of mixed integer programming and it has been applied for potential customers who live in city of Tabriz, Iran. Using a typical software package, the model detects appropriate places in various parts of the city.
Energy Technology Data Exchange (ETDEWEB)
Shamloo, H.; Haghighi, A. [K.N. Toosi Univ. of Technology, Tehran (Iran, Islamic Republic of). Dept. of Civil Engineering
2009-07-01
The flow properties of pipes are affected by leaks. Leak detection methods based on hydraulic modelling and real data records aim to find a pipe's leak parameters including their number, location and size. Inverse Transient Analysis (ITA), generally in time domain, is a powerful approach to develop leak detection methods with considerable benefits. This paper introduced an ITA based leak detection method along with a numerical model developed for direct transient analysis of leaks in pipes using method of characteristics (MOC). Transient state flow was generated in pipe and the pressure fluctuations were sampled only at the end valve location. To minimize the effects of unsteadiness and uncertainties due to the numerical modeling and also practical problems caused by water hammer, the downstream end valve was considered to be closed gradually within a long enough time. Then, using the sampled data and a direct transient analysis model, a mixed integer nonlinear program was developed. A mixed genetic algorithm was used in which the binary chromosomes were decoded as mixed integer leak locations and real leak areas. In order to find unknown leak parameters in a pipe, an objective function was defined using the least squares criterion of differences between observed and calculated pressure heads at the valve location. The genetic algorithm was found to be a powerful and easy to use optimization tool to solve complicated mixed integer nonlinear program (MINLP) problems in leak detection. 24 refs., 1 tab., 7 figs.
Optimizing Marine Corps Personnel Assignments Using an Integer Programming Model
2012-12-01
would assist the Monitors in the assignment process. Though these studies contain very thorough analyses, they differ from the approach taken in this...thesis in that they do not look into using a low cost, yet very efficient, decision modeling approach of integer programming as a method of...2012 BAH Rates-with Dependents. Defense Travel Mangement Office. (2011, December). 2012 BAH Rates-without Dependents. M ileage C ost 1 Per D iem
Partial Gr\\"obner bases for multiobjective integer programming
Blanco, Victor
2007-01-01
In this paper we present two new methodologies for solving multiobjective integer programming using tools from algebraic geometry. We introduce the concept of partial Gr\\"obner basis for a family of multiobjective programs where the right-hand side varies. This new structure extends the notion of usual Gr\\"obner basis for the single objective case, to the case of multiple objectives, i.e., a partial ordering instead of a total ordering over the feasible vectors. The main property of these bases is that partial reduction of the integer elements in the kernel of the constraint matrix by the different blocks of the basis is zero. It allows us to prove that this new construction is a test family for a family of multiobjective programs. An algorithm '\\`a la Buchberger' is developed to compute partial Gr\\"obner basis. Specifically, with this tool we compute the entire set of efficient solutions of any multiobjective integer linear problem (MOILP). Some examples illustrate the application of the algorithms and compu...
An integer optimization algorithm for robust identification of non-linear gene regulatory networks
Directory of Open Access Journals (Sweden)
Chemmangattuvalappil Nishanth
2012-09-01
Full Text Available Abstract Background Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. Results We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters
Fast numerical methods for mixed-integer nonlinear model-predictive control
Kirches, Christian
2011-01-01
Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and rounding.
Geng, Lingling; Yu, Yongguang; Zhang, Shuo
2016-09-01
In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.
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...
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...
Integer programming for the generalized high school timetabling problem
DEFF Research Database (Denmark)
Kristiansen, Simon; Sørensen, Matias; Stidsen, Thomas Riis
2015-01-01
Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby......, the XHSTT format serves as a common ground for researchers within this area. This paper describes the first exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a mixed-integer linear programming (MIP) model, which is solved in two steps with a commercial...
Non-linear time series extreme events and integer value problems
Turkman, Kamil Feridun; Zea Bermudez, Patrícia
2014-01-01
This book offers a useful combination of probabilistic and statistical tools for analyzing nonlinear time series. Key features of the book include a study of the extremal behavior of nonlinear time series and a comprehensive list of nonlinear models that address different aspects of nonlinearity. Several inferential methods, including quasi likelihood methods, sequential Markov Chain Monte Carlo Methods and particle filters, are also included so as to provide an overall view of the available tools for parameter estimation for nonlinear models. A chapter on integer time series models based on several thinning operations, which brings together all recent advances made in this area, is also included. Readers should have attended a prior course on linear time series, and a good grasp of simulation-based inferential methods is recommended. This book offers a valuable resource for second-year graduate students and researchers in statistics and other scientific areas who need a basic understanding of nonlinear time ...
Using Integer Programming for Airport Service Planning in Staff Scheduling
Directory of Open Access Journals (Sweden)
W.H. Ip
2010-09-01
Full Text Available Reliability and safety in flight is extremely necessary and that depend on the adoption of proper maintenance system. Therefore, it is essential for aircraft maintenance companies to perform the manpower scheduling efficiently. One of the objectives of this paper is to provide an Integer Programming approach to determine the optimal solutions to aircraft maintenance planning and scheduling and hence the planning and scheduling processes can become more efficient and effective. Another objective is to develop a set of computational schedules for maintenance manpower to cover all scheduled flights. In this paper, a sequential methodology consisting of 3 stages is proposed. They are initial maintenance demand schedule, the maintenance pairing and the maintenance group(s assignment. Since scheduling would split up into different stages, different mathematical techniques have been adopted to cater for their own problem characteristics. Microsoft Excel would be used. Results from the first stage and second stage would be inputted into integer programming model using Microsoft Excel Solver to find the optimal solution. Also, Microsoft Excel VBA is used for devising a scheduling system in order to reduce the manual process and provide a user friendly interface. For the results, all can be obtained optimal solution and the computation time is reasonable and acceptable. Besides, the comparison of the peak time and non-peak time is discussed.
A virtual network mapping algorithm based on integer programming
Institute of Scientific and Technical Information of China (English)
Bo LU; Jian-ya CHEN; Hong-yan CUI; Tao HUANG; Yun-jie LIU
2013-01-01
The virtual network (VN) embedding/mapping problem is recognized as an essential question of network virtualiza-tion. The VN embedding problem is a major challenge in this field. Its target is to efficiently map the virtual nodes and virtual links onto the substrate network resources. Previous research focused on designing heuristic-based algorithms or attempting two-stage solutions by solving node mapping in the first stage and link mapping in the second stage. In this study, we propose a new VN embedding algorithm based on integer programming. We build a model of an augmented substrate graph, and formulate the VN embedding problem as an integer program with an objective function and some constraints. A factor of topology-awareness is added to the objective function. The VN embedding problem is solved in one stage. Simulation results show that our algorithm greatly enhances the acceptance ratio, and increases the revenue/cost (R/C) ratio and the revenue while decreasing the cost of the VN embedding problem.
Split diversity in constrained conservation prioritization using integer linear programming.
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.
An Integer Programming Approach to Solving Tantrix on Fixed Boards
Directory of Open Access Journals (Sweden)
Yushi Uno
2012-03-01
Full Text Available Tantrix (Tantrix R ⃝ is a registered trademark of Colour of Strategy Ltd. in New Zealand, and of TANTRIX JAPAN in Japan, respectively, under the license of M. McManaway, the inventor. is a puzzle to make a loop by connecting lines drawn on hexagonal tiles, and the objective of this research is to solve it by a computer. For this purpose, we first give a problem setting of solving Tantrix as making a loop on a given fixed board. We then formulate it as an integer program by describing the rules of Tantrix as its constraints, and solve it by a mathematical programming solver to have a solution. As a result, we establish a formulation that can solve Tantrix of moderate size, and even when the solutions are invalid only by elementary constraints, we achieved it by introducing additional constraints and re-solve it. By this approach we succeeded to solve Tantrix of size up to 60.
Optimal power system management via mixed integer dynamic programming
Energy Technology Data Exchange (ETDEWEB)
Kwatny, H.G.; Mensah, E. [Drexel Univ., Philadelphia, PA (United States). Dept. of Mechanical Engineering and Mechanics; Niebur, D. [Drexel Univ., Philadelphia, PA (United States). Dept. of Electrical and Computer Engineering; Teolis, C. [Techno-Sciences Inc., Lanham, MD (United States)
2006-07-01
Power systems are comprised of continuous and discrete acting components and subsystems. This paper discussed a logical specification that was used to define the transition dynamics of the discrete subsystem. It also presented a computational tool that reduced the logical specification to a set of inequalities as well as the use of the transformed model in a dynamic programming approach to the design of the optimal feedback controls. An example of optimal load shedding within a power system with an aggregate induction motor and constant admittance loads was presented. Specifically, the paper outlined the problem and discussed the modeling of hybrid systems and the control problem. A solution to the optimal control problem was presented. The essential feature of the model was the characterization of the discrete subsystem in terms of a set of mixed-integer formulas. The case example showed how logical constraints involving system real variables, such as case excitation voltage, could be incorporated in the problem via transformation to mixed-integer formulas. 10 refs., 4 figs.
An Integer Programming-based Local Search for Large-scale Maximal Covering Problems
Directory of Open Access Journals (Sweden)
Junha Hwang
2011-02-01
Full Text Available Maximal covering problem (MCP is classified as a linear integer optimization problem which can be effectively solved by integer programming technique. However, as the problem size grows, integerprogramming requires excessive time to get an optimal solution. This paper suggests a method for applying integer programming-based local search (IPbLS to solve large-scale maximal covering problems. IPbLS, which is a hybrid technique combining integer programming and local search, is a kind of local search using integer programming for neighbor generation. IPbLS itself is very effective for MCP. In addition, we improve the performance of IPbLS for MCP through problem reduction based on the current solution. Experimental results show that the proposed method considerably outperforms any other local search techniques and integer programming.
New Integer Programming Formulations of the Generalized Travelling Salesman Problem
Directory of Open Access Journals (Sweden)
P. C. Pop
2007-01-01
Full Text Available The Generalized Travelling Salesman Problem, denoted by GTSP, is a variant of the classical travelling salesman problem (TSP, in which the nodes of an undirected graph are partitioned into node sets (clusters and the salesman has to visit exactly one node from every cluster. In this paper we described six distinct formulations of the GTSP as an integer programming. Apart from the standard formulations all the new formulations that we describe are 'compact' in the sense that the number of constraints and variables is a polynomial function of the number of nodes in the problem. In order to provide compact formulations for the GTSP we used two approaches using auxiliary flow variables beyond the natural binary edge and node variables and the second one by distinguishing between global and local variables. Comparisons of the polytopes corresponding to their linear relaxations are established.
Integer programming model for optimizing bus timetable using genetic algorithm
Wihartiko, F. D.; Buono, A.; Silalahi, B. P.
2017-01-01
Bus timetable gave an information for passengers to ensure the availability of bus services. Timetable optimal condition happened when bus trips frequency could adapt and suit with passenger demand. In the peak time, the number of bus trips would be larger than the off-peak time. If the number of bus trips were more frequent than the optimal condition, it would make a high operating cost for bus operator. Conversely, if the number of trip was less than optimal condition, it would make a bad quality service for passengers. In this paper, the bus timetabling problem would be solved by integer programming model with modified genetic algorithm. Modification was placed in the chromosomes design, initial population recovery technique, chromosomes reconstruction and chromosomes extermination on specific generation. The result of this model gave the optimal solution with accuracy 99.1%.
Developing optimal nurses work schedule using integer programming
Shahidin, Ainon Mardhiyah; Said, Mohd Syazwan Md; Said, Noor Hizwan Mohamad; Sazali, Noor Izatie Amaliena
2017-08-01
Time management is the art of arranging, organizing and scheduling one's time for the purpose of generating more effective work and productivity. Scheduling is the process of deciding how to commit resources between varieties of possible tasks. Thus, it is crucial for every organization to have a good work schedule for their staffs. The job of Ward nurses at hospitals runs for 24 hours every day. Therefore, nurses will be working using shift scheduling. This study is aimed to solve the nurse scheduling problem at an emergency ward of a private hospital. A 7-day work schedule for 7 consecutive weeks satisfying all the constraints set by the hospital will be developed using Integer Programming. The work schedule for the nurses obtained gives an optimal solution where all the constraints are being satisfied successfully.
An integer linear programming for a comprehensive reverse supply chain
Directory of Open Access Journals (Sweden)
Hoda Mahmoudi
2014-12-01
Full Text Available Reverse supply chain is a cycle of recovery for the products and materials used by the customers but can be returned to the chain performing some operations. Due to significance of reverse supply chain in the content of environmental and economical aspects, we formulate a mathematical model of reverse multi-layer multi-product supply chain for minimizing the total costs including returning, disassembly, processing, recycling, remanufacturing, and distribution centers. The presented model is an integer linear programming model being solved using Lingo 9 software. Numerical experiments are conducted to gain insight into the proposed model. The solutions provide a decision aid stream strengthening the concept of reverse supply network design and analysis for profit-making organization.
Distributing Earthquakes Among California's Faults: A Binary Integer Programming Approach
Geist, E. L.; Parsons, T.
2016-12-01
Statement of the problem is simple: given regional seismicity specified by a Gutenber-Richter (G-R) relation, how are earthquakes distributed to match observed fault-slip rates? The objective is to determine the magnitude-frequency relation on individual faults. The California statewide G-R b-value and a-value are estimated from historical seismicity, with the a-value accounting for off-fault seismicity. UCERF3 consensus slip rates are used, based on geologic and geodetic data and include estimates of coupling coefficients. The binary integer programming (BIP) problem is set up such that each earthquake from a synthetic catalog spanning millennia can occur at any location along any fault. The decision vector, therefore, consists of binary variables, with values equal to one indicating the location of each earthquake that results in an optimal match of slip rates, in an L1-norm sense. Rupture area and slip associated with each earthquake are determined from a magnitude-area scaling relation. Uncertainty bounds on the UCERF3 slip rates provide explicit minimum and maximum constraints to the BIP model, with the former more important to feasibility of the problem. There is a maximum magnitude limit associated with each fault, based on fault length, providing an implicit constraint. Solution of integer programming problems with a large number of variables (>105 in this study) has been possible only since the late 1990s. In addition to the classic branch-and-bound technique used for these problems, several other algorithms have been recently developed, including pre-solving, sifting, cutting planes, heuristics, and parallelization. An optimal solution is obtained using a state-of-the-art BIP solver for M≥6 earthquakes and California's faults with slip-rates > 1 mm/yr. Preliminary results indicate a surprising diversity of on-fault magnitude-frequency relations throughout the state.
Han, Kyung T.; Rudner, Lawrence M.
2014-01-01
This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information…
Deleting Outliers in Robust Regression with Mixed Integer Programming
Institute of Scientific and Technical Information of China (English)
Georgios Zioutas; Antonios Avramidis
2005-01-01
In robust regression we often have to decide how many are the unusual observations, which should be removed from the sample in order to obtain better fitting for the rest of the observations. Generally, we use the basic principle of LTS, which is to fit the majority of the data, identifying as outliers those points that cause the biggest damage to the robust fit. However, in the LTS regression method the choice of default values for high break down-point affects seriously the efficiency of the estimator. In the proposed approach we introduce penalty cost for discarding an outlier, consequently, the best fit for the majority of the data is obtained by discarding only catastrophic observations. This penalty cost is based on robust design weights and high break down-point residual scale taken from the LTS estimator. The robust estimation is obtained by solving a convex quadratic mixed integer programming problem, where in the objective function the sum of the squared residuals and penalties for discarding observations is minimized. The proposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct a simulation study to compare other robust estimators with our approach in terms of their efficiency and robustness.
On Column-restricted and Priority Covering Integer Programs
Chakrabarty, Deeparnab; Koenemann, Jochen
2010-01-01
In a column-restricted covering integer program (CCIP), all the non-zero entries of any column of the constraint matrix are equal. Such programs capture capacitated versions of covering problems. In this paper, we study the approximability of CCIPs, in particular, their relation to the integrality gaps of the underlying 0,1-CIP. If the underlying 0,1-CIP has an integrality gap O(gamma), and assuming that the integrality gap of the priority version of the 0,1-CIP is O(omega), we give a factor O(gamma + omega) approximation algorithm for the CCIP. Priority versions of 0,1-CIPs (PCIPs) naturally capture quality of service type constraints in a covering problem. We investigate priority versions of the line (PLC) and the (rooted) tree cover (PTC) problems. Apart from being natural objects to study, these problems fall in a class of fundamental geometric covering problems. We bound the integrality of certain classes of this PCIP by a constant. Algorithmically, we give a polytime exact algorithm for PLC, show that t...
A Generalized Fuzzy Integer Programming Approach for Environmental Management under Uncertainty
Directory of Open Access Journals (Sweden)
Y. R. Fan
2014-01-01
Full Text Available In this study, a generalized fuzzy integer programming (GFIP method is developed for planning waste allocation and facility expansion under uncertainty. The developed method can (i deal with uncertainties expressed as fuzzy sets with known membership functions regardless of the shapes (linear or nonlinear of these membership functions, (ii allow uncertainties to be directly communicated into the optimization process and the resulting solutions, and (iii reflect dynamics in terms of waste-flow allocation and facility-capacity expansion. A stepwise interactive algorithm (SIA is proposed to solve the GFIP problem and generate solutions expressed as fuzzy sets. The procedures of the SIA method include (i discretizing the membership function grade of fuzzy parameters into a set of α-cut levels; (ii converting the GFIP problem into an inexact mixed-integer linear programming (IMILP problem under each α-cut level; (iii solving the IMILP problem through an interactive algorithm; and (iv approximating the membership function for decision variables through statistical regression methods. The developed GFIP method is applied to a municipal solid waste (MSW management problem to facilitate decision making on waste flow allocation and waste-treatment facilities expansion. The results, which are expressed as discrete or continuous fuzzy sets, can help identify desired alternatives for managing MSW under uncertainty.
An integer programming model for assigning students to elective courses
Directory of Open Access Journals (Sweden)
Ivo Beroš
2015-10-01
Full Text Available This paper deals with the problem of assigning students to elective courses according to their preferences. This process of assigning students to elective courses according to their preferences often places before academic institutions numerous obstacles, the most typical being a limited number of students who can be assigned to any particular class. Furthermore, due to financial or technical reasons, the maximum number of the elective courses is determined in advance, meaning that the institution decides which courses to conduct. Therefore, the expectation that all the students will be assigned to their first choice of courses is not realistic (perfect satisfaction. This paper presents an integer programming model that maximizes the total student satisfaction in line with a number of different constraints. The measure of student satisfaction is based on a student's order of preference according to the principle: the more a choice is met the higher the satisfaction. Following the basic model, several versions of the models are generated to cover possible real-life situations, while taking into consideration the manner student satisfaction is measured, as well as the preference of academic institution within set technical and financial constraints. The main contribution of the paper is introducing the concept of the minimal student satisfaction level that reduces the number of students dissatised with the courses to which they were assigned.
Constrained spacecraft reorientation using mixed integer convex programming
Tam, Margaret; Glenn Lightsey, E.
2016-10-01
A constrained attitude guidance (CAG) system is developed using convex optimization to autonomously achieve spacecraft pointing objectives while meeting the constraints imposed by on-board hardware. These constraints include bounds on the control input and slew rate, as well as pointing constraints imposed by the sensors. The pointing constraints consist of inclusion and exclusion cones that dictate permissible orientations of the spacecraft in order to keep objects in or out of the field of view of the sensors. The optimization scheme drives a body vector towards a target inertial vector along a trajectory that consists solely of permissible orientations in order to achieve the desired attitude for a given mission mode. The non-convex rotational kinematics are handled by discretization, which also ensures that the quaternion stays unity norm. In order to guarantee an admissible path, the pointing constraints are relaxed. Depending on how strict the pointing constraints are, the degree of relaxation is tuneable. The use of binary variables permits the inclusion of logical expressions in the pointing constraints in the case that a set of sensors has redundancies. The resulting mixed integer convex programming (MICP) formulation generates a steering law that can be easily integrated into an attitude determination and control (ADC) system. A sample simulation of the system is performed for the Bevo-2 satellite, including disturbance torques and actuator dynamics which are not modeled by the controller. Simulation results demonstrate the robustness of the system to disturbances while meeting the mission requirements with desirable performance characteristics.
Mixed integer linear programming for maximum-parsimony phylogeny inference.
Sridhar, Srinath; Lam, Fumei; Blelloch, Guy E; Ravi, R; Schwartz, Russell
2008-01-01
Reconstruction of phylogenetic trees is a fundamental problem in computational biology. While excellent heuristic methods are available for many variants of this problem, new advances in phylogeny inference will be required if we are to be able to continue to make effective use of the rapidly growing stores of variation data now being gathered. In this paper, we present two integer linear programming (ILP) formulations to find the most parsimonious phylogenetic tree from a set of binary variation data. One method uses a flow-based formulation that can produce exponential numbers of variables and constraints in the worst case. The method has, however, proven extremely efficient in practice on datasets that are well beyond the reach of the available provably efficient methods, solving several large mtDNA and Y-chromosome instances within a few seconds and giving provably optimal results in times competitive with fast heuristics than cannot guarantee optimality. An alternative formulation establishes that the problem can be solved with a polynomial-sized ILP. We further present a web server developed based on the exponential-sized ILP that performs fast maximum parsimony inferences and serves as a front end to a database of precomputed phylogenies spanning the human genome.
Learning oncogenetic networks by reducing to mixed integer linear programming.
Shahrabi Farahani, Hossein; Lagergren, Jens
2013-01-01
Cancer can be a result of accumulation of different types of genetic mutations such as copy number aberrations. The data from tumors are cross-sectional and do not contain the temporal order of the genetic events. Finding the order in which the genetic events have occurred and progression pathways are of vital importance in understanding the disease. In order to model cancer progression, we propose Progression Networks, a special case of Bayesian networks, that are tailored to model disease progression. Progression networks have similarities with Conjunctive Bayesian Networks (CBNs) [1],a variation of Bayesian networks also proposed for modeling disease progression. We also describe a learning algorithm for learning Bayesian networks in general and progression networks in particular. We reduce the hard problem of learning the Bayesian and progression networks to Mixed Integer Linear Programming (MILP). MILP is a Non-deterministic Polynomial-time complete (NP-complete) problem for which very good heuristics exists. We tested our algorithm on synthetic and real cytogenetic data from renal cell carcinoma. We also compared our learned progression networks with the networks proposed in earlier publications. The software is available on the website https://bitbucket.org/farahani/diprog.
Accurate construction of consensus genetic maps via integer linear programming.
Wu, Yonghui; Close, Timothy J; Lonardi, Stefano
2011-01-01
We study the problem of merging genetic maps, when the individual genetic maps are given as directed acyclic graphs. The computational problem is to build a consensus map, which is a directed graph that includes and is consistent with all (or, the vast majority of) the markers in the input maps. However, when markers in the individual maps have ordering conflicts, the resulting consensus map will contain cycles. Here, we formulate the problem of resolving cycles in the context of a parsimonious paradigm that takes into account two types of errors that may be present in the input maps, namely, local reshuffles and global displacements. The resulting combinatorial optimization problem is, in turn, expressed as an integer linear program. A fast approximation algorithm is proposed, and an additional speedup heuristic is developed. Our algorithms were implemented in a software tool named MERGEMAP which is freely available for academic use. An extensive set of experiments shows that MERGEMAP consistently outperforms JOINMAP, which is the most popular tool currently available for this task, both in terms of accuracy and running time. MERGEMAP is available for download at http://www.cs.ucr.edu/~yonghui/mgmap.html.
Maximum likelihood pedigree reconstruction using integer linear programming.
Cussens, James; Bartlett, Mark; Jones, Elinor M; Sheehan, Nuala A
2013-01-01
Large population biobanks of unrelated individuals have been highly successful in detecting common genetic variants affecting diseases of public health concern. However, they lack the statistical power to detect more modest gene-gene and gene-environment interaction effects or the effects of rare variants for which related individuals are ideally required. In reality, most large population studies will undoubtedly contain sets of undeclared relatives, or pedigrees. Although a crude measure of relatedness might sometimes suffice, having a good estimate of the true pedigree would be much more informative if this could be obtained efficiently. Relatives are more likely to share longer haplotypes around disease susceptibility loci and are hence biologically more informative for rare variants than unrelated cases and controls. Distant relatives are arguably more useful for detecting variants with small effects because they are less likely to share masking environmental effects. Moreover, the identification of relatives enables appropriate adjustments of statistical analyses that typically assume unrelatedness. We propose to exploit an integer linear programming optimisation approach to pedigree learning, which is adapted to find valid pedigrees by imposing appropriate constraints. Our method is not restricted to small pedigrees and is guaranteed to return a maximum likelihood pedigree. With additional constraints, we can also search for multiple high-probability pedigrees and thus account for the inherent uncertainty in any particular pedigree reconstruction. The true pedigree is found very quickly by comparison with other methods when all individuals are observed. Extensions to more complex problems seem feasible.
Mixed integer (0-1) fractional programming for decision support in paper production industry
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 p
Li, Hong; Zhang, Li; Jiao, Yong-Chang
2016-07-01
This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.
Directory of Open Access Journals (Sweden)
Tessa Vanina Soetanto
2004-01-01
Full Text Available This paper presents a study about new heuristic algorithm performance compared to Mixed Integer Programming (MIP method in solving flowshop scheduling problem to reach minimum makespan. Performance appraisal is based on Efficiency Index (EI, Relative Error (RE and Elapsed Runtime. Abstract in Bahasa Indonesia : Makalah ini menyajikan penelitian tentang performance algoritma heuristik Pour terhadap metode Mixed Integer Programming (MIP dalam menyelesaikan masalah penjadwalan flowshop dengan tujuan meminimalkan makespan. Penilaian performance dilakukan berdasarkan nilai Efficiency Index (EI, Relative Error (RE dan Elapsed Runtime. Kata kunci: flowshop, makespan, algoritma heuristik Pour, Mixed Integer Programming.
IESIP - AN IMPROVED EXPLORATORY SEARCH TECHNIQUE FOR PURE INTEGER LINEAR PROGRAMMING PROBLEMS
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.
Integer Programming and m-irreducibility of numerical semigroups
Blanco, Víctor
2011-01-01
This paper addresses the problem of decomposing a numerical semigroup into m-irreducible numerical semigroups. The problem originally stated in algebraic terms is translated, introducing the so called Kunz-coordinates, to resolve a series of several discrete optimization problems. First, we prove that finding a minimal m-irreducible decomposition is equivalent to solve a multiobjective linear integer problem. Then, we restate that problem as the problem of finding all the optimal solutions of a finite number of single objective integer linear problems plus a set covering problem. Finally, we prove that there is a suitable transformation that reduces the original problem to find an optimal solution of a compact integer linear problem. This result ensures a polynomial time algorithm for each given multiplicity m. We have implemented the different algorithms and have performed some computational experiments to show the efficiency of our methodology.
Stochastic level-value approximation for quadratic integer convex programming
Institute of Scientific and Technical Information of China (English)
PENG Zheng; WU Dong-hua
2008-01-01
We propose a stochastic level value approximation method for a quadratic integer convex minimizing problem in this paper. This method applies an importance sampling technique, and make use of the cross-entropy method to update the sample density functions. We also prove the asymptotic convergence of this algorithm, and re-port some numerical results to illuminate its effectiveness.
A generalization of the MDS method by mixed integer linear and nonlinear mathematical models
Directory of Open Access Journals (Sweden)
Sadegh Niroomand
2014-09-01
Full Text Available The Multi-Dimensional Scaling (MDS method is used in statistics to detect hidden interrelations among multi-dimensional data and it has a wide range of applications. The method’s input is a matrix that describes the similarity/dissimilarity among objects of unknown dimension. The objects are generally reconstructed as points of a lower dimensional space to reveal the geometric configuration of the objects. The original MDS method uses Euclidean distance, for measuring both the distance of the reconstructed points and the bias of the reconstructed distances from the original similarity values. In this paper, these distances are distinguished, and distances other than Euclidean are also used, generalizing the MDS method. Two different distances may be used for the two different purposes. Therefore the instances of the generalized MDS model are denoted as model, where the first distance is the type of distance of the reconstructed points and the second one measures the bias of the reconstructed distances and the similarity values. In the case of and distances mixed-integer programming models are provided. The computational experiences show that the generalized model can catch the key properties of the original configuration, if any exist. Keywords: Multivariate Analysis; Multi-Dimensional Scaling; Optimization; Mixed Integer Linear Programming; Statistics.
Meyer, Richard; DeCarlo, Raymond A
2012-01-01
This paper compares the embedding approach for solving hybrid optimal control problems to multi-parameter programming, mixed-integer programming, and gradient-descent based methods in the context of four published examples. The four examples include a spring-mass system, moving-target tracking for a mobile robot, two-tank filling, and a DC-DC boost converter. Numerical advantages of the embedding approach are set forth and validated for each example: significantly faster solution time, no ad hoc assumptions (such as predetermined mode sequences) or control models, lower performance index costs, and algorithm convergence when other methods fail. Specific (theoretical) advantages of the embedding approach over the other methods are also described: guaranteed existence of a solution under mild conditions, convexity of the embedded optimization problem solvable with traditional techniques such as sequential quadratic programming with no need for any mixed-integer programming, applicability to nonlinear systems, e...
Integer Programming Formulation of the Problem of Generating Milton Babbitt's All-partition Arrays
DEFF Research Database (Denmark)
Tanaka, Tsubasa; Bemman, Brian; Meredith, David
2016-01-01
integer partition of 12. Integer programming (IP) has proven to be effective for solving such combinatorial prob- lems, however, it has never before been applied to the problem addressed in this paper. We introduce a new way of viewing this problem as one in which restricted overlaps between integer......Milton Babbitt (1916–2011) was a composer of twelve-tone serial music noted for creating the all-partition array. The problem of generating an all-partition array involves finding a rectangular array of pitch-class integers that can be partitioned into regions, each of which represents a distinct...... partition regions are allowed. This permits us to describe the problem using a set of linear constraints necessary for IP. In particular, we show that this problem can be defined as a special case of the well-known problem of set-covering (SCP), modified with additional constraints. Due to the difficulty...
An extension of the Lovasz Local Lemma, and its applications to integer programming
Energy Technology Data Exchange (ETDEWEB)
Srinivasan, A. [National univ. of Singapore (Singapore)
1996-12-31
The Lovasz Local Lemma (LLL) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mean. We consider three classes of NP-hard integer programs: minimax, packing, and covering integer programs. A key technique, randomized rounding of linear relaxations, was developed by Raghavan & Thompson to derive good approximation algorithms for such problems. We use our extended LLL to prove that randomized rounding produces, with non-zero probability, much better feasible solutions than known be- fore, if the constraint matrices of these integer programs are sparse (e.g., VLSI routing using short paths, problems on hypergraphs with small dimension/degree). We also generalize the method of pessimistic estimators due to Raghavan, to constructivize our packing and covering results.
Metamorphic Testing Integer Overflow Faults of Mission Critical Program: A Case Study
Directory of Open Access Journals (Sweden)
Zhanwei Hui
2013-01-01
Full Text Available For mission critical programs, integer overflow is one of the most dangerous faults. Different testing methods provide several effective ways to detect the defect. However, it is hard to validate the testing outputs, because the oracle of testing is not always available or too expensive to get, unless the program throws an exception obviously. In the present study, the authors conduct a case study, where the authors apply a metamorphic testing (MT method to detect the integer overflow defect and alleviate the oracle problem in testing critical program of Traffic Collision Avoidance System (TCAS. Experimental results show that, in revealing typical integer mutations, compared with traditional safety property testing method, MT with a novel symbolic metamorphic relation is more effective than the traditional method in some cases.
A mixed integer program to model spatial wildfire behavior and suppression placement decisions
Erin J. Belval; Yu Wei; Michael. Bevers
2015-01-01
Wildfire suppression combines multiple objectives and dynamic fire behavior to form a complex problem for decision makers. This paper presents a mixed integer program designed to explore integrating spatial fire behavior and suppression placement decisions into a mathematical programming framework. Fire behavior and suppression placement decisions are modeled using...
Xia, Yong; Han, Ying-Wei
2014-01-01
In this paper, we propose a mixed-binary convex quadratic programming reformulation for the box-constrained nonconvex quadratic integer program and then implement IBM ILOG CPLEX 12.6 to solve the new model. Computational results demonstrate that our approach clearly outperform the very recent state-of-the-art solvers.
Modified Filled Function to Solve NonlinearProgramming Problem
Institute of Scientific and Technical Information of China (English)
2015-01-01
Filled function method is an approach to find the global minimum of nonlinear functions. Many Problems, such as computing,communication control, and management, in real applications naturally result in global optimization formulations in a form ofnonlinear global integer programming. This paper gives a modified filled function method to solve the nonlinear global integerprogramming problem. The properties of the proposed modified filled function are also discussed in this paper. The results ofpreliminary numerical experiments are also reported.
A Polynomial Time Algorithm for a Special Case of Linear Integer Programming
Ghasemiesfeh, Golnaz; Tabesh, Yahya
2011-01-01
According to the wide use of integer programming in many fields, affords toward finding and solving sub classes of these problems which are solvable in polynomial time seems to be important and useful. Integer linear programming (ILP) problems have the general form: $Min \\{C^{T}x: Ax=b, x\\geq 0, x\\in Z^{n}\\}$ where $Z^{n}$ is the set of n-dimensional integer vectors. Algorithmic solution of ILP is at great interest, in this paper we have presented a polynomial algorithm for a special case of the ILP problems; we have used a graph theoretical formulation of the problem which leads to an $O[mn(m+n)]$ solution where $m$ and $n$ are dimensions of coefficient matrix $X$.
Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Xiujuan; Chen, Jiapei
2017-03-01
Due to the existence of complexities of heterogeneities, hierarchy, discreteness, and interactions in municipal solid waste management (MSWM) systems such as Beijing, China, a series of socio-economic and eco-environmental problems may emerge or worsen and result in irredeemable damages in the following decades. Meanwhile, existing studies, especially ones focusing on MSWM in Beijing, could hardly reflect these complexities in system simulations and provide reliable decision support for management practices. Thus, a framework of distributed mixed-integer fuzzy hierarchical programming (DMIFHP) is developed in this study for MSWM under these complexities. Beijing is selected as a representative case. The Beijing MSWM system is comprehensively analyzed in many aspects such as socio-economic conditions, natural conditions, spatial heterogeneities, treatment facilities, and system complexities, building a solid foundation for system simulation and optimization. Correspondingly, the MSWM system in Beijing is discretized as 235 grids to reflect spatial heterogeneity. A DMIFHP model which is a nonlinear programming problem is constructed to parameterize the Beijing MSWM system. To enable scientific solving of it, a solution algorithm is proposed based on coupling of fuzzy programming and mixed-integer linear programming. Innovations and advantages of the DMIFHP framework are discussed. The optimal MSWM schemes and mechanism revelations will be discussed in another companion paper due to length limitation.
Mixed integer programming for the resolution of GPS carrier phase ambiguities
Xu, Peiliang; Lachapelle, Gerard
2010-01-01
This arXiv upload is to clarify that the now well-known sorted QR MIMO decoder was first presented in the 1995 IUGG General Assembly. We clearly go much further in the sense that we directly incorporated reduction into this one step, non-exact suboptimal integer solution. Except for these first few lines up to this point, this paper is an unaltered version of the paper presented at the IUGG1995 Assembly in Boulder. Ambiguity resolution of GPS carrier phase observables is crucial in high precision geodetic positioning and navigation applications. It consists of two aspects: estimating the integer ambiguities in the mixed integer observation model and examining whether they are sufficiently accurate to be fixed as known nonrandom integers. We shall discuss the first point in this paper from the point of view of integer programming. A one-step nonexact approach is proposed by employing minimum diagonal pivoting Gaussian decompositions, which may be thought of as an improvement of the simple rounding-off method, ...
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...
The "Best" Algorithm for Solving Stochastic Mixed Integer Programs
2006-01-01
focuses on solving problems for which all second-stage scenarios can be enu- merated (Klein Haneveld and van der Vlerk 1998, Ahmed 2004). Two exceptions... Haneveld , W. K. and M. H. van der Vlerk. 1998. Stochastic integer programming: state of the art. Available via <http://citeseer.ist.psu. edu
Khan, Sahubar Ali Bin Mohamed Nadhar; Ahmarofi, Ahmad Afif Bin
2014-12-01
In manufacturing sector, production planning or scheduling is the most important managerial task in order to achieve profit maximization and cost minimization. With limited resources, the management has to satisfy customer demand and at the same time fulfill company's objective, which is to maximize profit or minimize cost. Hence, planning becomes a significant task for production site in order to determine optimal number of units for each product to be produced. In this study, integer programming technique is used to develop an appropriate product-mix planning to obtain the optimal number of audio speaker products that should be produced in order to maximize profit. Branch-and-bound method is applied to obtain exact integer solutions when non-integer solutions occurred. Three major resource constraints are considered in this problem: raw materials constraint, demand constraint and standard production time constraint. It is found that, the developed integer programming model gives significant increase in profit compared to the existing method used by the company. At the end of the study, sensitivity analysis was performed to evaluate the effects of changes in objective function coefficient and available resources on the developed model. This will enable the management to foresee the effects on the results when some changes happen to the profit of its products or available resources.
Improved Sorting-Based Procedure for Integer Programming
DEFF Research Database (Denmark)
Dantchev, Stefan
2002-01-01
Recently, Cornuéjols and Dawande have considered a special class of 0-1 programs that turns out to be hard for existing IP solvers. One of them is a sorting-based algorithm, based on an idea of Wolsey. In this paper, we show how to improve both the running time and the space requirements of this ......Recently, Cornuéjols and Dawande have considered a special class of 0-1 programs that turns out to be hard for existing IP solvers. One of them is a sorting-based algorithm, based on an idea of Wolsey. In this paper, we show how to improve both the running time and the space requirements...... of this algorithm. The drastic reduction of space needed allows us to solve much larger instances than was possible before using this technique....
Fitting boxes to Manhattan scenes using linear integer programming
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.
PON and WiMAX Convergence Network Planning Based on Mixed Integer Programming Model
Institute of Scientific and Technical Information of China (English)
Lv Miao; Chen Xue
2011-01-01
This article analyzes the characteristics of PON and WiMAX convergence network planning.Based on user coverage ratio,WiMAX channel allocation,cell radius,carrier-to-noise ratio threshold,and bandwidth constraint,we propose a mixed integer programming model solved by a Branch-Band and Heuristic Search method.Finally,the simulation result is given and analyzed.The planning method based on a mixed integer programming model can save 20 percentage of the overall planning cost,compared with the greedy algorithm.The relationship between the convergence network planning cost and frequency usage is also analyzed.The optimized planning result with the lowest cost can be acquired through the best frequency usage.
Enhanced index tracking modeling in portfolio optimization with mixed-integer programming z approach
Siew, Lam Weng; Jaaman, Saiful Hafizah Hj.; Ismail, Hamizun bin
2014-09-01
Enhanced index tracking is a popular form of portfolio management in stock market investment. Enhanced index tracking aims to construct an optimal portfolio to generate excess return over the return achieved by the stock market index without purchasing all of the stocks that make up the index. The objective of this paper is to construct an optimal portfolio using mixed-integer programming model which adopts regression approach in order to generate higher portfolio mean return than stock market index return. In this study, the data consists of 24 component stocks in Malaysia market index which is FTSE Bursa Malaysia Kuala Lumpur Composite Index from January 2010 until December 2012. The results of this study show that the optimal portfolio of mixed-integer programming model is able to generate higher mean return than FTSE Bursa Malaysia Kuala Lumpur Composite Index return with only selecting 30% out of the total stock market index components.
Smart-Grid Backbone Network Real-Time Delay Reduction via Integer Programming.
Pagadrai, Sasikanth; Yilmaz, Muhittin; Valluri, Pratyush
2016-08-01
This research investigates an optimal delay-based virtual topology design using integer linear programming (ILP), which is applied to the current backbone networks such as smart-grid real-time communication systems. A network traffic matrix is applied and the corresponding virtual topology problem is solved using the ILP formulations that include a network delay-dependent objective function and lightpath routing, wavelength assignment, wavelength continuity, flow routing, and traffic loss constraints. The proposed optimization approach provides an efficient deterministic integration of intelligent sensing and decision making, and network learning features for superior smart grid operations by adaptively responding the time-varying network traffic data as well as operational constraints to maintain optimal virtual topologies. A representative optical backbone network has been utilized to demonstrate the proposed optimization framework whose simulation results indicate that superior smart-grid network performance can be achieved using commercial networks and integer programming.
A Mixed Integer Programming Model Formulation for Solving the Lot-Sizing Problem
Mohammadi, Maryam
2012-01-01
This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0.
Persistent Phylogeny: A Galled-Tree and Integer Linear Programming Approach
Gusfield, Dan
2015-01-01
The Persistent-Phylogeny Model is an extension of the widely studied Perfect-Phylogeny Model, encompassing a broader range of evolutionary phenomena. Biological and algorithmic questions concerning persistent phylogeny have been intensely investigated in recent years. In this paper, we explore two alternative approaches to the persistent-phylogeny problem that grow out of our previous work on perfect phylogeny, and on galled trees. We develop an integer programming solution to the Persistent-...
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.
Directory of Open Access Journals (Sweden)
Renata Melo e Silva de Oliveira
2015-03-01
Full Text Available Scheduling is a key factor for operations management as well as for business success. From industrial Job-shop Scheduling problems (JSSP, many optimization challenges have emerged since de 1960s when improvements have been continuously required such as bottlenecks allocation, lead-time reductions and reducing response time to requests. With this in perspective, this work aims to discuss 3 different optimization models for minimizing Makespan. Those 3 models were applied on 17 classical problems of examples JSSP and produced different outputs. The first model resorts on Mixed and Integer Programming (MIP and it resulted on optimizing 60% of the studied problems. The other models were based on Constraint Programming (CP and approached the problem in two different ways: a model CP1 is a standard IBM algorithm whereof restrictions have an interval structure that fail to solve 53% of the proposed instances, b Model CP-2 approaches the problem with disjunctive constraints and optimized 88% of the instances. In this work, each model is individually analyzed and then compared considering: i Optimization success performance, ii Computational processing time, iii Greatest Resource Utilization and, iv Minimum Work-in-process Inventory. Results demonstrated that CP-2 presented best results on criteria i and ii, but MIP was superior on criteria iii and iv and those findings are discussed at the final section of this work.
Nonlinear programming analysis and methods
Avriel, Mordecai
2012-01-01
This text provides an excellent bridge between principal theories and concepts and their practical implementation. Topics include convex programming, duality, generalized convexity, analysis of selected nonlinear programs, techniques for numerical solutions, and unconstrained optimization methods.
Energy Technology Data Exchange (ETDEWEB)
DRIESSEN,BRIAN; SADEGH,NADER
2000-04-25
This work presents a method of finding near global optima to minimum-time trajectory generation problem for systems that would be linear if it were not for the presence of Coloumb friction. The required final state of the system is assumed to be maintainable by the system, and the input bounds are assumed to be large enough so that they can overcome the maximum static Coloumb friction force. Other than the previous work for generating minimum-time trajectories for non redundant robotic manipulators for which the path in joint space is already specified, this work represents, to the best of the authors' knowledge, the first approach for generating near global optima for minimum-time problems involving a nonlinear class of dynamic systems. The reason the optima generated are near global optima instead of exactly global optima is due to a discrete-time approximation of the system (which is usually used anyway to simulate such a system numerically). The method closely resembles previous methods for generating minimum-time trajectories for linear systems, where the core operation is the solution of a Phase I linear programming problem. For the nonlinear systems considered herein, the core operation is instead the solution of a mixed integer linear programming problem.
Solution for integer linear bilevel programming problems using orthogonal genetic algorithm
Institute of Scientific and Technical Information of China (English)
Hong Li; Li Zhang; Yongchang Jiao
2014-01-01
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit program-ming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the ortho-gonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as off-spring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algo-rithm.
On nonlinear control design for autonomous chaotic systems of integer and fractional orders
Energy Technology Data Exchange (ETDEWEB)
Ahmad, Wajdi M. E-mail: wajdi@sharjah.ac.ae; Harb, Ahmad M. E-mail: aharb@just.edu.jo
2003-11-01
In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations.
An Integer Linear Programming Model for the Radiotherapy Treatment Scheduling Problem
Burke, Edmund K; Petrovic, Sanja
2011-01-01
Radiotherapy represents an important phase of treatment for a large number of cancer patients. It is essential that resources used to deliver this treatment are employed effectively. This paper presents a new integer linear programming model for real-world radiotherapy treatment scheduling and analyses the effectiveness of using this model on a daily basis in a hospital. Experiments are conducted varying the days on which schedules can be created. Results obtained using real-world data from the Nottingham University Hospitals NHS Trust, UK, are presented and show how the proposed model can be used with different policies in order to achieve good quality schedules.
An Integer Programming Formulation of the Minimum Common String Partition Problem.
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S M Ferdous
Full Text Available We consider the problem of finding a minimum common string partition (MCSP of two strings, which is an NP-hard problem. The MCSP problem is closely related to genome comparison and rearrangement, an important field in Computational Biology. In this paper, we map the MCSP problem into a graph applying a prior technique and using this graph, we develop an Integer Linear Programming (ILP formulation for the problem. We implement the ILP formulation and compare the results with the state-of-the-art algorithms from the literature. The experimental results are found to be promising.
Edit distance for marked point processes revisited: An implementation by binary integer programming
Energy Technology Data Exchange (ETDEWEB)
Hirata, Yoshito; Aihara, Kazuyuki [Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505 (Japan)
2015-12-15
We implement the edit distance for marked point processes [Suzuki et al., Int. J. Bifurcation Chaos 20, 3699–3708 (2010)] as a binary integer program. Compared with the previous implementation using minimum cost perfect matching, the proposed implementation has two advantages: first, by using the proposed implementation, we can apply a wide variety of software and hardware, even spin glasses and coherent ising machines, to calculate the edit distance for marked point processes; second, the proposed implementation runs faster than the previous implementation when the difference between the numbers of events in two time windows for a marked point process is large.
DEFF Research Database (Denmark)
Jensen, Toke Koldborg; Kjærsgaard, Niels Christian
Slaughterhouses are major players in the pork supply chain, and supply and demand must be matched in order to generate the highest proﬁt. In particular, carcasses must be sorted in order to produce the “right” ﬁnal products from the “right” carcasses. We develop a mixed-integer programming (MIP) ...... at slaughterhouses. Finally, we comment on the expected effect of variations in the raw material supply and the demand as well as future research concerning joint modelling of supply chain aspects....
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.
Huang, Kai; Huang, Gordon; Dai, Liming; Fan, Yurui
2016-08-01
This article introduces an inexact fuzzy integer chance constraint programming (IFICCP) approach for identifying noise reduction strategy under uncertainty. The IFICCP method integrates the interval programming and fuzzy chance constraint programming approaches into a framework, which is able to deal with uncertainties expressed as intervals and fuzziness. The proposed IFICCP model can be converted into two deterministic submodels corresponding to the optimistic and pessimistic conditions. The modelling approach is applied to a hypothetical control measure selection problem for noise reduction. Results of the case study indicate that useful solutions for noise control practices can be acquired. Three acceptable noise levels for two communities are considered. For each acceptable noise level, several decision alternatives have been obtained and analysed under different fuzzy confidence levels, which reflect the trade-offs between environmental and economic considerations.
Nonlinear programming analysis and methods
Avriel, Mordecai
2003-01-01
Comprehensive and complete, this overview provides a single-volume treatment of key algorithms and theories. The author provides clear explanations of all theoretical aspects, with rigorous proof of most results. The two-part treatment begins with the derivation of optimality conditions and discussions of convex programming, duality, generalized convexity, and analysis of selected nonlinear programs. The second part concerns techniques for numerical solutions and unconstrained optimization methods, and it presents commonly used algorithms for constrained nonlinear optimization problems. This g
Sakakibara, Kazutoshi; Tian, Yajie; Nishikawa, Ikuko
We discuss the planning of transportation by trucks over a multi-day period. Each truck collects loads from suppliers and delivers them to assembly plants or a truck terminal. By exploiting the truck terminal as a temporal storage, we aim to increase the load ratio of each truck and to minimize the lead time for transportation. In this paper, we show a mixed integer programming model which represents each product explicitly, and discuss the decomposition of the problem into a problem of delivery and storage, and a problem of vehicle routing. Based on this model, we propose a relax-and-fix type heuristic in which decision variables are fixed one by one by mathematical programming techniques such as branch-and-bound methods.
A Base Integer Programming Model and Benchmark Suite for Liner-Shipping Network Design
DEFF Research Database (Denmark)
Brouer, Berit Dangaard; Alvarez, Fernando; Plum, Christian Edinger Munk
2014-01-01
sources of liner shipping for OR researchers in general. We describe and analyze the liner-shipping domain applied to network design and present a rich integer programming model based on services that constitute the fixed schedule of a liner shipping company. We prove the liner-shipping network design...... problem to be strongly NP-hard. A benchmark suite of data instances to reflect the business structure of a global liner shipping network is presented. The design of the benchmark suite is discussed in relation to industry standards, business rules, and mathematical programming. The data are based on real......The liner-shipping network design problem is to create a set of nonsimple cyclic sailing routes for a designated fleet of container vessels that jointly transports multiple commodities. The objective is to maximize the revenue of cargo transport while minimizing the costs of operation...
Gorissen, Bram L; Hoffmann, Aswin L
2014-01-01
Current inverse treatment planning methods that optimize both catheter positions and dwell times in prostate HDR brachytherapy use surrogate linear or quadratic objective functions that have no direct interpretation in terms of dose-volume histogram (DVH) criteria, do not result in an optimum or have long solution times. We decrease the solution time of existing linear and quadratic dose-based programming models (LP and QP, respectively) to allow optimizing over potential catheter positions using mixed integer programming. An additional average speed-up of 75% can be obtained by stopping the solver at an early stage, without deterioration of the plan quality. For a fixed catheter configuration, the dwell time optimization model LP solves to optimality in less than 15 seconds, which confirms earlier results. We propose an iterative procedure for QP that allows to prescribe the target dose as an interval, while retaining independence between the solution time and the number of dose calculation points. This iter...
Donoghue, John R.
2015-01-01
At the heart of van der Linden's approach to automated test assembly (ATA) is a linear programming/integer programming (LP/IP) problem. A variety of IP solvers are available, ranging in cost from free to hundreds of thousands of dollars. In this paper, I compare several approaches to solving the underlying IP problem. These approaches range from…
Wu, Z; Zhang, Y
2008-01-01
The double digestion problem for DNA restriction mapping has been proved to be NP-complete and intractable if the numbers of the DNA fragments become large. Several approaches to the problem have been tested and proved to be effective only for small problems. In this paper, we formulate the problem as a mixed-integer linear program (MIP) by following (Waterman, 1995) in a slightly different form. With this formulation and using state-of-the-art integer programming techniques, we can solve randomly generated problems whose search space sizes are many-magnitude larger than previously reported testing sizes.
Canepa, Edward S.
2012-09-01
This article presents a new mixed integer programming formulation of the traffic density estimation problem in highways modeled by the Lighthill Whitham Richards equation. We first present an equivalent formulation of the problem using an Hamilton-Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton-Jacobi equation result in linear constraints, albeit with unknown integers. We then pose the problem of estimating the density at the initial time given incomplete and inaccurate traffic data as a Mixed Integer Program. We then present a numerical implementation of the method using experimental flow and probe data obtained during Mobile Century experiment. © 2012 IEEE.
A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm
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Godfrey Chagwiza
2016-01-01
Full Text Available In this paper, a feed ration problem is presented as a mixed integer programming problem. An attempt to find the optimal quantities of Moringa oleifera inclusion into the poultry feed ration was done and the problem was solved using the Bat algorithm and the Cplex solver. The study used findings of previous research to investigate the effects of Moringa oleifera inclusion in poultry feed ration. The results show that the farmer is likely to gain US$0.89 more if Moringa oleifera is included in the feed ration. Results also show superiority of the Bat algorithm in terms of execution time and number of iterations required to find the optimum solution as compared with the results obtained by the Cplex solver. Results revealed that there is a significant economic benefit of Moringa oleifera inclusion into the poultry feed ration.
A ZERO-ONE INTEGER PROGRAMMING MODEL FOR THE DESIGN OF MANUFACTURING CELLS
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C R SHIYAS
2012-01-01
Full Text Available Cellular manufacturing is an efficient approach for implementing the principles of Group Technology in a manufacturing environment wherein families of parts with similar manufacturing processes are grouped together to process in different manufacturing cells. The issues and different approaches used for a cellular manufacturing system (CMS design are described and its merits and demerits are discussed in this paper. A linear integer programming model for the design of manufacturing cells is suggested and the model minimizes the intercell moves for the given part-machine incidence matrix. A genetic algorithm (GA based solution procedure is suggested for the mathematical model which provides cell configuration. This GA is integrated with a part assignment rule to get both the cell and part family configurations. The GA is validated using software package, LINGO. Illustrative examples show the validity of the formulation and efficiency of the model.
An Integer Linear Programming Solution to the Telescope Network Scheduling Problem
Lampoudi, Sotiria; Eastman, Jason
2015-01-01
Telescope networks are gaining traction due to their promise of higher resource utilization than single telescopes and as enablers of novel astronomical observation modes. However, as telescope network sizes increase, the possibility of scheduling them completely or even semi-manually disappears. In an earlier paper, a step towards software telescope scheduling was made with the specification of the Reservation formalism, through the use of which astronomers can express their complex observation needs and preferences. In this paper we build on that work. We present a solution to the discretized version of the problem of scheduling a telescope network. We derive a solvable integer linear programming (ILP) model based on the Reservation formalism. We show computational results verifying its correctness, and confirm that our Gurobi-based implementation can address problems of realistic size. Finally, we extend the ILP model to also handle the novel observation requests that can be specified using the more advanc...
Mixed-Integer Linear Programming Models for Teaching Assistant Assignment and Extensions
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Xiaobo Qu
2017-01-01
Full Text Available In this paper, we develop mixed-integer linear programming models for assigning the most appropriate teaching assistants to the tutorials in a department. The objective is to maximize the number of tutorials that are taught by the most suitable teaching assistants, accounting for the fact that different teaching assistants have different capabilities and each teaching assistant’s teaching load cannot exceed a maximum value. Moreover, with optimization models, the teaching load allocation, a time-consuming process, does not need to be carried out in a manual manner. We have further presented a number of extensions that capture more practical considerations. Extensive numerical experiments show that the optimization models can be solved by an off-the-shelf solver and used by departments in universities.
An integer programming framework for inferring disease complexes from network data
Mazza, Arnon; Klockmeier, Konrad; Wanker, Erich; Sharan, Roded
2016-01-01
Motivation: Unraveling the molecular mechanisms that underlie disease calls for methods that go beyond the identification of single causal genes to inferring larger protein assemblies that take part in the disease process. Results: Here, we develop an exact, integer-programming-based method for associating protein complexes with disease. Our approach scores proteins based on their proximity in a protein–protein interaction network to a prior set that is known to be relevant for the studied disease. These scores are combined with interaction information to infer densely interacting protein complexes that are potentially disease-associated. We show that our method outperforms previous ones and leads to predictions that are well supported by current experimental data and literature knowledge. Availability and Implementation: The datasets we used, the executables and the results are available at www.cs.tau.ac.il/roded/disease_complexes.zip Contact: roded@post.tau.ac.il PMID:27307626
Applicability of a Novel Integer Programming Model for Wireless Sensor Networks
de Aguiar, Alexei Barbosa; Pinheiro, Placido Rogerio; Coelho, Andre L V
2009-01-01
This paper presents an applicability analysis over a novel integer programming model devoted to optimize power consumption efficiency in heterogeneous wireless sensor networks. This model is based upon a schedule of sensor allocation plans in multiple time intervals subject to coverage and connectivity constraints. By turning off a specific set of redundant sensors in each time interval, it is possible to reduce the total energy consumption in the network and, at the same time, avoid partitioning the whole network by losing some strategic sensors too prematurely. Since the network is heterogeneous, sensors can sense different phenomena from different demand points, with different sample rates. As the problem instances grows the time spent to the execution turns impracticable.
An integer programming model for gate assignment problem at airline terminals
Chun, Chong Kok; Nordin, Syarifah Zyurina
2015-05-01
In this paper, we concentrate on a gate assignment problem (GAP) at the airlines terminal. Our problem is to assign an arrival plane to a suitable gate. There are two considerations needed to take. One of its is passenger walking distance from arrival gate to departure gate while another consideration is the transport baggage distance from one gate to another. Our objective is to minimize the total distance between the gates that related to assign the arrival plane to the suitable gates. An integer linear programming (ILP) model is proposed to solve this gate assignment problem. We also conduct a computational experiment using CPLEX 12.1 solver in AIMMS 3.10 software to analyze the performance of the model. Results of the computational experiments are presented. The efficiency of flights assignment is depends on the ratio of the weight for both total passenger traveling distances and total baggage transport distances.
Energy Technology Data Exchange (ETDEWEB)
Souza Filho, Erito M.; Bahiense, Laura; Ferreira Filho, Virgilio J.M. [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia (COPPE); Lima, Leonardo [Centro Federal de Educacao Tecnologica Celso Sukow da Fonseca (CEFET-RJ), Rio de Janeiro, RJ (Brazil)
2008-07-01
Pipeline are known as the most reliable and economical mode of transportation for petroleum and its derivatives, especially when large amounts of products have to be pumped for large distances. In this work we address the short-term schedule of a pipeline system comprising the distribution of several petroleum derivatives from a single oil refinery to several depots, connected to local consumer markets, through a single multi-product pipeline. We propose an integer linear programming formulation and a variable neighborhood search meta-heuristic in order to compare the performances of the exact and heuristic approaches to the problem. Computational tests in C language and MOSEL/XPRESS-MP language are performed over a real Brazilian pipeline system. (author)
An integer programming model and benchmark suite for liner shipping network design
DEFF Research Database (Denmark)
Løfstedt, Berit; Alvarez, Jose Fernando; Plum, Christian Edinger Munk
along with a rich integer programming model based on the services, that constitute the fixed schedule of a liner shipping company. The model may be relaxed as well as decomposed. The design of a benchmark suite of data instances to reflect the business structure of a global liner shipping network......Maritime transportation is accountable for 2.7% of the worlds CO2 emissions and the liner shipping industry is committed to a slow steaming policy to provide low cost and environmentally conscious global transport of goods without compromising the level of service. The potential for making cost...... effective and energy efficient liner shipping networks using operations research is huge and neglected. The implementation of logistic planning tools based upon operations research has enhanced performance of both airlines, railways and general transportation companies, but within the field of liner...
DEFF Research Database (Denmark)
Liu, Zhaoxi; Wu, Qiuwei; Oren, Shmuel S.
2016-01-01
This paper presents a distribution locational marginal pricing (DLMP) method through chance constrained mixed-integer programming designed to alleviate the possible congestion in the future distribution network with high penetration of electric vehicles (EVs). In order to represent the stochastic...... the driving requirement is below the predetermined confidence parameter. The efficacy of the proposed approach was demonstrated by case studies using a 33-bus distribution system of the Bornholm power system and the Danish driving data. The case study results show that the DLMP method through chance...... constrained MIP can successfully alleviate the congestion in the distribution network due to the EV charging while keeping the failure probability of EV charging not meeting driving needs below the predefined confidence....
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 problem...
1980-05-31
34 AIIE Transac- tions, Vol. 11, Nc, 1, March 1979, pp. 61-69. (8] Taylor, Bernard and Keown , Arthur J., "A Goal Programming Application of Capital...Programming," OMEGA, Vol. 1, No. 2, April 1973, pp. 193-205. [29] Lee, S. M., and Keown , Arthur J., "Integer Goal Programming Model for Capital...Hadley, G., Linear Algebra, Addison-Wesley Publishing Co., Inc., Reading, MA, 1961. [60] Zuckerman, Martin M., Sets and Transfinite Numbers, Macmillan
LINEAR AND NONLINEAR SEMIDEFINITE PROGRAMMING
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Walter Gómez Bofill
2014-12-01
Full Text Available This paper provides a short introduction to optimization problems with semidefinite constraints. Basic duality and optimality conditions are presented. For linear semidefinite programming some advances by dealing with degeneracy and the semidefinite facial reduction are discussed. Two relatively recent areas of application are presented. Finally a short overview of relevant literature on algorithmic approaches for efficiently solving linear and nonlinear semidefinite programming is provided.
Application of mixed-integer linear programming in a car seats assembling process
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Jorge Iván Perez Rave
2011-12-01
Full Text Available In this paper, a decision problem involving a car parts manufacturing company is modeled in order to prepare the company for an increase in demand. Mixed-integer linear programming was used with the following decision variables: creating a second shift, purchasing additional equipment, determining the required work force, and other alternatives involving new manners of work distribution that make it possible to separate certain operations from some workplaces and integrate them into others to minimize production costs. The model was solved using GAMS. The solution consisted of programming 19 workers under a configuration that merges two workplaces and separates some operations from some workplaces. The solution did not involve purchasing additional machinery or creating a second shift. As a result, the manufacturing paradigms that had been valid in the company for over 14 years were broken. This study allowed the company to increase its productivity and obtain significant savings. It also shows the benefits of joint work between academia and companies, and provides useful information for professors, students and engineers regarding production and continuous improvement.
Mixed Integer Linear Programming For Exact Finite-Horizon Planning In Decentralized Pomdps
Aras, Raghav; Charpillet, Fran\\ccois
2007-01-01
We consider the problem of finding an n-agent joint-policy for the optimal finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem of very high complexity (NEXP-hard in n >= 2). In this paper, we propose a new mathematical programming approach for the problem. Our approach is based on two ideas: First, we represent each agent's policy in the sequence-form and not in the tree-form, thereby obtaining a very compact representation of the set of joint-policies. Second, using this compact representation, we solve this problem as an instance of combinatorial optimization for which we formulate a mixed integer linear program (MILP). The optimal solution of the MILP directly yields an optimal joint-policy for the Dec-Pomdp. Computational experience shows that formulating and solving the MILP requires significantly less time to solve benchmark Dec-Pomdp problems than existing algorithms. For example, the multi-agent tiger problem for horizon 4 is solved in 72 secs with the MILP whereas existing ...
Serna, Maria; Trevisan, Luca; Xhafa, Fatos
We present parallel approximation algorithms for maximization problems expressible by integer linear programs of a restricted syntactic form introduced by Barland et al. [BKT96]. One of our motivations was to show whether the approximation results in the framework of Barland et al. holds in the parallel setting. Our results are a confirmation of this, and thus we have a new common framework for both computational settings. Also, we prove almost tight non-approximability results, thus solving a main open question of Barland et al. We obtain the results through the constraint satisfaction problem over multi-valued domains, for which we show non-approximability results and develop parallel approximation algorithms. Our parallel approximation algorithms are based on linear programming and random rounding; they are better than previously known sequential algorithms. The non-approximability results are based on new recent progress in the fields of Probabilistically Checkable Proofs and Multi-Prover One-Round Proof Systems [Raz95, Hås97, AS97, RS97].
Uncovering signal transduction networks from high-throughput data by integer linear programming.
Zhao, Xing-Ming; Wang, Rui-Sheng; Chen, Luonan; Aihara, Kazuyuki
2008-05-01
Signal transduction is an important process that transmits signals from the outside of a cell to the inside to mediate sophisticated biological responses. Effective computational models to unravel such a process by taking advantage of high-throughput genomic and proteomic data are needed to understand the essential mechanisms underlying the signaling pathways. In this article, we propose a novel method for uncovering signal transduction networks (STNs) by integrating protein interaction with gene expression data. Specifically, we formulate STN identification problem as an integer linear programming (ILP) model, which can be actually solved by a relaxed linear programming algorithm and is flexible for handling various prior information without any restriction on the network structures. The numerical results on yeast MAPK signaling pathways demonstrate that the proposed ILP model is able to uncover STNs or pathways in an efficient and accurate manner. In particular, the prediction results are found to be in high agreement with current biological knowledge and available information in literature. In addition, the proposed model is simple to be interpreted and easy to be implemented even for a large-scale system.
He, Li; Huang, Guo-He; Zeng, Guang-Ming; Lu, Hong-Wei
2009-01-01
The previous inexact mixed-integer linear programming (IMILP) method can only tackle problems with coefficients of the objective function and constraints being crisp intervals, while the existing inexact mixed-integer semi-infinite programming (IMISIP) method can only deal with single-objective programming problems as it merely allows the number of constraints to be infinite. This study proposes, an inexact mixed-integer bi-infinite programming (IMIBIP) method by incorporating the concept of functional intervals into the programming framework. Different from the existing methods, the IMIBIP can tackle the inexact programming problems that contain both infinite objectives and constraints. The developed method is applied to capacity planning of waste management systems under a variety of uncertainties. Four scenarios are considered for comparing the solutions of IMIBIP with those of IMILP. The results indicate that reasonable solutions can be generated by the IMIBIP method. Compared with IMILP, the system cost from IMIBIP would be relatively high since the fluctuating market factors are considered; however, the IMILP solutions are associated with a raised system reliability level and a reduced constraint violation risk level.
A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem
Montoya, Justin Vincent; Wood, Zachary Paul; Rathinam, Sivakumar; Malik, Waqar Ahmad
2010-01-01
Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.
Optimal Airport Surface Traffic Planning Using Mixed-Integer Linear Programming
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P. C. Roling
2008-01-01
Full Text Available We describe an ongoing research effort pertaining to the development of a surface traffic automation system that will help controllers to better coordinate surface traffic movements related to arrival and departure traffic. More specifically, we describe the concept for a taxi-planning support tool that aims to optimize the routing and scheduling of airport surface traffic in such a way as to deconflict the taxi plans while optimizing delay, total taxi-time, or some other airport efficiency metric. Certain input parameters related to resource demand, such as the expected landing times and the expected pushback times, are rather difficult to predict accurately. Due to uncertainty in the input data driving the taxi-planning process, the taxi-planning tool is designed such that it produces solutions that are robust to uncertainty. The taxi-planning concept presented herein, which is based on mixed-integer linear programming, is designed such that it is able to adapt to perturbations in these input conditions, as well as to account for failure in the actual execution of surface trajectories. The capabilities of the tool are illustrated in a simple hypothetical airport.
Real-Time Hybrid In-Station Bus Dispatching Strategy Based on Mixed Integer Programming
Directory of Open Access Journals (Sweden)
Shi An
2016-07-01
Full Text Available The actual bus headway often deviates from the planned departure frequency because of external factors, such as traffic conditions and public transport demand, leading to transit resource waste and reducing the quality of service. In view of the existing shortcomings of the current dispatching strategy, a mixed integer programming model, integrating a bus-holding and stop-skipping strategy, is constructed to improve transit service with a minimum cost. The real-time optimal holding and stop-skipping strategies can be obtained by solving the proposed model using the Lagrangian relaxation algorithm. A numerical example is conducted using real transit GPS (Global Position System and IC (Intelligent Card data in Harbin. The results show that compared to a single control strategy, the proposed hybrid model is a better trade-off between the quality of the transit service and the operation cost. Notably, such a strategy would produce a minimal passengers’ average travel time coefficient. It is a great help for promoting the transit service level and increasing competitiveness.
Poos, Alexandra M; Maicher, André; Dieckmann, Anna K; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
2016-06-02
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments.
Poos, Alexandra M.; Maicher, André; Dieckmann, Anna K.; Oswald, Marcus; Eils, Roland; Kupiec, Martin; Luke, Brian; König, Rainer
2016-01-01
Understanding telomere length maintenance mechanisms is central in cancer biology as their dysregulation is one of the hallmarks for immortalization of cancer cells. Important for this well-balanced control is the transcriptional regulation of the telomerase genes. We integrated Mixed Integer Linear Programming models into a comparative machine learning based approach to identify regulatory interactions that best explain the discrepancy of telomerase transcript levels in yeast mutants with deleted regulators showing aberrant telomere length, when compared to mutants with normal telomere length. We uncover novel regulators of telomerase expression, several of which affect histone levels or modifications. In particular, our results point to the transcription factors Sum1, Hst1 and Srb2 as being important for the regulation of EST1 transcription, and we validated the effect of Sum1 experimentally. We compiled our machine learning method leading to a user friendly package for R which can straightforwardly be applied to similar problems integrating gene regulator binding information and expression profiles of samples of e.g. different phenotypes, diseases or treatments. PMID:26908654
A mixed integer linear programming model applied in barge planning for Omya
Directory of Open Access Journals (Sweden)
David Bredström
2015-12-01
Full Text Available This article presents a mathematical model for barge transport planning on the river Rhine, which is part of a decision support system (DSS recently taken into use by the Swiss company Omya. The system is operated by Omya’s regional office in Cologne, Germany, responsible for distribution planning at the regional distribution center (RDC in Moerdijk, the Netherlands. The distribution planning is a vital part of supply chain management of Omya’s production of Norwegian high quality calcium carbonate slurry, supplied to European paper manufacturers. The DSS operates within a vendor managed inventory (VMI setting, where the customer inventories are monitored by Omya, who decides upon the refilling days and quantities delivered by barges. The barge planning problem falls into the category of inventory routing problems (IRP and is further characterized with multiple products, heterogeneous fleet with availability restrictions (the fleet is owned by third party, vehicle compartments, dependency of barge capacity on water-level, multiple customer visits, bounded customer inventories and rolling planning horizon. There are additional modelling details which had to be considered to make it possible to employ the model in practice at a sufficient level of detail. To the best of our knowledge, we have not been able to find similar models covering all these aspects in barge planning. This article presents the developed mixed-integer programming model and discusses practical experience with its solution. Briefly, it also puts the model into the context of the entire business case of value chain optimization in Omya.
iPoint: an integer programming based algorithm for inferring protein subnetworks.
Atias, Nir; Sharan, Roded
2013-07-01
Large scale screening experiments have become the workhorse of molecular biology, producing data at an ever increasing scale. The interpretation of such data, particularly in the context of a protein interaction network, has the potential to shed light on the molecular pathways underlying the phenotype or the process in question. A host of approaches have been developed in recent years to tackle this reconstruction challenge. These approaches aim to infer a compact subnetwork that connects the genes revealed by the screen while optimizing local (individual path lengths) or global (likelihood) aspects of the subnetwork. Yosef et al. [Mol. Syst. Biol., 2009, 5, 248] were the first to provide a joint optimization of both criteria, albeit approximate in nature. Here we devise an integer linear programming formulation for the joint optimization problem, allowing us to solve it to optimality in minutes on current networks. We apply our algorithm, iPoint, to various data sets in yeast and human and evaluate its performance against state-of-the-art algorithms. We show that iPoint attains very compact and accurate solutions that outperform previous network inference algorithms with respect to their local and global attributes, their consistency across multiple experiments targeting the same pathway, and their agreement with current biological knowledge.
Uncluttered Single-Image Visualization of Vascular Structures Using GPU and Integer Programming.
Won, Joong-Ho; Jeon, Yongkweon; Rosenberg, Jarrett K; Yoon, Sungroh; Rubin, Geoffrey D; Napel, Sandy
2013-01-01
Direct projection of 3D branching structures, such as networks of cables, blood vessels, or neurons onto a 2D image creates the illusion of intersecting structural parts and creates challenges for understanding and communication. We present a method for visualizing such structures, and demonstrate its utility in visualizing the abdominal aorta and its branches, whose tomographic images might be obtained by computed tomography or magnetic resonance angiography, in a single 2D stylistic image, without overlaps among branches. The visualization method, termed uncluttered single-image visualization (USIV), involves optimization of geometry. This paper proposes a novel optimization technique that utilizes an interesting connection of the optimization problem regarding USIV to the protein structure prediction problem. Adopting the integer linear programming-based formulation for the protein structure prediction problem, we tested the proposed technique using 30 visualizations produced from five patient scans with representative anatomical variants in the abdominal aortic vessel tree. The novel technique can exploit commodity-level parallelism, enabling use of general-purpose graphics processing unit (GPGPU) technology that yields a significant speedup. Comparison of the results with the other optimization technique previously reported elsewhere suggests that, in most aspects, the quality of the visualization is comparable to that of the previous one, with a significant gain in the computation time of the algorithm.
Li, Zhenping; Zhang, Xiang-Sun; Wang, Rui-Sheng; Liu, Hongwei; Zhang, Shihua
2013-01-01
Identification of communities in complex networks is an important topic and issue in many fields such as sociology, biology, and computer science. Communities are often defined as groups of related nodes or links that correspond to functional subunits in the corresponding complex systems. While most conventional approaches have focused on discovering communities of nodes, some recent studies start partitioning links to find overlapping communities straightforwardly. In this paper, we propose a new quantity function for link community identification in complex networks. Based on this quantity function we formulate the link community partition problem into an integer programming model which allows us to partition a complex network into overlapping communities. We further propose a genetic algorithm for link community detection which can partition a network into overlapping communities without knowing the number of communities. We test our model and algorithm on both artificial networks and real-world networks. The results demonstrate that the model and algorithm are efficient in detecting overlapping community structure in complex networks.
A mixed-integer linear programming approach to the reduction of genome-scale metabolic networks.
Röhl, Annika; Bockmayr, Alexander
2017-01-03
Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement. Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways. Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.
An integer programming for airplane rounting in the U.S. Center-TRACON
Directory of Open Access Journals (Sweden)
Srisawat Supsomboon
2015-06-01
Full Text Available Air travel has been a major transportation for commerce and tour in many countries. As the demand of air traffic has been increasing, air traffic management has confronted with poverty of handling the increase of the demand of runway facilities where congestion often takes place. In order to cope with such problems, runway efficiency enhancement or capacity increasing are taken into account. In air traffic management, the effective air space utilization and air control workload management can be improved by the use of many up-to-date technologies in forms of decision support tools. This study developed a computer-aided decision support model in the form of integer programming. The purpose of the model was to allocate airplanes arrival at U.S. Center-TRACON airspace to enter feeder gates and to design optimal routes along the track to runway. Results of optimal path of the airplanes throughout the TRACON air space system which yield a minimum delay were presented.
Directory of Open Access Journals (Sweden)
Vahid Reza Ghezavati
2011-01-01
Full Text Available This research defines a new application of mathematical modeling to design a cellular manufacturing system integrated with group scheduling and layout aspects in an uncertain decision space under a supply chain characteristics. The aim is to present a mixed integer programming (MIP which optimizes cell formation, scheduling and layout decisions, concurrently where the suppliers are required to operate exceptional products. For this purpose, the time in which parts need to be operated on machines and also products' demand are uncertain and explained by set of scenarios. This model tries to optimize expected holding cost and the costs regarded to the suppliers network in a supply chain in order to outsource exceptional operations. Scheduling decisions in a cellular manufacturing framework is treated as group scheduling problem, which assumes that all parts in a part group are operated in the same cell and no inter-cellular transfer is required. An efficient hybrid method made of genetic algorithm (GA and simulated annealing (SA will be proposed to solve such a complex problem under an optimization rule as a sub-ordinate section. This integrative combination algorithm is compared with global solutions and also, a benchmark heuristic algorithm introduced in the literature. Finally, performance of the algorithm will be verified through some test problems.
Energy Technology Data Exchange (ETDEWEB)
Santos Coelho, Leandro dos [Industrial and Systems Engineering Graduate Program, LAS/PPGEPS, Pontifical Catholic University of Parana, PUCPR, Imaculada Conceicao, 1155, 80215-901 Curitiba, Parana (Brazil)], E-mail: leandro.coelho@pucpr.br
2009-04-15
The reliability-redundancy optimization problems can involve the selection of components with multiple choices and redundancy levels that produce maximum benefits, and are subject to the cost, weight, and volume constraints. Many classical mathematical methods have failed in handling nonconvexities and nonsmoothness in reliability-redundancy optimization problems. As an alternative to the classical optimization approaches, the meta-heuristics have been given much attention by many researchers due to their ability to find an almost global optimal solutions. One of these meta-heuristics is the particle swarm optimization (PSO). PSO is a population-based heuristic optimization technique inspired by social behavior of bird flocking and fish schooling. This paper presents an efficient PSO algorithm based on Gaussian distribution and chaotic sequence (PSO-GC) to solve the reliability-redundancy optimization problems. In this context, two examples in reliability-redundancy design problems are evaluated. Simulation results demonstrate that the proposed PSO-GC is a promising optimization technique. PSO-GC performs well for the two examples of mixed-integer programming in reliability-redundancy applications considered in this paper. The solutions obtained by the PSO-GC are better than the previously best-known solutions available in the recent literature.
Baran, Richard; Northen, Trent R
2013-10-15
Untargeted metabolite profiling using liquid chromatography and mass spectrometry coupled via electrospray ionization is a powerful tool for the discovery of novel natural products, metabolic capabilities, and biomarkers. However, the elucidation of the identities of uncharacterized metabolites from spectral features remains challenging. A critical step in the metabolite identification workflow is the assignment of redundant spectral features (adducts, fragments, multimers) and calculation of the underlying chemical formula. Inspection of the data by experts using computational tools solving partial problems (e.g., chemical formula calculation for individual ions) can be performed to disambiguate alternative solutions and provide reliable results. However, manual curation is tedious and not readily scalable or standardized. Here we describe an automated procedure for the robust automated mass spectra interpretation and chemical formula calculation using mixed integer linear programming optimization (RAMSI). Chemical rules among related ions are expressed as linear constraints and both the spectra interpretation and chemical formula calculation are performed in a single optimization step. This approach is unbiased in that it does not require predefined sets of neutral losses and positive and negative polarity spectra can be combined in a single optimization. The procedure was evaluated with 30 experimental mass spectra and was found to effectively identify the protonated or deprotonated molecule ([M + H](+) or [M - H](-)) while being robust to the presence of background ions. RAMSI provides a much-needed standardized tool for interpreting ions for subsequent identification in untargeted metabolomics workflows.
Integer Linear Programming for Constrained Multi-Aspect Committee Review Assignment.
Karimzadehgan, Maryam; Zhai, Chengxiang
2012-07-01
Automatic review assignment can significantly improve the productivity of many people such as conference organizers, journal editors and grant administrators. A general setup of the review assignment problem involves assigning a set of reviewers on a committee to a set of documents to be reviewed under the constraint of review quota so that the reviewers assigned to a document can collectively cover multiple topic aspects of the document. No previous work has addressed such a setup of committee review assignments while also considering matching multiple aspects of topics and expertise. In this paper, we tackle the problem of committee review assignment with multi-aspect expertise matching by casting it as an integer linear programming problem. The proposed algorithm can naturally accommodate any probabilistic or deterministic method for modeling multiple aspects to automate committee review assignments. Evaluation using a multi-aspect review assignment test set constructed using ACM SIGIR publications shows that the proposed algorithm is effective and efficient for committee review assignments based on multi-aspect expertise matching.
Energy Technology Data Exchange (ETDEWEB)
Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami
2017-03-27
Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Results: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs.
Energy Technology Data Exchange (ETDEWEB)
Doolittle, R. [ONR, Arlington, VA (United States)
1994-11-15
The title integer anatomy is intended to convey the idea of a systematic method for displaying the prime decomposition of the integers. Just as the biological study of anatomy does not teach us all things about behavior of species neither would we expect to learn everything about the number theory from a study of its anatomy. But, some number-theoretic theorems are illustrated by inspection of integer anatomy, which tend to validate the underlying structure and the form as developed and displayed in this treatise. The first statement to be made in this development is: the way structure of the natural numbers is displayed depends upon the allowed operations.
Puchinger, Jakob; Raidl, Günther,
2004-01-01
International audience; We consider the 3-stage two-dimensional bin packing problem , which occurs in real-world problems such as glass cutting. For it, we present a new integer linear programming formulation and a branch and price algorithm. Column generation is performed by applying either a greedy heuristic or an Evolutionary Algorithm (EA). Computational experiments show the benefits of the EA-based approach. The higher computational effort of the EA pays off in terms of better final solu...
Institute of Scientific and Technical Information of China (English)
Ahmad A. Moreb
2007-01-01
Reliability allocation problem is commonly treated using a closed-form expression relating the cost to reliability. A recent approach has introduced the use of discrete integer technique for un-repairable systems. This research addresses the allocation problem for repairable systems. It presents an integer formulation for finding the optimum selection of components based on the integer values of their Mean Time to Failure (MTTF) and Mean Time to Repair (MTTR). The objective is to minimize the total cost under a system reliability constraint, in addition to other physical constraints. Although, a closed-form expression relating the cost to reliability may not be a linear; however, in this research, the objective function will always be linear regardless of the shape of the equivalent continuous closed-form function. An example is solved using the proposed method and compared with the solution of the continuous closed-form version. The formulation for all possible system configurations, components and subsystems are also considered.
Mixed-integer programming methods for transportation and power generation problems
Damci Kurt, Pelin
This dissertation conducts theoretical and computational research to solve challenging problems in application areas such as supply chain and power systems. The first part of the dissertation studies a transportation problem with market choice (TPMC) which is a variant of the classical transportation problem in which suppliers with limited capacities have a choice of which demands (markets) to satisfy. We show that TPMC is strongly NP-complete. We consider a version of the problem with a service level constraint on the maximum number of markets that can be rejected and show that if the original problem is polynomial, its cardinality-constrained version is also polynomial. We propose valid inequalities for mixed-integer cover and knapsack sets with variable upper bound constraints, which appear as substructures of TPMC and use them in a branch-and-cut algorithm to solve this problem. The second part of this dissertation studies a unit commitment (UC) problem in which the goal is to minimize the operational cost of power generators over a time period subject to physical constraints while satisfying demand. We provide several exponential classes of multi-period ramping and multi-period variable upper bound inequalities. We prove the strength of these inequalities and describe polynomial-time separation algorithms. Computational results show the effectiveness of the proposed inequalities when used as cuts in a branch-and-cut algorithm to solve the UC problem. The last part of this dissertation investigates the effects of uncertain wind power on the UC problem. A two-stage robust model and a three-stage stochastic program are compared.
Automated integer programming based separation of arteries and veins from thoracic CT images.
Payer, Christian; Pienn, Michael; Bálint, Zoltán; Shekhovtsov, Alexander; Talakic, Emina; Nagy, Eszter; Olschewski, Andrea; Olschewski, Horst; Urschler, Martin
2016-12-01
Automated computer-aided analysis of lung vessels has shown to yield promising results for non-invasive diagnosis of lung diseases. To detect vascular changes which affect pulmonary arteries and veins differently, both compartments need to be identified. We present a novel, fully automatic method that separates arteries and veins in thoracic computed tomography images, by combining local as well as global properties of pulmonary vessels. We split the problem into two parts: the extraction of multiple distinct vessel subtrees, and their subsequent labeling into arteries and veins. Subtree extraction is performed with an integer program (IP), based on local vessel geometry. As naively solving this IP is time-consuming, we show how to drastically reduce computational effort by reformulating it as a Markov Random Field. Afterwards, each subtree is labeled as either arterial or venous by a second IP, using two anatomical properties of pulmonary vessels: the uniform distribution of arteries and veins, and the parallel configuration and close proximity of arteries and bronchi. We evaluate algorithm performance by comparing the results with 25 voxel-based manual reference segmentations. On this dataset, we show good performance of the subtree extraction, consisting of very few non-vascular structures (median value: 0.9%) and merged subtrees (median value: 0.6%). The resulting separation of arteries and veins achieves a median voxel-based overlap of 96.3% with the manual reference segmentations, outperforming a state-of-the-art interactive method. In conclusion, our novel approach provides an opportunity to become an integral part of computer aided pulmonary diagnosis, where artery/vein separation is important.
Aspect-object alignment with Integer Linear Programming in opinion mining.
Directory of Open Access Journals (Sweden)
Yanyan Zhao
Full Text Available Target extraction is an important task in opinion mining. In this task, a complete target consists of an aspect and its corresponding object. However, previous work has always simply regarded the aspect as the target itself and has ignored the important "object" element. Thus, these studies have addressed incomplete targets, which are of limited use for practical applications. This paper proposes a novel and important sentiment analysis task, termed aspect-object alignment, to solve the "object neglect" problem. The objective of this task is to obtain the correct corresponding object for each aspect. We design a two-step framework for this task. We first provide an aspect-object alignment classifier that incorporates three sets of features, namely, the basic, relational, and special target features. However, the objects that are assigned to aspects in a sentence often contradict each other and possess many complicated features that are difficult to incorporate into a classifier. To resolve these conflicts, we impose two types of constraints in the second step: intra-sentence constraints and inter-sentence constraints. These constraints are encoded as linear formulations, and Integer Linear Programming (ILP is used as an inference procedure to obtain a final global decision that is consistent with the constraints. Experiments on a corpus in the camera domain demonstrate that the three feature sets used in the aspect-object alignment classifier are effective in improving its performance. Moreover, the classifier with ILP inference performs better than the classifier without it, thereby illustrating that the two types of constraints that we impose are beneficial.
Aspect-object alignment with Integer Linear Programming in opinion mining.
Zhao, Yanyan; Qin, Bing; Liu, Ting; Yang, Wei
2015-01-01
Target extraction is an important task in opinion mining. In this task, a complete target consists of an aspect and its corresponding object. However, previous work has always simply regarded the aspect as the target itself and has ignored the important "object" element. Thus, these studies have addressed incomplete targets, which are of limited use for practical applications. This paper proposes a novel and important sentiment analysis task, termed aspect-object alignment, to solve the "object neglect" problem. The objective of this task is to obtain the correct corresponding object for each aspect. We design a two-step framework for this task. We first provide an aspect-object alignment classifier that incorporates three sets of features, namely, the basic, relational, and special target features. However, the objects that are assigned to aspects in a sentence often contradict each other and possess many complicated features that are difficult to incorporate into a classifier. To resolve these conflicts, we impose two types of constraints in the second step: intra-sentence constraints and inter-sentence constraints. These constraints are encoded as linear formulations, and Integer Linear Programming (ILP) is used as an inference procedure to obtain a final global decision that is consistent with the constraints. Experiments on a corpus in the camera domain demonstrate that the three feature sets used in the aspect-object alignment classifier are effective in improving its performance. Moreover, the classifier with ILP inference performs better than the classifier without it, thereby illustrating that the two types of constraints that we impose are beneficial.
Integer Programming Formulation of the Problem of Generating Milton Babbitt's All-partition Arrays
DEFF Research Database (Denmark)
Tanaka, Tsubasa; Bemman, Brian; Meredith, David
2016-01-01
Milton Babbitt (1916–2011) was a composer of twelve-tone serial music noted for creating the all-partition array. The problem of generating an all-partition array involves finding a rectangular array of pitch-class integers that can be partitioned into regions, each of which represents a distinct...
An algorithm for the construction of convex hulls in simple integer recourse programming
Klein Haneveld, W.K.; Stougie, L.; van der Vlerk, M.H.
1996-01-01
We consider the objective function of a simple integer recourse problem with fixed technology matrix and discretely distributed right-hand sides. Exploiting the special structure of this problem, we devise an algorithm that determines the convex hull of this function efficiently. The results are imp
A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs
DEFF Research Database (Denmark)
Stidsen, Thomas Riis; Andersen, Kim Allan; Dammann, Bernd
2014-01-01
Pareto-optimal front). In this paper, we first give a survey of the newly developed branch and bound methods for solving MOMIP problems. After that, we propose a new branch and bound method for solving a subclass of MOMIP problems, where only two objectives are allowed, the integer variables are binary...
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...
Song, Hyun-Seob; Goldberg, Noam; Mahajan, Ashutosh; Ramkrishna, Doraiswami
2017-08-01
Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. The software is implemented in Matlab, and is provided as supplementary information . hyunseob.song@pnnl.gov. Supplementary data are available at Bioinformatics online.
Directory of Open Access Journals (Sweden)
Luis A. Rivera-Morales
2014-01-01
Full Text Available In this paper we propose a stochastic integer programming optimization model to determine the optimal location and number of rain water collectors (RWCs for forest firefighting. The objective is to minimize expected total cost to control forest fires. The model is tested using a real case and several additional realistic scenarios. The impact on the solution of varying the limit on the number of RWCs, the RWC water capacity, the aircraft capacity, the water demands, and the aircraft operating cost is explored. Some observations are that the objective value improves with larger RWCs and with the use of aircraft with greater capacity.
Safikhani, Zhaleh; Sadeghi, Mehdi; Pezeshk, Hamid; Eslahchi, Changiz
2013-01-01
Recent advances in the sequencing technologies have provided a handful of RNA-seq datasets for transcriptome analysis. However, reconstruction of full-length isoforms and estimation of the expression level of transcripts with a low cost are challenging tasks. We propose a novel de novo method named SSP that incorporates interval integer linear programming to resolve alternatively spliced isoforms and reconstruct the whole transcriptome from short reads. Experimental results show that SSP is fast and precise in determining different alternatively spliced isoforms along with the estimation of reconstructed transcript abundances. The SSP software package is available at http://www.bioinf.cs.ipm.ir/software/ssp.
Canepa, Edward S.
2013-09-01
Traffic sensing systems rely more and more on user generated (insecure) data, which can pose a security risk whenever the data is used for traffic flow control. In this article, we propose a new formulation for detecting malicious data injection in traffic flow monitoring systems by using the underlying traffic flow model. The state of traffic is modeled by the Lighthill- Whitham-Richards traffic flow model, which is a first order scalar conservation law with concave flux function. Given a set of traffic flow data generated by multiple sensors of different types, we show that the constraints resulting from this partial differential equation are mixed integer linear inequalities for a specific decision variable. We use this fact to pose the problem of detecting spoofing cyber attacks in probe-based traffic flow information systems as mixed integer linear feasibility problem. The resulting framework can be used to detect spoofing attacks in real time, or to evaluate the worst-case effects of an attack offliine. A numerical implementation is performed on a cyber attack scenario involving experimental data from the Mobile Century experiment and the Mobile Millennium system currently operational in Northern California. © American Institute of Mathematical Sciences.
Canepa, Edward S.
2013-01-01
Traffic sensing systems rely more and more on user generated (insecure) data, which can pose a security risk whenever the data is used for traffic flow control. In this article, we propose a new formulation for detecting malicious data injection in traffic flow monitoring systems by using the underlying traffic flow model. The state of traffic is modeled by the Lighthill-Whitham- Richards traffic flow model, which is a first order scalar conservation law with concave flux function. Given a set of traffic flow data, we show that the constraints resulting from this partial differential equation are mixed integer linear inequalities for some decision variable. We use this fact to pose the problem of detecting spoofing cyber-attacks in probe-based traffic flow information systems as mixed integer linear feasibility problem. The resulting framework can be used to detect spoofing attacks in real time, or to evaluate the worst-case effects of an attack offline. A numerical implementation is performed on a cyber-attack scenario involving experimental data from the Mobile Century experiment and the Mobile Millennium system currently operational in Northern California. © 2013 IEEE.
Integer and combinatorial optimization
Nemhauser, George L
1999-01-01
Rave reviews for INTEGER AND COMBINATORIAL OPTIMIZATION ""This book provides an excellent introduction and survey of traditional fields of combinatorial optimization . . . It is indeed one of the best and most complete texts on combinatorial optimization . . . available. [And] with more than 700 entries, [it] has quite an exhaustive reference list.""-Optima ""A unifying approach to optimization problems is to formulate them like linear programming problems, while restricting some or all of the variables to the integers. This book is an encyclopedic resource for such f
Directory of Open Access Journals (Sweden)
Wei Lu
Full Text Available In this paper, we consider the Minimum Reaction Insertion (MRI problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html."
Song, Jiangning; Akutsu, Tatsuya
2014-01-01
In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at “http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html.” PMID:24651476
Lu, Wei; Tamura, Takeyuki; Song, Jiangning; Akutsu, Tatsuya
2014-01-01
In this paper, we consider the Minimum Reaction Insertion (MRI) problem for finding the minimum number of additional reactions from a reference metabolic network to a host metabolic network so that a target compound becomes producible in the revised host metabolic network in a Boolean model. Although a similar problem for larger networks is solvable in a flux balance analysis (FBA)-based model, the solution of the FBA-based model tends to include more reactions than that of the Boolean model. However, solving MRI using the Boolean model is computationally more expensive than using the FBA-based model since the Boolean model needs more integer variables. Therefore, in this study, to solve MRI for larger networks in the Boolean model, we have developed an efficient Integer Programming formalization method in which the number of integer variables is reduced by the notion of feedback vertex set and minimal valid assignment. As a result of computer experiments conducted using the data of metabolic networks of E. coli and reference networks downloaded from the Kyoto Encyclopedia of Genes and Genomes (KEGG) database, we have found that the developed method can appropriately solve MRI in the Boolean model and is applicable to large scale-networks for which an exhaustive search does not work. We have also compared the developed method with the existing connectivity-based methods and FBA-based methods, and show the difference between the solutions of our method and the existing methods. A theoretical analysis of MRI is also conducted, and the NP-completeness of MRI is proved in the Boolean model. Our developed software is available at "http://sunflower.kuicr.kyoto-u.ac.jp/~rogi/minRect/minRect.html."
An Effective Branch-and-Bound Algorithm for Convex Quadratic Integer Programming
Buchheim, Christoph; Caprara, Alberto; Lodi, Andrea
We present a branch-and-bound algorithm for minimizing a convex quadratic objective function over integer variables subject to convex constraints. In a given node of the enumeration tree, corresponding to the fixing of a subset of the variables, a lower bound is given by the continuous minimum of the restricted objective function. We improve this bound by exploiting the integrality of the variables using suitably-defined lattice-free ellipsoids. Experiments show that our approach is very fast on both unconstrained problems and problems with box constraints. The main reason is that all expensive calculations can be done in a preprocessing phase, while a single node in the enumeration tree can be processed in linear time in the problem dimension.
Recent advances in multiparametric nonlinear programming
Domínguez, Luis F.
2010-05-01
In this paper, we present recent developments in multiparametric nonlinear programming. For the case of convex problems, we highlight key issues regarding the full characterization of the parametric solution space and we discuss, through an illustrative example problem, four alternative state-of-the-art multiparametric nonlinear programming algorithms. We also identify a number of main challenges for the non-convex case and highlight future research directions. © 2009 Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Mbarek Elbounjimi
2015-11-01
Full Text Available Closed-loop supply chain network design is a critical issue due to its impact on both economic and environmental performances of the supply chain. In this paper, we address the problem of designing a multi-echelon, multi-product and capacitated closed-loop supply chain network. First, a mixed-integer linear programming formulation is developed to maximize the total profit. The main contribution of the proposed model is addressing two economic viability issues of closed-loop supply chain. The first issue is the collection of sufficient quantity of end-of-life products are assured by retailers against an acquisition price. The second issue is exploiting the benefits of colocation of forward facilities and reverse facilities. The presented model is solved by LINGO for some test problems. Computational results and sensitivity analysis are conducted to show the performance of the proposed model.
Directory of Open Access Journals (Sweden)
H Kazemipoor
2012-04-01
Full Text Available A multi-skilled project scheduling problem (MSPSP has been generally presented to schedule a project with staff members as resources. Each activity in project network requires different skills and also staff members have different skills, too. This causes the MSPSP becomes a special type of a multi-mode resource-constrained project scheduling problem (MM-RCPSP with a huge number of modes. Given the importance of this issue, in this paper, a mixed integer linear programming for the MSPSP is presented. Due to the complexity of the problem, a meta-heuristic algorithm is proposed in order to find near optimal solutions. To validate performance of the algorithm, results are compared against exact solutions solved by the LINGO solver. The results are promising and show that optimal or near-optimal solutions are derived for small instances and good solutions for larger instances in reasonable time.
Institute of Scientific and Technical Information of China (English)
Hai-ning KONG
2015-01-01
Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to construct an integrated optimized system, taking economics, energy consumption and environment into consideration. Therefore, the environmental cost caused by pollutants discharge should be factored in total cost when optimizing byproduct gas distribution. A green mixed integer linear programming (MILP) model for the optimization of byproduct gases was established to reduce total cost, including both operation cost and environmental cost. The operation cost included penalty for gas deviation, costs of fuel and water consumption, holder booster trip penalty, and so forth; while the environmental cost consisted of penalties for both direct and indirect pollutants discharge. Case study showed that the proposed model brought an optimum solution and 2.2% of the total cost could be reduced compared with previous one.
Catanzaro, Daniele; Shackney, Stanley E; Schaffer, Alejandro A; Schwartz, Russell
2016-01-01
Ductal Carcinoma In Situ (DCIS) is a precursor lesion of Invasive Ductal Carcinoma (IDC) of the breast. Investigating its temporal progression could provide fundamental new insights for the development of better diagnostic tools to predict which cases of DCIS will progress to IDC. We investigate the problem of reconstructing a plausible progression from single-cell sampled data of an individual with synchronous DCIS and IDC. Specifically, by using a number of assumptions derived from the observation of cellular atypia occurring in IDC, we design a possible predictive model using integer linear programming (ILP). Computational experiments carried out on a preexisting data set of 13 patients with simultaneous DCIS and IDC show that the corresponding predicted progression models are classifiable into categories having specific evolutionary characteristics. The approach provides new insights into mechanisms of clonal progression in breast cancers and helps illustrate the power of the ILP approach for similar problems in reconstructing tumor evolution scenarios under complex sets of constraints.
Integer Quadratic Quasi-polyhedra
Letchford, Adam N.
This paper introduces two fundamental families of 'quasi-polyhedra' - polyhedra with a countably infinite number of facets - that arise in the context of integer quadratic programming. It is shown that any integer quadratic program can be reduced to the minimisation of a linear function over a quasi-polyhedron in the first family. Some fundamental properties of the quasi-polyhedra are derived, along with connections to some other well-studied convex sets. Several classes of facet-inducing inequalities are also derived. Finally, extensions to the mixed-integer case are briefly examined.
Mixed integer evolution strategies for parameter optimization.
Li, Rui; Emmerich, Michael T M; Eggermont, Jeroen; Bäck, Thomas; Schütz, M; Dijkstra, J; Reiber, J H C
2013-01-01
Evolution strategies (ESs) are powerful probabilistic search and optimization algorithms gleaned from biological evolution theory. They have been successfully applied to a wide range of real world applications. The modern ESs are mainly designed for solving continuous parameter optimization problems. Their ability to adapt the parameters of the multivariate normal distribution used for mutation during the optimization run makes them well suited for this domain. In this article we describe and study mixed integer evolution strategies (MIES), which are natural extensions of ES for mixed integer optimization problems. MIES can deal with parameter vectors consisting not only of continuous variables but also with nominal discrete and integer variables. Following the design principles of the canonical evolution strategies, they use specialized mutation operators tailored for the aforementioned mixed parameter classes. For each type of variable, the choice of mutation operators is governed by a natural metric for this variable type, maximal entropy, and symmetry considerations. All distributions used for mutation can be controlled in their shape by means of scaling parameters, allowing self-adaptation to be implemented. After introducing and motivating the conceptual design of the MIES, we study the optimality of the self-adaptation of step sizes and mutation rates on a generalized (weighted) sphere model. Moreover, we prove global convergence of the MIES on a very general class of problems. The remainder of the article is devoted to performance studies on artificial landscapes (barrier functions and mixed integer NK landscapes), and a case study in the optimization of medical image analysis systems. In addition, we show that with proper constraint handling techniques, MIES can also be applied to classical mixed integer nonlinear programming problems.
The Quadratic Graver Cone, Quadratic Integer Minimization, and Extensions
Lee, Jon; Romanchuk, Lyubov; Weismantel, Robert
2010-01-01
We consider the nonlinear integer programming problem of minimizing a quadratic function over the integer points in variable dimension satisfying a system of linear inequalities. We show that when the Graver basis of the matrix defining the system is given, and the quadratic function lies in a suitable {\\em dual Graver cone}, the problem can be solved in polynomial time. We discuss the relation between this cone and the cone of positive semidefinite matrices, and show that none contains the other. So we can minimize in polynomial time some non-convex and some (including all separable) convex quadrics. We conclude by extending our results to efficient integer minimization of multivariate polynomial functions of arbitrary degree lying in suitable cones.
Solutions manual to accompany Nonlinear programming
Bazaraa, Mokhtar S; Shetty, C M
2014-01-01
As the Solutions Manual, this book is meant to accompany the main title, Nonlinear Programming: Theory and Algorithms, Third Edition. This book presents recent developments of key topics in nonlinear programming (NLP) using a logical and self-contained format. The volume is divided into three sections: convex analysis, optimality conditions, and dual computational techniques. Precise statements of algortihms are given along with convergence analysis. Each chapter contains detailed numerical examples, graphical illustrations, and numerous exercises to aid readers in understanding the concepts a
A Stability Theory in Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
We propose a new method for finding the local optimal points ofthe constrained nonlinear programming by Ordinary Differential Equations (ODE), and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
Optimality conditions in smooth nonlinear programming
Still, G.; Streng, M.
1996-01-01
This survey is concerned with necessary and sufficient optimality conditions for smooth nonlinear programming problems with inequality and equality constraints. These conditions deal with strict local minimizers of order one and two and with isolated minimizers. In most results, no constraint qualif
Solving a Class of Stochastic Mixed-Integer Programs With Branch and Price
2006-01-01
with time windows (Desrosiers et al. [26], Ribeiro and Soumis [46]) The vehicle routing problem with time windows (VRPTW) is one important exemplar from...procedures for solving mixed-variables programming problems. Numerische Mathematik 4, 238–252 (1962) 10. Bertsimas, D.J.: A vehicle routing problem with...Oper. Res. 45, 649–661 (1997) 24. Desrochers, M., Desrosiers, J., Solomon, M.: 1992. A new optimization algorithm for the vehicle routing problem with
Energy Technology Data Exchange (ETDEWEB)
Li, Y.F. [Energy and Environmental Research Center, North China Electric Power University, Beijing 102206 (China); Huang, G.H., E-mail: gordon.huang@uregina.c [Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan, S4S 0A2 (Canada); College of Urban and Environmental Sciences, Peking University, Beijing 100871 (China); Li, Y.P. [College of Urban and Environmental Sciences, Peking University, Beijing 100871 (China); Xu, Y.; Chen, W.T. [Energy and Environmental Research Center, North China Electric Power University, Beijing 102206 (China)
2010-01-15
In this study, a multistage interval-stochastic regional-scale energy model (MIS-REM) is developed for supporting electric power system (EPS) planning under uncertainty that is based on a multistage interval-stochastic integer linear programming method. The developed MIS-REM can deal with uncertainties expressed as both probability distributions and interval values existing in energy system planning problems. Moreover, it can reflect dynamic decisions for electricity generation schemes and capacity expansions through transactions at discrete points of a multiple representative scenario set over a multistage context. It can also analyze various energy-policy scenarios that are associated with economic penalties when the regulated targets are violated. A case study is provided for demonstrating the applicability of the developed model, where renewable and non-renewable energy resources, economic concerns, and environmental requirements are integrated into a systematic optimization process. The results obtained are helpful for supporting (a) adjustment or justification of allocation patterns of regional energy resources and services, (b) formulation of local policies regarding energy consumption, economic development, and energy structure, and (c) analysis of interactions among economic cost, environmental requirement, and energy-supply security.
Energy Technology Data Exchange (ETDEWEB)
Li, Y.F.; Xu, Y.; Chen, W.T. [Energy and Environmental Research Center, North China Electric Power University, Beijing 102206 (China); Huang, G.H. [Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan (Canada); College of Urban and Environmental Sciences, Peking University, Beijing 100871 (China); Li, Y.P. [College of Urban and Environmental Sciences, Peking University, Beijing 100871 (China)
2010-01-15
In this study, a multistage interval-stochastic regional-scale energy model (MIS-REM) is developed for supporting electric power system (EPS) planning under uncertainty that is based on a multistage interval-stochastic integer linear programming method. The developed MIS-REM can deal with uncertainties expressed as both probability distributions and interval values existing in energy system planning problems. Moreover, it can reflect dynamic decisions for electricity generation schemes and capacity expansions through transactions at discrete points of a multiple representative scenario set over a multistage context. It can also analyze various energy-policy scenarios that are associated with economic penalties when the regulated targets are violated. A case study is provided for demonstrating the applicability of the developed model, where renewable and non-renewable energy resources, economic concerns, and environmental requirements are integrated into a systematic optimization process. The results obtained are helpful for supporting (a) adjustment or justification of allocation patterns of regional energy resources and services, (b) formulation of local policies regarding energy consumption, economic development, and energy structure, and (c) analysis of interactions among economic cost, environmental requirement, and energy-supply security. (author)
Ryan, Jason C; Banerjee, Ashis Gopal; Cummings, Mary L; Roy, Nicholas
2014-06-01
Planning operations across a number of domains can be considered as resource allocation problems with timing constraints. An unexplored instance of such a problem domain is the aircraft carrier flight deck, where, in current operations, replanning is done without the aid of any computerized decision support. Rather, veteran operators employ a set of experience-based heuristics to quickly generate new operating schedules. These expert user heuristics are neither codified nor evaluated by the United States Navy; they have grown solely from the convergent experiences of supervisory staff. As unmanned aerial vehicles (UAVs) are introduced in the aircraft carrier domain, these heuristics may require alterations due to differing capabilities. The inclusion of UAVs also allows for new opportunities for on-line planning and control, providing an alternative to the current heuristic-based replanning methodology. To investigate these issues formally, we have developed a decision support system for flight deck operations that utilizes a conventional integer linear program-based planning algorithm. In this system, a human operator sets both the goals and constraints for the algorithm, which then returns a proposed schedule for operator approval. As a part of validating this system, the performance of this collaborative human-automation planner was compared with that of the expert user heuristics over a set of test scenarios. The resulting analysis shows that human heuristics often outperform the plans produced by an optimization algorithm, but are also often more conservative.
Directory of Open Access Journals (Sweden)
S. Mohammad Arabzad
2012-06-01
Full Text Available In recent years, numerous methods have been proposed to deal with supplier evaluation and selection problem, but a point which has been usually neglected by researchers is the role of purchasing items. The aim of this paper is to propose an integrated approach to select suppliers and allocate orders on the basis of the nature of the purchasing items which means that this issue plays an important role in supplier selection and order allocation. Therefore, items are first categorized according to the Kraljic’s model by the use of FMEA technique. Then, suppliers are categorized and evaluated in four phases with respect to different types of purchasing items (Strategic, Bottleneck, Leverage and Routine. Finally, an integer linear programming is utilized to allocate purchasing orders to suppliers. Furthermore, an empirical example is conducted to illustrate the stage of proposed approach. Results imply that ranking of suppliers and allocation of purchasing items based on the nature of purchasing items will create more capabilities in managing purchasing items and suppliers .
Directory of Open Access Journals (Sweden)
Dongyul Lee
2014-01-01
Full Text Available The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC with adaptive modulation and coding (AMC provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm.
Lee, Dongyul; Lee, Chaewoo
2014-01-01
The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm.
Lee, Chaewoo
2014-01-01
The advancement in wideband wireless network supports real time services such as IPTV and live video streaming. However, because of the sharing nature of the wireless medium, efficient resource allocation has been studied to achieve a high level of acceptability and proliferation of wireless multimedia. Scalable video coding (SVC) with adaptive modulation and coding (AMC) provides an excellent solution for wireless video streaming. By assigning different modulation and coding schemes (MCSs) to video layers, SVC can provide good video quality to users in good channel conditions and also basic video quality to users in bad channel conditions. For optimal resource allocation, a key issue in applying SVC in the wireless multicast service is how to assign MCSs and the time resources to each SVC layer in the heterogeneous channel condition. We formulate this problem with integer linear programming (ILP) and provide numerical results to show the performance under 802.16 m environment. The result shows that our methodology enhances the overall system throughput compared to an existing algorithm. PMID:25276862
Directory of Open Access Journals (Sweden)
Esten I. Grøtli
2016-04-01
Full Text Available Large amounts of data are typically generated in applications such as surveillance of power lines and railways, inspection of gas pipes, and security surveillance. In the latter application it is a necessity that the data is transmitted to the control centre ``on-the-fly'' for analysis. Also missions related to other applications would greatly benefit from near real-time analysis and operator interaction based on captured data. This is the motivation behind this paper on coarse offline motion- and communication-planning for cooperating Unmanned Aerial Vehicles (UAVs. A Mixed-Integer Linear Programming (MILP problem is defined in order to solve the surveillance mission. To efficiently transmit the data back to the base station the vehicles are allowed to store data for later transmission and transmit via other vehicles, in addition to direct transmission. The paths obtained by solving the optimization problem are analyzed using a realistic radio propagation path loss simulator. If the radio propagation path loss exceeds the maximum design criterion the optimization problem is solved again with a stricter communication constraint, and the procedure is continued in an iterative manner until the criterion is met. The proposed algorithm is supported by simulations showing the resulting paths and communication topologies for different choices of delay tolerance.
Lee, E K; Gallagher, R J; Silvern, D; Wuu, C S; Zaider, M
1999-01-01
An integer linear programming model is proposed as a framework for optimizing seed placement and dose distribution in brachytherapy treatment planning. The basic model involves using 0/1 indicator variables to describe the placement or non-placement of seeds in a prespecified three-dimensional grid of potential locations. The dose delivered to each point in a discretized representation of the diseased organ and neighbouring healthy tissue can then be modelled as a linear combination of the indicator variables. A system of linear constraints is imposed to attempt to keep the dose level at each point to within specified target bounds. Since it is physically impossible to satisfy all constraints simultaneously, each constraint uses a variable to either record when the target dose level is achieved, or to record the deviation from the desired level. These additional variables are embedded into an objective function to be optimized. Variations on this model are discussed and two computational approaches--a branch-and-bound algorithm and a genetic algorithm--for finding 'optimal' seed placements are described. Results of computational experiments on a collection of prostate cancer cases are reported. The results indicate that both optimization algorithms are capable of producing good solutions within 5 to 15 min, and that small variations in model parameters can have a measurable effect on the dose distribution of the resulting plans.
Modelling with Integer Variables.
1984-01-01
H. Korte, North-Holland Publishing Co., Amsterdam, pp. 3-53, 1979. 2. Bazaraa , M. and Shetty, M., Non-Linear Programming, John Wiley & Sons, Inc., New...Survey," SIAM Review 18 (1976), pp. 710-760. 5. Bazaraa , M. and Shetty, M., Non-Linear Programming, John Wiley & Sons, Inc., New York 1979. 6. Beale
Li, Yanning
2013-10-01
This article presents a new robust control framework for transportation problems in which the state is modeled by a first order scalar conservation law. Using an equivalent formulation based on a Hamilton-Jacobi equation, we pose the problem of controlling the state of the system on a network link, using boundary flow control, as a Linear Program. Unlike many previously investigated transportation control schemes, this method yields a globally optimal solution and is capable of handling shocks (i.e. discontinuities in the state of the system). We also demonstrate that the same framework can handle robust control problems, in which the uncontrollable components of the initial and boundary conditions are encoded in intervals on the right hand side of inequalities in the linear program. The lower bound of the interval which defines the smallest feasible solution set is used to solve the robust LP (or MILP if the objective function depends on boolean variables). Since this framework leverages the intrinsic properties of the Hamilton-Jacobi equation used to model the state of the system, it is extremely fast. Several examples are given to demonstrate the performance of the robust control solution and the trade-off between the robustness and the optimality. © 2013 IEEE.
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Jørgensen, John Bagterp
2012-01-01
from the wind farm model, enabling us to use a very simple linear relationship for describing the turbine interactions. In addition, we allow individual turbines to be turned on or off introducing integer variables into the optimization problem. We solve this within the same framework of iterative...... is far superior to, a more naive distribution scheme. We employ a fast convex quadratic programming solver to carry out the iterations in the range of microseconds for even large wind farms....
Some Duality Results for Fuzzy Nonlinear Programming Problem
Sangeeta Jaiswal; Geetanjali Panda
2012-01-01
The concept of duality plays an important role in optimization theory. This paper discusses some relations between primal and dual nonlinear programming problems in fuzzy environment. Here, fuzzy feasible region for a general fuzzy nonlinear programming is formed and the concept of fuzzy feasible solution is defined. First order dual relation for fuzzy nonlinear programming problem is studied.
Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Jiapei; Chen, Xiujuan; Li, Kailong
2017-02-16
As presented in the first companion paper, distributed mixed-integer fuzzy hierarchical programming (DMIFHP) was developed for municipal solid waste management (MSWM) under complexities of heterogeneities, hierarchy, discreteness, and interactions. Beijing was selected as a representative case. This paper focuses on presenting the obtained schemes and the revealed mechanisms of the Beijing MSWM system. The optimal MSWM schemes for Beijing under various solid waste treatment policies and their differences are deliberated. The impacts of facility expansion, hierarchy, and spatial heterogeneities and potential extensions of DMIFHP are also discussed. A few of findings are revealed from the results and a series of comparisons and analyses. For instance, DMIFHP is capable of robustly reflecting these complexities in MSWM systems, especially for Beijing. The optimal MSWM schemes are of fragmented patterns due to the dominant role of the proximity principle in allocating solid waste treatment resources, and they are closely related to regulated ratios of landfilling, incineration, and composting. Communities without significant differences among distances to different types of treatment facilities are more sensitive to these ratios than others. The complexities of hierarchy and heterogeneities pose significant impacts on MSWM practices. Spatial dislocation of MSW generation rates and facility capacities caused by unreasonable planning in the past may result in insufficient utilization of treatment capacities under substantial influences of transportation costs. The problems of unreasonable MSWM planning, e.g., severe imbalance among different technologies and complete vacancy of ten facilities, should be gained deliberation of the public and the municipal or local governments in Beijing. These findings are helpful for gaining insights into MSWM systems under these complexities, mitigating key challenges in the planning of these systems, improving the related management
Zhang, Huiling; Huang, Qingsheng; Bei, Zhendong; Wei, Yanjie; Floudas, Christodoulos A
2016-03-01
In this article, we present COMSAT, a hybrid framework for residue contact prediction of transmembrane (TM) proteins, integrating a support vector machine (SVM) method and a mixed integer linear programming (MILP) method. COMSAT consists of two modules: COMSAT_SVM which is trained mainly on position-specific scoring matrix features, and COMSAT_MILP which is an ab initio method based on optimization models. Contacts predicted by the SVM model are ranked by SVM confidence scores, and a threshold is trained to improve the reliability of the predicted contacts. For TM proteins with no contacts above the threshold, COMSAT_MILP is used. The proposed hybrid contact prediction scheme was tested on two independent TM protein sets based on the contact definition of 14 Å between Cα-Cα atoms. First, using a rigorous leave-one-protein-out cross validation on the training set of 90 TM proteins, an accuracy of 66.8%, a coverage of 12.3%, a specificity of 99.3% and a Matthews' correlation coefficient (MCC) of 0.184 were obtained for residue pairs that are at least six amino acids apart. Second, when tested on a test set of 87 TM proteins, the proposed method showed a prediction accuracy of 64.5%, a coverage of 5.3%, a specificity of 99.4% and a MCC of 0.106. COMSAT shows satisfactory results when compared with 12 other state-of-the-art predictors, and is more robust in terms of prediction accuracy as the length and complexity of TM protein increase. COMSAT is freely accessible at http://hpcc.siat.ac.cn/COMSAT/.
Melas, Ioannis N; Samaga, Regina; Alexopoulos, Leonidas G; Klamt, Steffen
2013-01-01
Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely
Nonlinear programming with feedforward neural networks.
Energy Technology Data Exchange (ETDEWEB)
Reifman, J.
1999-06-02
We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.
Dirks, Michael K.
1984-01-01
The abacus method for instruction on addition, subtraction, and multiplication with integers is explained. How to represent the integers for each operation is detailed with words and illustrations. (MNS)
Pong, Wai Yan
2007-01-01
We begin by answering the question, "Which natural numbers are sums of consecutive integers?" We then go on to explore the set of lengths (numbers of summands) in the decompositions of an integer as such sums.
96 International Conference on Nonlinear Programming
1998-01-01
About 60 scientists and students attended the 96' International Conference on Nonlinear Programming, which was held September 2-5 at Institute of Compu tational Mathematics and Scientific/Engineering Computing (ICMSEC), Chi nese Academy of Sciences, Beijing, China. 25 participants were from outside China and 35 from China. The conference was to celebrate the 60's birthday of Professor M.J.D. Powell (Fellow of Royal Society, University of Cambridge) for his many contributions to nonlinear optimization. On behalf of the Chinese Academy of Sciences, vice president Professor Zhi hong Xu attended the opening ceremony of the conference to express his warm welcome to all the participants. After the opening ceremony, Professor M.J.D. Powell gave the keynote lecture "The use of band matrices for second derivative approximations in trust region methods". 13 other invited lectures on recent advances of nonlinear programming were given during the four day meeting: "Primal-dual methods for nonconvex optimization" by...
STEW A Nonlinear Data Modeling Computer Program
Chen, H
2000-01-01
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross sections. This report presents results of the modeling of the sup 2 sup 3 sup 9 Pu(n,f) and sup 2 sup 3 sup 5 U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
A New Approach to Solving Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
SHEN Jie; CHEN Ling
2002-01-01
A method for solving nonlinear programming using genetic algorithm is presented. In the operations of crossover and mutation in each generation, to ensure the new solutions are all feasible, we present a method in which the bounds of every variable in the solution are estimated beforehand according to the constrained conditions. For the operation of mutation, we present two methods of cube bounding and variable bounding. The experimental results are given and analyzed. They show that the method is efficient and can obtain the results in less generation.
STEW: A Nonlinear Data Modeling Computer Program
Energy Technology Data Exchange (ETDEWEB)
Chen, H.
2000-03-04
A nonlinear data modeling computer program, STEW, employing the Levenberg-Marquardt algorithm, has been developed to model the experimental {sup 239}Pu(n,f) and {sup 235}U(n,f) cross sections. This report presents results of the modeling of the {sup 239}Pu(n,f) and {sup 235}U(n,f) cross-section data. The calculation of the fission transmission coefficient is based on the double-humped-fission-barrier model of Bjornholm and Lynn. Incident neutron energies of up to 5 MeV are considered.
Bifurcations and sensitivity in parametric nonlinear programming
Lundberg, Bruce N.; Poore, Aubrey B.
1990-01-01
The parametric nonlinear programming problem is that of determining the behavior of solution(s) as a parameter or vector of parameters alpha belonging to R(sup r) varies over a region of interest for the problem: Minimize over x the set f(x, alpha):h(x, alpha) = 0, g(x, alpha) is greater than or equal to 0, where f:R(sup (n+r)) approaches R, h:R(sup (n+r)) approaches R(sup q) and g:R(sup (n+r)) approaches R(sup p) are assumed to be at least twice continuously differentiable. Some of these parameters may be fixed but not known precisely and others may be varied to enhance the performance of the system. In both cases a fundamentally important problem in the investigation of global sensitivity of the system is to determine the stability boundaries of the regions in parameter space which define regions of qualitatively similar solutions. The objective is to explain how numerical continuation and bifurcation techniques can be used to investigate the parametric nonlinear programming problem in a global sense. Thus, first the problem is converted to a closed system of parameterized nonlinear equations whose solution set contains all local minimizers of the original problem. This system, which will be represented as F(z,alpha) = O, will include all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points of the problem. The local existence and uniqueness of a solution path (z(alpha), alpha) of this system as well as the solution type persist as long as a singularity in the Jacobian D(sub z)F(z,alpha) is not encountered. Thus the nonsingularity of this Jacobian is characterized in terms of conditions on the problem itself. Then, a class of efficient predictor-corrector continuation procedures for tracing solution paths of the system F(z,alpha) = O which are tailored specifically to the parametric programming problem are described. Finally, these procedures and the obtained information are illustrated
Energy Technology Data Exchange (ETDEWEB)
Waddell, Lucas; Muldoon, Frank; Henry, Stephen Michael; Hoffman, Matthew John; Zwerneman, April Marie; Backlund, Peter; Melander, Darryl J.; Lawton, Craig R.; Rice, Roy Eugene
2017-09-01
In order to effectively plan the management and modernization of their large and diverse fleets of vehicles, Program Executive Office Ground Combat Systems (PEO GCS) and Program Executive Office Combat Support and Combat Service Support (PEO CS&CSS) commis- sioned the development of a large-scale portfolio planning optimization tool. This software, the Capability Portfolio Analysis Tool (CPAT), creates a detailed schedule that optimally prioritizes the modernization or replacement of vehicles within the fleet - respecting numerous business rules associated with fleet structure, budgets, industrial base, research and testing, etc., while maximizing overall fleet performance through time. This paper contains a thor- ough documentation of the terminology, parameters, variables, and constraints that comprise the fleet management mixed integer linear programming (MILP) mathematical formulation. This paper, which is an update to the original CPAT formulation document published in 2015 (SAND2015-3487), covers the formulation of important new CPAT features.
An SQP Algorithm for Recourse-based Stochastic Nonlinear Programming
Directory of Open Access Journals (Sweden)
Xinshun Ma
2016-05-01
Full Text Available The stochastic nonlinear programming problem with completed recourse and nonlinear constraints is studied in this paper. We present a sequential quadratic programming method for solving the problem based on the certainty extended nonlinear model. This algorithm is obtained by combing the active set method and filter method. The convergence of the method is established under some standard assumptions. Moreover, a practical design is presented and numerical results are provided.
Introduction to stochastic programming and its applications to finance
Şimşek, Koray Deniz; Simsek, Koray Deniz
2008-01-01
Mathematical programming is one of a number of operations research techniques that employs mathematical optimization models to assist in decision making. Mathematical programming includes linear programming, integer programming, mixed-integer programming, nonlinear programming, stochastic programming, and goal programming. Mathematical programming models allow the decision maker to identify the “best” solution. This is in contrast to other mathematical tools that are in the arsenal of decisio...
An Algorithm for Linearly Constrained Nonlinear Programming Programming Problems.
1980-01-01
ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS Mokhtar S. Bazaraa and Jamie J. Goode In this paper an algorithm for solving a linearly...distance pro- gramr.ing, as in the works of Bazaraa and Goode 12], and Wolfe [16 can be used for solving this problem. Special methods that take advantage of...34 Pacific Journal of Mathematics, Volume 16, pp. 1-3, 1966. 2. M. S. Bazaraa and J. j. Goode, "An Algorithm for Finding the Shortest Element of a
Parallel Integer Relation Detection: Techniques and Applications
Bailey, David H.; Broadhurst, David J.
1999-01-01
Let $\\{x_1, x_2, ..., x_n\\}$ be a vector of real numbers. An integer relation algorithm is a computational scheme to find the $n$ integers $a_k$, if they exist, such that $a_1 x_1 + a_2 x_2 + ... + a_n x_n= 0$. In the past few years, integer relation algorithms have been utilized to discover new results in mathematics and physics. Existing programs for this purpose require very large amounts of computer time, due in part to the requirement for multiprecision arithmetic, yet are poorly suited ...
Landman, Bruce
2014-01-01
""Integers"" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. This work presents all papers of the 2013 volume in book form.
基于整数规划的物流配送中心选址研究%The location of logistics distribution centers based on integer programming
Institute of Scientific and Technical Information of China (English)
章海燕
2016-01-01
本文从物流配送中心的运营成本和运输时间限制着手，在满足连锁店服务要求的前提下，利用混合整数规划对物流配送中心进行选址模型研究，并结合实例给出了求解。%In this paper, under the premise of meeting the service requirements of the chain store, with the operation cost and transportation time limit of the logistics distribution center, research on logistics distribution center location model based on mixed integer programming. And the solution is given with an example.
Albuquerque, Fabio; Beier, Paul
2015-01-01
Here we report that prioritizing sites in order of rarity-weighted richness (RWR) is a simple, reliable way to identify sites that represent all species in the fewest number of sites (minimum set problem) or to identify sites that represent the largest number of species within a given number of sites (maximum coverage problem). We compared the number of species represented in sites prioritized by RWR to numbers of species represented in sites prioritized by the Zonation software package for 11 datasets in which the size of individual planning units (sites) ranged from algorithms remain superior for conservation prioritizations that consider compactness and multiple near-optimal solutions in addition to species representation. But because RWR can be implemented easily and quickly in R or a spreadsheet, it is an attractive alternative to integer programming or heuristic algorithms in some conservation prioritization contexts.
Optimal in silico target gene deletion through nonlinear programming for genetic engineering.
Hong, Chung-Chien; Song, Mingzhou
2010-02-24
Optimal selection of multiple regulatory genes, known as targets, for deletion to enhance or suppress the activities of downstream genes or metabolites is an important problem in genetic engineering. Such problems become more feasible to address in silico due to the availability of more realistic dynamical system models of gene regulatory and metabolic networks. The goal of the computational problem is to search for a subset of genes to knock out so that the activity of a downstream gene or a metabolite is optimized. Based on discrete dynamical system modeling of gene regulatory networks, an integer programming problem is formulated for the optimal in silico target gene deletion problem. In the first result, the integer programming problem is proved to be NP-hard and equivalent to a nonlinear programming problem. In the second result, a heuristic algorithm, called GKONP, is designed to approximate the optimal solution, involving an approach to prune insignificant terms in the objective function, and the parallel differential evolution algorithm. In the third result, the effectiveness of the GKONP algorithm is demonstrated by applying it to a discrete dynamical system model of the yeast pheromone pathways. The empirical accuracy and time efficiency are assessed in comparison to an optimal, but exhaustive search strategy. Although the in silico target gene deletion problem has enormous potential applications in genetic engineering, one must overcome the computational challenge due to its NP-hardness. The presented solution, which has been demonstrated to approximate the optimal solution in a practical amount of time, is among the few that address the computational challenge. In the experiment on the yeast pheromone pathways, the identified best subset of genes for deletion showed advantage over genes that were selected empirically. Once validated in vivo, the optimal target genes are expected to achieve higher genetic engineering effectiveness than a trial
Optimal in silico target gene deletion through nonlinear programming for genetic engineering.
Directory of Open Access Journals (Sweden)
Chung-Chien Hong
Full Text Available BACKGROUND: Optimal selection of multiple regulatory genes, known as targets, for deletion to enhance or suppress the activities of downstream genes or metabolites is an important problem in genetic engineering. Such problems become more feasible to address in silico due to the availability of more realistic dynamical system models of gene regulatory and metabolic networks. The goal of the computational problem is to search for a subset of genes to knock out so that the activity of a downstream gene or a metabolite is optimized. METHODOLOGY/PRINCIPAL FINDINGS: Based on discrete dynamical system modeling of gene regulatory networks, an integer programming problem is formulated for the optimal in silico target gene deletion problem. In the first result, the integer programming problem is proved to be NP-hard and equivalent to a nonlinear programming problem. In the second result, a heuristic algorithm, called GKONP, is designed to approximate the optimal solution, involving an approach to prune insignificant terms in the objective function, and the parallel differential evolution algorithm. In the third result, the effectiveness of the GKONP algorithm is demonstrated by applying it to a discrete dynamical system model of the yeast pheromone pathways. The empirical accuracy and time efficiency are assessed in comparison to an optimal, but exhaustive search strategy. SIGNIFICANCE: Although the in silico target gene deletion problem has enormous potential applications in genetic engineering, one must overcome the computational challenge due to its NP-hardness. The presented solution, which has been demonstrated to approximate the optimal solution in a practical amount of time, is among the few that address the computational challenge. In the experiment on the yeast pheromone pathways, the identified best subset of genes for deletion showed advantage over genes that were selected empirically. Once validated in vivo, the optimal target genes are
A nonlinear bi-level programming approach for product portfolio management.
Ma, Shuang
2016-01-01
Product portfolio management (PPM) is a critical decision-making for companies across various industries in today's competitive environment. Traditional studies on PPM problem have been motivated toward engineering feasibilities and marketing which relatively pay less attention to other competitors' actions and the competitive relations, especially in mathematical optimization domain. The key challenge lies in that how to construct a mathematical optimization model to describe this Stackelberg game-based leader-follower PPM problem and the competitive relations between them. The primary work of this paper is the representation of a decision framework and the optimization model to leverage the PPM problem of leader and follower. A nonlinear, integer bi-level programming model is developed based on the decision framework. Furthermore, a bi-level nested genetic algorithm is put forward to solve this nonlinear bi-level programming model for leader-follower PPM problem. A case study of notebook computer product portfolio optimization is reported. Results and analyses reveal that the leader-follower bi-level optimization model is robust and can empower product portfolio optimization.
Constrained optimization for image restoration using nonlinear programming
Yeh, C.-L.; Chin, R. T.
1985-01-01
The constrained optimization problem for image restoration, utilizing incomplete information and partial constraints, is formulated using nonlinear proramming techniques. This method restores a distorted image by optimizing a chosen object function subject to available constraints. The penalty function method of nonlinear programming is used. Both linear or nonlinear object function, and linear or nonlinear constraint functions can be incorporated in the formulation. This formulation provides a generalized approach to solve constrained optimization problems for image restoration. Experiments using this scheme have been performed. The results are compared with those obtained from other restoration methods and the comparative study is presented.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially effcient.
On filter-successive linearization methods for nonlinear semidefinite programming
Institute of Scientific and Technical Information of China (English)
LI ChengJin; SUN WenYui
2009-01-01
In this paper we present a filter-successive linearization method with trust region for solutions of nonlinear semidefinite programming. Such a method is based on the concept of filter for nonlinear programming introduced by Fletcher and Leyffer in 2002. We describe the new algorithm and prove its global convergence under weaker assumptions. Some numerical results are reported and show that the new method is potentially efficient.
Directory of Open Access Journals (Sweden)
Guillermo Cabrera G.
2012-01-01
Full Text Available We present a hybridization of two different approaches applied to the well-known Capacitated Facility Location Problem (CFLP. The Artificial Bee algorithm (BA is used to select a promising subset of locations (warehouses which are solely included in the Mixed Integer Programming (MIP model. Next, the algorithm solves the subproblem by considering the entire set of customers. The hybrid implementation allows us to bypass certain inherited weaknesses of each algorithm, which means that we are able to find an optimal solution in an acceptable computational time. In this paper we demonstrate that BA can be significantly improved by use of the MIP algorithm. At the same time, our hybrid implementation allows the MIP algorithm to reach the optimal solution in a considerably shorter time than is needed to solve the model using the entire dataset directly within the model. Our hybrid approach outperforms the results obtained by each technique separately. It is able to find the optimal solution in a shorter time than each technique on its own, and the results are highly competitive with the state-of-the-art in large-scale optimization. Furthermore, according to our results, combining the BA with a mathematical programming approach appears to be an interesting research area in combinatorial optimization.
Gusfield, Dan
2010-03-01
The Multi-State Perfect Phylogeny Problem is an extension of the Binary Perfect Phylogeny Problem, allowing characters to take on more than two states. In this article, we consider three problems that extend the utility of the multi-state perfect phylogeny model: (1) the Missing Data (MD) Problem, where some entries in the input are missing and the question is whether (bounded) values for the missing data can be imputed so that the resulting data has a multi-state perfect phylogeny; (2) the Character-Removal (CR) Problem, where we want to minimize the number of characters to remove from the data so that the resulting data has a multi-state perfect phylogeny; and (3) the Missing-Data Character-Removal (MDCR) Problem, where the input has missing data and we want to impute values for the missing data to minimize the solution to the resulting Character-Removal Problem. We discuss Integer Linear Programming (ILP) solutions to these problems for the special case of three, four, and five permitted states per character, and we report on extensive empirical testing of these solutions. Then we develop a general theory to solve the MD problem for an arbitrary number of permitted states, using chordal graph theory and results on minimal triangulation of non-chordal graphs. This establishes new necessary and sufficient conditions for the existence of a perfect phylogeny with (or without) missing data. We implement the general theory using integer linear programming, although other optimization methods are possible. We extensively explore the empirical behavior of the general solution, showing that the methods are very practical for data of size and complexity that is characteristic of many current applications in phylogenetics. Some of the empirical results for the MD problem with an arbitrary number of permitted states are very surprising, suggesting the existence of additional combinatorial structure in multi-state perfect phylogenies. Finally, we note some relationships
Energy Technology Data Exchange (ETDEWEB)
Meyers, C A; Schulz, A S
2009-01-07
The integer equal flow problem is an NP-hard network flow problem, in which all arcs in given sets R{sub 1}, ..., R{sub {ell}} must carry equal flow. We show this problem is effectively inapproximable, even if the cardinality of each set R{sub k} is two. When {ell} is fixed, it is solvable in polynomial time.
Veugen, P.J.M.
2010-01-01
When processing signals in the encrypted domain, homomorphic encryption can be used to enable linear operations on encrypted data. Integer division of encrypted data however requires an additional protocol with the server and will be relatively expensive. We present new solutions for dividing encryp
An Adaptive Neural Network Model for Nonlinear Programming Problems
Institute of Scientific and Technical Information of China (English)
Xiang-sun Zhang; Xin-jian Zhuo; Zhu-jun Jing
2002-01-01
In this paper a canonical neural network with adaptively changing synaptic weights and activation function parameters is presented to solve general nonlinear programming problems. The basic part of the model is a sub-network used to find a solution of quadratic programming problems with simple upper and lower bounds. By sequentially activating the sub-network under the control of an external computer or a special analog or digital processor that adjusts the weights and parameters, one then solves general nonlinear programming problems. Convergence proof and numerical results are given.
Using genetic programming to discover nonlinear variable interactions.
Westbury, Chris; Buchanan, Lori; Sanderson, Michael; Rhemtulla, Mijke; Phillips, Leah
2003-05-01
Psychology has to deal with many interacting variables. The analyses usually used to uncover such relationships have many constraints that limit their utility. We briefly discuss these and describe recent work that uses genetic programming to evolve equations to combine variables in nonlinear ways in a number of different domains. We focus on four studies of interactions from lexical access experiments and psychometric problems. In all cases, genetic programming described nonlinear combinations of items in a manner that was subsequently independently verified. We discuss the general implications of genetic programming and related computational methods for multivariate problems in psychology.
Robust adaptive dynamic programming and feedback stabilization of nonlinear systems.
Jiang, Yu; Jiang, Zhong-Ping
2014-05-01
This paper studies the robust optimal control design for a class of uncertain nonlinear systems from a perspective of robust adaptive dynamic programming (RADP). The objective is to fill up a gap in the past literature of adaptive dynamic programming (ADP) where dynamic uncertainties or unmodeled dynamics are not addressed. A key strategy is to integrate tools from modern nonlinear control theory, such as the robust redesign and the backstepping techniques as well as the nonlinear small-gain theorem, with the theory of ADP. The proposed RADP methodology can be viewed as an extension of ADP to uncertain nonlinear systems. Practical learning algorithms are developed in this paper, and have been applied to the controller design problems for a jet engine and a one-machine power system.
An Evaluation and Comparison of Three Nonlinear Programming Codes
1976-03-01
sixth problem was selected from the Himmelblau collection [Ref. 11] and the remaining two were adaptations cf an inventory model and an entropy model...both require utilization of the main nonlinear codes with their high core and corresponding time requirements. Himmelblau estimated preparation times...Nonlinear Program mincf Moclel for "Determining a Huni/Eions ITix, By R*.J. CTasen, E.¥.Graves ana J.Y7 Iu, 3arch 1974. 11. Himmelblau . D.M., Applied
Extended gcd of quadratic integers
Miled, Abdelwaheb
2010-01-01
Computation of the extended gcd of two quadratic integers. The ring of integers considered is principal but could be euclidean or not euclidean ring. This method rely on principal ideal ring and reduction of binary quadratic forms.
Purnomo, Muhammad Ridwan Andi; Satrio Wiwoho, Yoga
2016-01-01
Facility layout becomes one of production system factor that should be managed well, as it is designated for the location of production. In managing the layout, designing the layout by considering the optimal layout condition that supports the work condition is essential. One of the method for facility layout optimization is Mixed Integer Programming (MIP). In this study, the MIP is solved using Lingo 9.0 software and considering quantitative and qualitative objectives to be achieved simultaneously: minimizing material handling cost, maximizing closeness rating, and minimizing re-layout cost. The research took place in Rekayasa Wangdi as a make to order company, focusing on the making of concrete brick dough stirring machine with 10 departments involved. The result shows an improvement in the new layout for 333,72 points of objective value compared with the initial layout. As the conclusion, the proposed MIP is proven to be used to model facility layout problem under multi objective consideration for a more realistic look.
A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Xin-wei Liu; Ya-xiang Yuan
2001-01-01
The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.
Directory of Open Access Journals (Sweden)
L. Ferrer
2004-01-01
Full Text Available En este artículo se presenta un modelo de transporte de distribución usando programación lineal. El proceso global de distribución se considera dividido en sucesivos niveles entre la empresa y sus clientes. En cada nivel se distinguen unidades de origen-destino, entre un origen y varios destinos, con transporte directo y con ventanas en las fechas de entrega de los pedidos a transportar. La programación de la distribución se realiza en cada unidad, mediante programación lineal entera, considerando en la formulación flota limitada de vehículos y flota ilimitada. La programación global se obtiene como superposición de las programaciones de todas las unidades origen-destino. Para validar el modelo se han utilizado los datos proporcionados por una empresa del sector textil que cumple las características requeridas. Se concluye que el modelo presentado, resulta ser adecuado para modelar las empresas caracterizadas y ha permitido diseñar e implementar un procedimiento exacto para la programación de la distribución del producto de la empresaThis article presents a model of distribution transport using linear programming. The overall distribution process is considered to be divided into successive levels between the company and its clients. Origin-destination units are distinguished at each level between an origin and various destinations, with direct transport and with windows in the delivery dates of the orders to be transported. The distribution programming is carried out in each unit through integer linear programming considering in the formulation both limited and unlimited fleets of vehicles. The overall programming is obtained as a superposition of the programming of all the origin-destination units. Validation of the model was carried out using data obtained from a textile company having the required characteristics. It is concluded that the model presented is useful in modeling the companies described, and has permitted the
An Image Steganography Algorithm Combined with Integer Programming and YASS%一种结合整数规划和YASS的图像隐写算法
Institute of Scientific and Technical Information of China (English)
忻佳琳; 王士林
2013-01-01
In order to increase the steganography rate, this paper proposes a new scheme of steganography which is based on YASS algorithm. After discussing the inherent relationship between Discrete Cosine Transform(DCT) coefficients in different blocks, a method of iterative programming is proposed which is referenced to integer programming, and the carrier which has steganography has been corrected. In aspect of anti-detection, 98 degree’s Markov steganalysis method is used to detect the stego images. Experimental result shows that this optimization algorithm is proved to effectively decrease the errors caused by JPEG compression during YASS steganography. In this way, steganographic rate is increased to a great extent. This method is also proved to get the same outstanding performance in common anti-detection.%为提高图像隐写率，在 YASS 算法的基础上，提出一种改进的图像隐写算法。分析不同图像分块离散余弦变换系数之间的固有联系，借鉴整数规划的思想设计迭代算法，对已隐写的载体进行数据校正。使用98维马尔科夫通用图像检测方法进行实验，结果表明，该算法能减少YASS隐写过程中由JPEG图像压缩引入的误码，提高隐写率，同时可有效抵抗通用隐写检测。
Investigating Students’ Development of Learning Integer Concept and Integer Addition
Directory of Open Access Journals (Sweden)
Nenden Octavarulia Shanty
2016-09-01
Full Text Available This research aimed at investigating students’ development of learning integer concept and integer addition. The investigation was based on analyzing students’ works in solving the given mathematical problems in each instructional activity designed based on Realistic Mathematics Education (RME levels. Design research was chosen to achieve and to contribute in developing a local instruction theory for teaching and learning of integer concept and integer addition. In design research, the Hypothetical Learning Trajectory (HLT plays important role as a design and research instrument. It was designed in the phase of preliminary design and tested to three students of grade six OASIS International School, Ankara – Turkey. The result of the experiments showed that temperature in the thermometer context could stimulate students’ informal knowledge of integer concept. Furthermore, strategies and tools used by the students in comparing and relating two temperatures were gradually be developed into a more formal mathematics. The representation of line inside thermometer which then called the number line could bring the students to the last activity levels, namely rules for adding integer, and became the model for more formal reasoning. Based on these findings, it can be concluded that students’ learning integer concept and integer addition developed through RME levels.Keywords: integer concept, integer addition, Realistic Mathematics Education DOI: http://dx.doi.org/10.22342/jme.7.2.3538.57-72
Incremental approximate dynamic programming for nonlinear flight control design
Zhou, Y.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
A self-learning adaptive flight control design for non-linear systems allows reliable and effective operation of flight vehicles in a dynamic environment. Approximate dynamic programming (ADP) provides a model-free and computationally effective process for designing adaptive linear optimal
A Novel Nonlinear Programming Model for Distribution Protection Optimization
Zambon, Eduardo; Bossois, Débora Z.; Garcia, Berilhes B.; Azeredo, Elias F.
2009-01-01
This paper presents a novel nonlinear binary programming model designed to improve the reliability indices of a distribution network. This model identifies the type and location of protection devices that should be installed in a distribution feeder and is a generalization of the classical optimizat
An SQP algorithm for mathematical programs with nonlinear complementarity constraints
Institute of Scientific and Technical Information of China (English)
Zhi-bin ZHU; Jin-bao JIAN; Cong ZHANG
2009-01-01
In this paper,we describe a successive approximation and smooth sequential quadratic programming (SQP) method for mathematical programs with nonlinear complementarity constraints (MPCC). We introduce a class of smooth programs to approximate the MPCC. Using an l1 penalty function,the line search assures global convergence,while the superlinear convergence rate is shown under the strictly complementary and second-order sufficient conditions. Moreover,we prove that the current iterated point is an exact stationary point of the mathematical programs with equilibrium constraints (MPEC) when the algorithm terminates finitely.
A Filter Method for Nonlinear Semidefinite Programming with Global Convergence
Institute of Scientific and Technical Information of China (English)
Zhi Bin ZHU; Hua Li ZHU
2014-01-01
In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the suffi cient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is eff ective.
A FORTRAN program for calculating nonlinear seismic ground response
Joyner, William B.
1977-01-01
The program described here was designed for calculating the nonlinear seismic response of a system of horizontal soil layers underlain by a semi-infinite elastic medium representing bedrock. Excitation is a vertically incident shear wave in the underlying medium. The nonlinear hysteretic behavior of the soil is represented by a model consisting of simple linear springs and Coulomb friction elements arranged as shown. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. A brief program description is provided here with instructions for preparing the input and a source listing. A more detailed discussion of the method is presented elsewhere as is the description of a different program employing implicit integration.
A novel neural network for nonlinear convex programming.
Gao, Xing-Bao
2004-05-01
In this paper, we present a neural network for solving the nonlinear convex programming problem in real time by means of the projection method. The main idea is to convert the convex programming problem into a variational inequality problem. Then a dynamical system and a convex energy function are constructed for resulting variational inequality problem. It is shown that the proposed neural network is stable in the sense of Lyapunov and can converge to an exact optimal solution of the original problem. Compared with the existing neural networks for solving the nonlinear convex programming problem, the proposed neural network has no Lipschitz condition, no adjustable parameter, and its structure is simple. The validity and transient behavior of the proposed neural network are demonstrated by some simulation results.
Approximate Augmented Lagrangian Functions and Nonlinear Semidefinite Programs
Institute of Scientific and Technical Information of China (English)
X. X. HUANG; K. L. TEO; X. Q. YANG
2006-01-01
In this paper, an approximate augmented Lagrangian function for nonlinear semidefinite programs is introduced. Some basic properties of the approximate augmented Lagrange function such as monotonicity and convexity are discussed. Necessary and sufficient conditions for approximate strong duality results are derived. Conditions for an approximate exact penalty representation in the framework of augmented Lagrangian are given. Under certain conditions, it is shown that any limit point of a sequence of stationary points of approximate augmented Lagrangian problems is a KKT point of the original semidefinite program and that a sequence of optimal solutions to augmented Lagrangian problems converges to a solution of the original semidefinite program.
Directory of Open Access Journals (Sweden)
Yılmaz GÖKŞEN
2016-11-01
to the personnel, a person’s contribution coefficients have been calculated. These values are used in the assignment model. This model has been solved and evaluated as 0-1 integer programming. Model outputs that have been solved again by using additional constraints like task type and disability conditions and these are compared with the previous figures.
Directory of Open Access Journals (Sweden)
Andrés Saldaña Crovo
2007-12-01
Full Text Available En esta investigación se formulan dos modelos de Programación Lineal Entera para un problema de Programación de Horarios para Universidades y se presentan dos estrategias de solución para cada uno de ellos. El problema consiste en programar las asignaturas a ser dictadas, considerando los profesores, días, horarios, aulas y la necesidad de dictar las asignaturas en periodos consecutivos determinados. El objetivo es minimizar la asignación en periodos no deseados, balanceando la carga de trabajo diaria para cada grupo de alumnos. Las estrategias de solución combinan modelos de asignación directa a aulas o asignación a tipos de aulas. Las estrategias de solución que consideran relajación de restricciones, permiten resolver problemas de gran tamaño, a niveles de calidad razonables y utilizando pequeños tiempos computacionales. Los enfoques fueron aplicados a instancias de la Facultad de Ingeniería de la Universidad de Concepción, Chile. Los modelos utilizados en esta investigación pueden ser aplicados a una gran cantidad de problemas de Programación de Horarios en Universidades , proporcionando una gran flexibilidad de resolución.In this research, two models of Integer Programming for a University Timetabling Problem are formulated and two solution strategies for each model are presented. The problem consists of programming the courses to be taught, considering teaching faculty, days, periods, classrooms and requirements for courses that are taught in consecutive periods. The objective is to minimize the allocation of undesired time slots as well as balancing the daily workload for each group of students. The solution strategies are based on either combining models of direct allocation to classrooms or types of classrooms. The solution strategies that include reducing constraints, allow solving big problems with reasonable levels of efficiency, using the computer system for a short time. The approaches were used with real data
Integer-valued trawl processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Lunde, Asger; Shephard, Neil;
2014-01-01
This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl processes, which are serially correlated, stationary, infinitely divisible processes. We analyse the proba......This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl processes, which are serially correlated, stationary, infinitely divisible processes. We analyse...
Sensor Network Design for Nonlinear Processes
Institute of Scientific and Technical Information of China (English)
李博; 陈丙珍
2003-01-01
This paper presents a method to design a cost-optimal nonredundant sensor network to observe all variables in a general nonlinear process. A mixed integer linear programming model was used to minimize the cost with data classification to check the observability of all unmeasured variables. This work is a starting point for designing sensor networks for general nonlinear processes based on various criteria, such as reliability and accuracy.
Integer roots of quadratic and cubic polynomials with integer coefficients
Zelator, Konstantine
2011-01-01
The subject matter of this work is quadratic and cubic polynomial functions with integer coefficients;and all of whose roots are integers. The material of this work is directed primarily at educators,students,and teachers of mathematics,grades K12 to K20.The results of this work are expressed in Theorems3,4,and5. Of these theorems, Theorem3, is the one that most likely, the general reader of this article will have some familiarity with.In Theorem3, precise coefficient conditions are given;in order that a quadratic trinomial(with integer) have two integer roots or zeros.On the other hand, Theorems4 and5 are largely unfamiliar territory. In Theorem4, precise coefficient conditions are stated; for a monic cubic polynomial to have a double(i.e.of multiplicity 2) integer root, and a single integer root(i.e.of multiplicity 1).The entire family of such cubics can be described in terms of four groups or subfamilies; each such group being a two-integer parameter subfamily. In Theorem5, a one-integer parameter family o...
Integer and Half-Integer Quantization Conditions in Quantum Mechanics
Institute of Scientific and Technical Information of China (English)
DUAN Yi-Shi; JIA Duo-Jie
2001-01-01
The integer and half-integer quantization conditions are found in quantum mechanics based on the topological structure of symmetry group of the singlet and spinor wavefunction. The internal symmetry of the physical system is shown to be sufficient to determine the topological structure in quantum mechanics without taking int account the dynamical details about the interaction.
Bonus algorithm for large scale stochastic nonlinear programming problems
Diwekar, Urmila
2015-01-01
This book presents the details of the BONUS algorithm and its real world applications in areas like sensor placement in large scale drinking water networks, sensor placement in advanced power systems, water management in power systems, and capacity expansion of energy systems. A generalized method for stochastic nonlinear programming based on a sampling based approach for uncertainty analysis and statistical reweighting to obtain probability information is demonstrated in this book. Stochastic optimization problems are difficult to solve since they involve dealing with optimization and uncertainty loops. There are two fundamental approaches used to solve such problems. The first being the decomposition techniques and the second method identifies problem specific structures and transforms the problem into a deterministic nonlinear programming problem. These techniques have significant limitations on either the objective function type or the underlying distributions for the uncertain variables. Moreover, these ...
An application of Matlab c on Dimensional Nonlinear Programming
Fernando Giménez Palomares; María José Marín Fernández
2014-01-01
[EN] Nonlinear Programming (NLP) is a widely applicable tool in modeling real life problems applied to business, economics and engineering. Is to maximize or minimize a scalar field whose domain is given as a set of constraints given by equalities and/or inequalities not necessarily linear. In this paper we present a virtual laboratory to study the PNL graphically and numerically in the case of two variables [EN] La Programación No Lineal (PNL) constituye una herramienta de amp...
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.
A hybrid nonlinear programming method for design optimization
Rajan, S. D.
1986-01-01
Solutions to engineering design problems formulated as nonlinear programming (NLP) problems usually require the use of more than one optimization technique. Moreover, the interaction between the user (analysis/synthesis) program and the NLP system can lead to interface, scaling, or convergence problems. An NLP solution system is presented that seeks to solve these problems by providing a programming system to ease the user-system interface. A simple set of rules is used to select an optimization technique or to switch from one technique to another in an attempt to detect, diagnose, and solve some potential problems. Numerical examples involving finite element based optimal design of space trusses and rotor bearing systems are used to illustrate the applicability of the proposed methodology.
Structural Optimization for Reliability Using Nonlinear Goal Programming
El-Sayed, Mohamed E.
1999-01-01
This report details the development of a reliability based multi-objective design tool for solving structural optimization problems. Based on two different optimization techniques, namely sequential unconstrained minimization and nonlinear goal programming, the developed design method has the capability to take into account the effects of variability on the proposed design through a user specified reliability design criterion. In its sequential unconstrained minimization mode, the developed design tool uses a composite objective function, in conjunction with weight ordered design objectives, in order to take into account conflicting and multiple design criteria. Multiple design criteria of interest including structural weight, load induced stress and deflection, and mechanical reliability. The nonlinear goal programming mode, on the other hand, provides for a design method that eliminates the difficulty of having to define an objective function and constraints, while at the same time has the capability of handling rank ordered design objectives or goals. For simulation purposes the design of a pressure vessel cover plate was undertaken as a test bed for the newly developed design tool. The formulation of this structural optimization problem into sequential unconstrained minimization and goal programming form is presented. The resulting optimization problem was solved using: (i) the linear extended interior penalty function method algorithm; and (ii) Powell's conjugate directions method. Both single and multi-objective numerical test cases are included demonstrating the design tool's capabilities as it applies to this design problem.
A convergence theory for a class of nonlinear programming problems.
Rauch, S. W.
1973-01-01
A recent convergence theory of Elkin concerning methods for unconstrained minimization is extended to a certain class of nonlinear programming problems. As in Elkin's original approach, the analysis of a variety of step-length algorithms is treated entirely separately from that of several direction algorithms. This allows for their combination into many different methods for solving the constrained problem. These include some of the methods of Rosen and Zoutendijk. We also extend the results of Topkis and Veinott to nonconvex sets and drop their requirement of the uniform feasibility of a subsequence of the search directions.
Penalized interior point approach for constrained nonlinear programming
Institute of Scientific and Technical Information of China (English)
LU Wen-ting; YAO Yi-rong; ZHANG Lian-sheng
2009-01-01
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton's method, the global convergence of interior point and line search algorithm is proven.Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method.
Frahm, K M; Shepelyansky, D L
2012-01-01
We build up a directed network tracing links from a given integer to its divisors and analyze the properties of the Google matrix of this network. The PageRank vector of this matrix is computed numerically and it is shown that its probability is inversely proportional to the PageRank index thus being similar to the Zipf law and the dependence established for the World Wide Web. The spectrum of the Google matrix of integers is characterized by a large gap and a relatively small number of nonzero eigenvalues. A simple semi-analytical expression for the PageRank of integers is derived that allows to find this vector for matrices of billion size. This network provides a new PageRank order of integers.
Directory of Open Access Journals (Sweden)
Horacio Hideki Yanasse
2013-01-01
Full Text Available Neste trabalho revemos alguns modelos lineares e não lineares inteiros para gerar padrões de corte bidimensionais guilhotinados de 2 estágios, incluindo os casos exato e não exato e restrito e irrestrito. Esses problemas são casos particulares do problema da mochila bidimensional. Apresentamos também novos modelos para gerar esses padrões de corte, baseados em adaptações ou extensões de modelos para gerar padrões de corte bidimensionais restritos 1-grupo. Padrões 2 estágios aparecem em diferentes processos de corte, como, por exemplo, em indústrias de móveis e de chapas de madeira. Os modelos são úteis para a pesquisa e o desenvolvimento de métodos de solução mais eficientes, explorando estruturas particulares, a decomposição do modelo, relaxações do modelo etc. Eles também são úteis para a avaliação do desempenho de heurísticas, já que permitem (pelo menos para problemas de tamanho moderado uma estimativa do gap de otimalidade de soluções obtidas por heurísticas. Para ilustrar a aplicação dos modelos, analisamos os resultados de alguns experimentos computacionais com exemplos da literatura e outros gerados aleatoriamente. Os resultados foram produzidos usando um software comercial conhecido e mostram que o esforço computacional necessário para resolver os modelos pode ser bastante diferente.In this work we review some linear and nonlinear integer models to generate two stage two-dimensional guillotine cutting patterns, including the constrained, non constrained, exact and non exact cases. These problems are particular cases of the two dimensional knapsack problems. We also present new models to generate these cutting patterns, based on adaptations and extensions of models that generate one-group constrained two dimensional cutting patterns. Two stage patterns arise in different cutting processes like, for instance, in the furniture industry and wooden hardboards. The models are useful for the research and
Image Watermarking Method Using Integer-to-Integer Wavelet Transforms
Institute of Scientific and Technical Information of China (English)
陈韬; 王京春
2002-01-01
Digital watermarking is an efficient method for copyright protection for text, image, audio, and video data. This paper presents a new image watermarking method based on integer-to-integer wavelet transforms. The watermark is embedded in the significant wavelet coefficients by a simple exclusive OR operation. The method avoids complicated computations and high computer memory requirements that are the main drawbacks of common frequency domain based watermarking algorithms. Simulation results show that the embedded watermark is perceptually invisible and robust to various operations, such as low quality joint picture expert group (JPEG) compression, random and Gaussian noises, and smoothing (mean filtering).
Exploiting Symmetry in Integer Convex Optimization using Core Points
Herr, Katrin; Schürmann, Achill
2012-01-01
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. We define a core point of such a symmetry group as an integral point for which the convex hull of its orbit does not contain integral points other than the orbit points themselves. These core points allow us to decompose symmetric integer convex programming problems. Especially for symmetric integer linear programs we describe two algorithms based on this decomposition. Using a characterization of core points for direct products of symmetric groups, we show that prototype implementations can compete with state-of-the art commercial solvers and solve an open MIPLIB problem.
Lu, Bao-Liang; Ito, Koji
2003-09-01
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques; (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown; (c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems.
A New Kind of Simple Smooth Exact Penalty Function of Constrained Nonlinear Programming
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The penalty function method is one basic method for solving constrained nonlinear programming, in which simple smooth exact penalty functions draw much attention for their simpleness and smoothness. This article offers a new kind of simple smooth approximative exact penalty function of general constrained nonlinear programmings and analyzes its properties.
A mixed integer bi-level DEA model for bank branch performance evaluation by Stackelberg approach
Shafiee, Morteza; Lotfi, Farhad Hosseinzadeh; Saleh, Hilda; Ghaderi, Mehdi
2016-11-01
One of the most complicated decision making problems for managers is the evaluation of bank performance, which involves various criteria. There are many studies about bank efficiency evaluation by network DEA in the literature review. These studies do not focus on multi-level network. Wu (Eur J Oper Res 207:856-864, 2010) proposed a bi-level structure for cost efficiency at the first time. In this model, multi-level programming and cost efficiency were used. He used a nonlinear programming to solve the model. In this paper, we have focused on multi-level structure and proposed a bi-level DEA model. We then used a liner programming to solve our model. In other hand, we significantly improved the way to achieve the optimum solution in comparison with the work by Wu (2010) by converting the NP-hard nonlinear programing into a mixed integer linear programming. This study uses a bi-level programming data envelopment analysis model that embodies internal structure with Stackelberg-game relationships to evaluate the performance of banking chain. The perspective of decentralized decisions is taken in this paper to cope with complex interactions in banking chain. The results derived from bi-level programming DEA can provide valuable insights and detailed information for managers to help them evaluate the performance of the banking chain as a whole using Stackelberg-game relationships. Finally, this model was applied in the Iranian bank to evaluate cost efficiency.
Note on Integer Factoring Methods IV
Carella, N. A.
2008-01-01
This note continues the theoretical development of deterministic integer factorization algorithms based on systems of polynomials equations. The main result establishes a new deterministic time complexity bench mark in integer factorization.
A Euclidean algorithm for integer matrices
DEFF Research Database (Denmark)
Lauritzen, Niels; Thomsen, Jesper Funch
2015-01-01
We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers.......We present a Euclidean algorithm for computing a greatest common right divisor of two integer matrices. The algorithm is derived from elementary properties of finitely generated modules over the ring of integers....
Nonlinear programming strategies for source detection of municipal water networks.
Energy Technology Data Exchange (ETDEWEB)
van Bloemen Waanders, Bart Gustaaf; Biegler, Lorenz T. (Carnegie Mellon University, Pittsburgh, PA); Bartlett, Roscoe Ainsworth; Laird, Carl Damon (Carnegie Mellon University, Pittsburgh, PA)
2003-01-01
Increasing concerns for the security of the national infrastructure have led to a growing need for improved management and control of municipal water networks. To deal with this issue, optimization offers a general and extremely effective method to identify (possibly harmful) disturbances, assess the current state of the network, and determine operating decisions that meet network requirements and lead to optimal performance. This paper details an optimization strategy for the identification of source disturbances in the network. Here we consider the source inversion problem modeled as a nonlinear programming problem. Dynamic behavior of municipal water networks is simulated using EPANET. This approach allows for a widely accepted, general purpose user interface. For the source inversion problem, flows and concentrations of the network will be reconciled and unknown sources will be determined at network nodes. Moreover, intrusive optimization and sensitivity analysis techniques are identified to assess the influence of various parameters and models in the network in a computational efficient manner. A number of numerical comparisons are made to demonstrate the effectiveness of various optimization approaches.
On minimal integer representations of weighted games
Freixas, Josep
2011-01-01
We study minimum integer representations for the weights of weighted games, which is linked with some solution concepts in game theory. Closing some gaps in the existing literature we prove that each weighted game with two types of voters admits a unique minimum integer presentation and give examples for more than two types of voters without a minimum integer representation. We characterize the possible weights in minimum integer representations and give examples for at least four types of voters without minimum integer representations preserving types.
Fast resolution of integer Vandermonde systems
Directory of Open Access Journals (Sweden)
Rosa di Salvo
2014-10-01
Full Text Available The resolution of polynomial interpolation problems with integer coefficients directly involves the open issue of the integer inversion of a general Vandermonde matrix defined over the field Z/pZ, for p prime number. The purpose of this paper is to demonstrate the possibility to invert a Vandermonde matrix with integer mod p coefficients and exactly compute the integer inverse matrix in the ring Mat(Z/pZ of square matrices over Z/pZ through the new fast algorithm InVanderMOD. The explicit formula derived for the integer inversion of Vandermonde matrices entirely develops inside the field of the integers mod p, with due consideration to the operation of integer division. The inversion procedure InVanderMOD is valid for any prime number p and competitive in terms of computational effort, since its computational cost is less than O(n^3.
Solving the Water Jugs Problem by an Integer Sequence Approach
Man, Yiu-Kwong
2012-01-01
In this article, we present an integer sequence approach to solve the classic water jugs problem. The solution steps can be obtained easily by additions and subtractions only, which is suitable for manual calculation or programming by computer. This approach can be introduced to secondary and undergraduate students, and also to teachers and…
Nonlinear programming technique for analyzing flocculent settling data.
Rashid, Md Mamunur; Hayes, Donald F
2014-04-01
The traditional graphical approach for drawing iso-concentration curves to analyze flocculent settling data and design sedimentation basins poses difficulties for computer-based design methods. Thus, researchers have developed empirical approaches to analyze settling data. In this study, the ability of five empirical approaches to fit flocculent settling test data is compared. Particular emphasis is given to compare rule-based SETTLE and rule-based nonlinear programming (NLP) techniques as a viable alternative to the modeling methods of Berthouex and Stevens (1982), San (1989), and Ozer (1994). Published flocculent settling data are used to test the suitability of these empirical approaches. The primary objective, however, is to determine if the results of a NLP optimization technique are more reliable than those of other approaches. For this, mathematical curve fitting is conducted and the modeled concentration data are graphically compared to the observed data. The design results in terms of average solid removal efficiency as a function of detention times are also compared. Finally, the sum of squared errors values from these approaches are compared. The results indicate a strong correlation between observed and NLP modeled concentration data. The SETTLE and NLP approaches tend to be more conservative at lower retention times and less conservative at longer retention times. The SETTLE approach appears to be the most conservative. In terms of sum of squared errors values, NLP appears to be rank number one (i.e., best model) for eight data sets and number two for six data sets among 15 data sets. Therefore, NLP is recommended for analyzing flocculent settling data as a logical extension of other approaches. The NLP approach is further recommended as it is an optimization technique and uses conventional mathematical algorithms that can be solved using widely available software such as EXCEL and LINGO.
DEFF Research Database (Denmark)
Hovgaard, Tobias Gybel; Larsen, Lars F. S.; Jørgensen, John Bagterp
2012-01-01
We consider the optimization of power set-points to a large number of wind turbines arranged within close vicinity of each other in a wind farm. The goal is to maximize the total electric power extracted from the wind, taking the wake effects that couple the individual turbines in the farm...... into account. For any mean wind speed, turbulence intensity, and direction we find the optimal static operating points for the wind farm. We propose an iterative optimization scheme to achieve this goal. When the complicated, nonlinear, dynamics of the aerodynamics in the turbines and of the fluid dynamics...... describing the turbulent wind fields’ propagation through the farm are included in a highly detailed black-box model, numerical results for any given values of the parameter sets can easily be evaluated. However, analytic expressions for model representation in the optimization algorithms might be hard...
Institute of Scientific and Technical Information of China (English)
李薇; 徐毅; 李继强; 孙晓伟; 杜晓文; 万军
2013-01-01
In this study, an optimization model was developed based on the integer programming methods to address the environmental risk during solid waste transformation process. The integer programming method can help to address the selection of solid waste transfer routes and expansion schemes. The objective of the developed model is to minimize the system cost in solid waste treatment process considering the environmental effects for the surroundings of driving routes. The results indicated that different types of solid waste may need different recycling stations, in addition, the optimal routes from transfer stations to recycling stations may change during different planning periods. The landfill is always the best option for solid waste treatment due to its lower operation cost. However, pyrolysis is promising in the future owing to its huge treatment volume and the minimum transport and operation costs. The proposed model can effectively optimize resources distributions of municipal solid waste system and provide science-based waste management evidences for decision-makers.%采用整数线性规划的系统分析方法建立模型,以整数规划解决运输路线及处理方式扩容方案的选择问题,以系统经济成本为优化目标,并着重考虑了运输过程产生的3种恶臭气体扩散对周围特殊区域造成的环境影响,优化固体废弃物运输路线.结果表明:不同时期不同的垃圾回收站适合回收的垃圾类别不同;不同时期不同回收站的运输路线最优选择不同;垃圾填埋处理由于处理费用低,一直是垃圾处理的优选方案,但热解处理量较大,增长幅度最大,且运输处理总费用最低,从长远看,热解厂的未来发展趋势较好;该模型能够有效解决城市固体废弃物系统资源优化配置问题,为决策者提供可靠的依据.
Nonlinear programming extensions to rational function approximations of unsteady aerodynamics
Tiffany, Sherwood H.; Adams, William M., Jr.
1987-01-01
This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.
The Expansion of Dynamic Solving Process About a Class of Non-linear Programming Problems
Institute of Scientific and Technical Information of China (English)
ZANG Zhen-chun
2001-01-01
In this paper, we research non-linear programming problems which have a given specialstructure, some simple forms of this kind structure have been solved in some papers, here we focus on othercomplex ones.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Energy Technology Data Exchange (ETDEWEB)
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
Optimality Condition and Wolfe Duality for Invex Interval-Valued Nonlinear Programming Problems
Directory of Open Access Journals (Sweden)
Jianke Zhang
2013-01-01
Full Text Available The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush-Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper.
System Identification for Nonlinear FOPDT Model with Input-Dependent Dead-Time
DEFF Research Database (Denmark)
Sun, Zhen; Yang, Zhenyu
2011-01-01
. In order to identify these parameters in an online manner, the considered system is discretized at first. Then, the nonlinear FOPDT identification problem is formulated as a stochastic Mixed Integer Non-Linear Programming problem, and an identification algorithm is proposed by combining the Branch......An on-line iterative method of system identification for a kind of nonlinear FOPDT system is proposed in the paper. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its dead time depends on the input signal and the other parameters are time dependent...
Nonlinear FOPDT Model Identification for the Superheat Dynamic in a Refrigeration System
DEFF Research Database (Denmark)
Yang, Zhenyu; Sun, Zhen; Andersen, Casper
2011-01-01
the considered system is discretized, the nonlinear FOPDT identification problem is formulated as a Mixed Integer Non-Linear Programming problem, and then an identification algorithm is proposed by combining the Branch-and-Bound method and Least Square technique, in order to on-line identify these time......An on-line nonlinear FOPDT system identification method is proposed and applied to model the superheat dynamic in a supermarket refrigeration system. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its parameters are time dependent. After...
Presolving and regularization in mixed-integer second-order cone optimization
DEFF Research Database (Denmark)
Friberg, Henrik Alsing
Mixed-integer second-order cone optimization is a powerful mathematical framework capable of representing both logical conditions and nonlinear relationships in mathematical models of industrial optimization problems. What is more, solution methods are already part of many major commercial solvers...... both continuous and mixed-integer conic optimization in general, is discovered and treated. This part of the thesis continues the studies of facial reduction preceding the work of Borwein and Wolkowicz [17] in 1981, when the first algorithmic cure for these kinds of reliability issues were formulated....... An important distinction to make between continuous and mixed-integer optimization, however, is that the reliability issues occurring in mixed-integer optimization cannot be blamed on the practitioner’s formulation of the problem. Specifically, as shown, the causes for these issues may well lie within...
Nonlinear programming for classification problems in machine learning
Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio
2016-10-01
We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.
Guevara, V R
2004-02-01
A nonlinear programming optimization model was developed to maximize margin over feed cost in broiler feed formulation and is described in this paper. The model identifies the optimal feed mix that maximizes profit margin. Optimum metabolizable energy level and performance were found by using Excel Solver nonlinear programming. Data from an energy density study with broilers were fitted to quadratic equations to express weight gain, feed consumption, and the objective function income over feed cost in terms of energy density. Nutrient:energy ratio constraints were transformed into equivalent linear constraints. National Research Council nutrient requirements and feeding program were used for examining changes in variables. The nonlinear programming feed formulation method was used to illustrate the effects of changes in different variables on the optimum energy density, performance, and profitability and was compared with conventional linear programming. To demonstrate the capabilities of the model, I determined the impact of variation in prices. Prices for broiler, corn, fish meal, and soybean meal were increased and decreased by 25%. Formulations were identical in all other respects. Energy density, margin, and diet cost changed compared with conventional linear programming formulation. This study suggests that nonlinear programming can be more useful than conventional linear programming to optimize performance response to energy density in broiler feed formulation because an energy level does not need to be set.
多约束非线性背包问题的一种有效算法%An efficient algorithm for multi-dimensional nonlinear knapsack problems
Institute of Scientific and Technical Information of China (English)
陈娟; 孙小玲; 郭慧娟
2006-01-01
Multi-dimensional nonlinear knapsack problem is a bounded nonlinear integer programming problem that maximizes a separable nondecreasing function subject to multiple separable nondecreasing constraints. This problem is often encountered in resource allocation, industrial planning and computer network. In this paper, a new convergent Lagrangian dual method was proposed for solving this problem. Cutting plane method was used to solve the dual problem and to compute the Lagrangian bounds of the primal problem. In order to eliminate the duality gap and thus to guarantee the convergence of the algorithm, domain cut technique was employed to remove certain integer boxes and partition the revised domain to a union of integer boxes. Extensive computational results show that the proposed method is efficient for solving large-scale multi-dimensional nonlinear knapsack problems. Our numerical results also indicate that the cutting plane method significantly outperforms the subgradient method as a dual search procedure.
Dynamic Simulations of Nonlinear Multi-Domain Systems Based on Genetic Programming and Bond Graphs
Institute of Scientific and Technical Information of China (English)
DI Wenhui; SUN Bo; XU Lixin
2009-01-01
A dynamic simulation method for non-linear systems based on genetic programming (GP) and bond graphs (BG) was developed to improve the design of nonlinear multi-domain energy conversion sys-tems. The genetic operators enable the embryo bond graph to evolve towards the target graph according to the fitness function. Better simulation requires analysis of the optimization of the eigenvalue and the filter circuit evolution. The open topological design and space search ability of this method not only gives a more optimized convergence for the operation, but also reduces the generation time for the new circuit graph for the design of nonlinear multi-domain systems.
Institute of Scientific and Technical Information of China (English)
孔云峰; 王震
2012-01-01
This paper aims to develop an optimal location-allocation methodology for school site selection using GIS and integer programming. According to the nearby enrollment policy, the authors propose two linear programming models (boolean and integer) with constrains of total school number and school capacity. The models are simplified by eliminating the unreasonable school-residence links for reducing the number of decision variables and therefore solving the problems efficiently. Since the constraint matrix of the boolean model is a sparse matrix with two non-zero elements per row, it can be solved optimally with very small tolerance using branch and cut algorithm. The constraint matrix of the integer model is similar to the totally unimodualr matrix and can be solved optimally. In ArcGIS 10 geoprocessing framework, the school site-selection tool is designed by integrating ArcGIS network analysis, Coin-or linear programming modeler (PuLP) and linear programming solver Cplex 12. School site selection of a county region with 1276 resident points and 50 schools is tested successfully. The related network analysis, model building, model solving and result visualization can be implemented speedily in normal personal computer with Intel Dual-Core 2. 44GHz CPU and 2GB memory. Case study shows that the mathematical models and solution method introduced in this paper are efficient, easy-to-use and practical for large-scale school location-allocation problems. The authors also argue that instead of using heuristic algorithms, many large-size location-allocation problems can be solved using branch and cut algorithm optimally or optimally with very small tolerance.%合理规划学校布局是实现义务教育均衡发展和落实就近入学政策的一个重要途径.为满足县市级中小学校空间布局规划需求,本文以区位配置优化方法解决学校区位选址问题.以平均入学距离为目标,以学校总数、学校学额为约束条件,分别构建P中
Institute of Scientific and Technical Information of China (English)
刘紫军; 王昊; 李佳燕; 赵豫红
2016-01-01
We propose an energy scheduling method of the heliostat field,based on integer programming,to meet the requirements of power generation and to save operation costs in a solar tower power plant.We adopt a greedy-PSO (particle swarm optimization)algorithm to solve the optimization problem.The simulation results show that the heliostat field can export a specified energy value in the case of DNI (direct normal insolation) change,which verifies the effectiveness of the proposed method.Furthermore,the method is applied to the control of a water-steam receiver and simulation results indicate that real-time energy demand can be satisfied with the proposed method.%针对塔式太阳能热发电过程中镜场调度既需要满足发电能量需求又需要节省操作成本的问题，提出了一种基于整数规划的镜场能量调度方法，同时采用了一种贪婪—粒子群优化算法进行求解，并通过模拟在DNI（太阳直射辐射，direct nor-mal insolation）变化的情况下，使镜场输出固定的能量值，验证了方法的有效性。将此方法应用于水／蒸汽接收器的系统控制中，仿真结果表明方法能够实时跟踪系统所需能量的变化。
Improvement of 0-1 integer programming based on triple-stranded DNA structure%基于三链DNA结构的0-1整数规划改进研究
Institute of Scientific and Technical Information of China (English)
任晓玲; 白雪; 刘希玉
2013-01-01
To realize the effective screening of solutions in DNA computing and to prevent the mismatch between probes, the formation of the hairpin structure etc, this paper presented an improved triple-stranded DNA model to solve 0- 1 integer programming problem. This method made a full array of all combinations of n 0-1 variables. Compared with the original one, the amount of DNA strands needed dropped from O((2n) !) to 0(2n n!) and the improved one made a better selection of feasible solutions. Triple-helix structure could be constructed by the homologous double-helix DNA with the oligodeoxyribonucleotides (ODN) in the mediated of RecA protein. It could make use of its special structure to promote it to the selection of solutions with the double-helix computing model.%为实现DNA计算中对解的有效筛选,防止探针与探针之间的错配、发夹结构等,以及便于检测最终解,提出了改进的三链DNA模型求解0-1规划的设计.该方法编码n个变量的每种组合的所有排列情况.此编码方式不仅使计算所需有效分子量从O((2n)!)下降到O(2nn!),并使对可行解的筛选更加有效.利用寡聚脱氧核苷酸(ODN)在RecA蛋白介导下与同源的双链DNA匹配成三螺旋DNA的特点,可推广到更多以双链DNA分子为计算模型的解的检测中.
Effective integer-to-integer transforms for JPEG2000 coder
Przelaskowski, Artur
2001-12-01
This paper considers reversible transforms which are used in wavelet compression according to nowadays JPEG2000 standard. Original data decomposition in a form of integer wavelet transformation realized in subband decomposition scheme is optimized by design and selection of the most effective transforms. Lifting scheme is used to construct new biorthogonal symmetric wavelets. Number and distribution of vanishing moments, subband coding gain, associated filter length, computational complexity and number of lifting steps were mainly analyzed in the optimization of designed transforms. Coming from many tests of compression efficiency evaluation in JPEG2000 standardization process, the best selected transforms have been compared to designed ones to conclude the most efficient for compression wavelet bases and their important features. Certain new transforms overcome all other in both phases of lossy-to-lossless compression (e.g. up to 0.5 dB of PSNR for 0.5 bpp in comparison to the state-of-art transforms of JPEG2000 compression, and up to 3dB over 5/3 standard reversible transform). Moreover, the lossy compression efficiency of proposed reversible wavelets is comparable to reference irreversible wavelets potential in several cases. The highest improvement over that reference PSNR values is close to 1.2 dB.
Directory of Open Access Journals (Sweden)
Paras Bhatnagar
2012-10-01
Full Text Available Kaul and Kaur [7] obtained necessary optimality conditions for a non-linear programming problem by taking the objective and constraint functions to be semilocally convex and their right differentials at a point to be lower semi-continuous. Suneja and Gupta [12] established the necessary optimality conditions without assuming the semilocal convexity of the objective and constraint functions but their right differentials at the optimal point to be convex. Suneja and Gupta [13] established necessary optimality conditions for an efficient solution of a multiobjective non-linear programming problem by taking the right differentials of the objective functions and constraintfunctions at the efficient point to be convex. In this paper we obtain some results for a properly efficient solution of a multiobjective non-linear fractional programming problem involving semilocally convex and related functions by assuming generalized Slater type constraint qualification.
Energy Technology Data Exchange (ETDEWEB)
Kim, D.; Ghanem, R. [State Univ. of New York, Buffalo, NY (United States)
1994-12-31
Multigrid solution technique to solve a material nonlinear problem in a visual programming environment using the finite element method is discussed. The nonlinear equation of equilibrium is linearized to incremental form using Newton-Rapson technique, then multigrid solution technique is used to solve linear equations at each Newton-Rapson step. In the process, adaptive mesh refinement, which is based on the bisection of a pair of triangles, is used to form grid hierarchy for multigrid iteration. The solution process is implemented in a visual programming environment with distributed computing capability, which enables more intuitive understanding of solution process, and more effective use of resources.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
Integer least-squares theory for the GNSS compass
Teunissen, P. J. G.
2010-07-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to high-precision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable to models for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses non-quadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory
Nonlinear Programming Approach to Optimal Scaling of Partially Ordered Categories
Nishisato, Shizuhiko; Arri, P. S.
1975-01-01
A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. Numerical examples were…
A computer program for predicting nonlinear uniaxial material responses using viscoplastic models
Chang, T. Y.; Thompson, R. L.
1984-01-01
A computer program was developed for predicting nonlinear uniaxial material responses using viscoplastic constitutive models. Four specific models, i.e., those due to Miller, Walker, Krieg-Swearengen-Rhode, and Robinson, are included. Any other unified model is easily implemented into the program in the form of subroutines. Analysis features include stress-strain cycling, creep response, stress relaxation, thermomechanical fatigue loop, or any combination of these responses. An outline is given on the theoretical background of uniaxial constitutive models, analysis procedure, and numerical integration methods for solving the nonlinear constitutive equations. In addition, a discussion on the computer program implementation is also given. Finally, seven numerical examples are included to demonstrate the versatility of the computer program developed.
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
Garbageless reversible implementation of integer linear transformations
DEFF Research Database (Denmark)
Burignat, Stéphane; Vermeirsch, Kenneth; De Vos, Alexis;
2013-01-01
Discrete linear transformations are important tools in information processing. Many such transforms are injective and therefore prime candidates for a physically reversible implementation into hardware. We present here reversible digital implementations of different integer transformations on fou...
On a correlational clustering of integers
Aszalós László; Hajdu Lajos (1968-) (matematikus); Pethő Attila (1950-) (matematikus, informatikus)
2016-01-01
Correlation clustering is a concept of machine learning. The ultimate goal of such a clustering is to find a partition with minimal conflicts. In this paper we investigate a correlation clustering of integers, based upon the greatest common divisor.
Ultimate limit state design of sheet pile walls by finite elements and nonlinear programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe....
A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints
Directory of Open Access Journals (Sweden)
Vasile Moraru
2012-02-01
Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.
Teren, F.
1977-01-01
Minimum time accelerations of aircraft turbofan engines are presented. The calculation of these accelerations was made by using a piecewise linear engine model, and an algorithm based on nonlinear programming. Use of this model and algorithm allows such trajectories to be readily calculated on a digital computer with a minimal expenditure of computer time.
Ultimate Limit State Design Of Sheet Pile Walls By Finite Elements And Nonlinear Programming
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars; Krabbenhøft, Sven
2005-01-01
as a nonlinear programming problem where the yield moment of the wall is minimized subject to equilibrium and yield conditions. The finite element discretization used enables exact fulfillment of these conditions and thus, according to the lower bound theorem, the solutions are safe...
Solving Parity Games on Integer Vectors
Abdulla, Parosh Aziz; Mayr, Richard; Sangnier, Arnaud; Sproston, Jeremy
2013-01-01
We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and multidimensional energy parity games. We show that the multidimensional energy parity game problem is inter-reducible with a subclass of single-sided parity games on vass where just one player can modify the integer counters and the opponent can only change contr...
Optimum sensitivity derivatives of objective functions in nonlinear programming
Barthelemy, J.-F. M.; Sobieszczanski-Sobieski, J.
1983-01-01
The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.
微电网日内调度计划的混合整数规划模型%Mixed Integer Programming Model for Microgrid Intra-day Scheduling
Institute of Scientific and Technical Information of China (English)
孙浩; 张磊; 许海林; 汪隆君
2015-01-01
为进一步调和微电网日内调度计划模型求解速度与精度的矛盾，提出了一种适用于微电网日内调度计划的混合整数规划模型。构建了蓄电池充放电过程模型，能有效计及充放电循环次数和老化成本；在现有微电网经济调度模型的基础上，建立了考虑电压幅值的线性化潮流方程、基于解析几何的线性化支路容量、公共连接点功率交换和功率因数限制等约束模型。通过算例验证所提模型，结果表明：①所提模型求解精度高，快速稳定收敛于全局最优解，且不依赖于初值；②蓄电池充放电过程模型符合工程实际，克服了现有模型中蓄电池频繁充放电加剧老化的局限性。%A mixed integer programming model,which can be used in microgrid intra-day scheduling,is put forward in order to conciliate further the desired attributes of accuracy and computational performance in existing intra-day scheduling model.The model of storage battery charge/discharge process,which considers charge/discharge cycles and aging cost,is proposed. Compared with the conventional model for microgrid economical dispatching,the linearized constraint model,such as power flow with voltage amplitude limitation,branch capacity based on Cartesian geometry,transferring power and power factor of point of common couple et al,is established.The numerical results of case studies demonstrate that the proposed model and its solution are of the fast convergence and independent of initial points,and the storage battery model is in line with the practical engineering,overcoming the limitations of the existing model,which accelerates deterioration due to switching frequently between charge and discharge of storage battery.
Institute of Scientific and Technical Information of China (English)
祝付营; 刘永强; 张慧
2016-01-01
In order to obtain more economic benefits, most water conservancy enterprises now adopt portfolio management ori-ented towards a number of related projects under the guidance of their overall strategic targets rather than managing a single pro-ject individually. According to the relevance of different projects, a mathematical model is established for water conservancy en-terprises to select projects in the process of portfolio management based on integer programming, which aims at the optimal combi-nation of projects and the maximum benefits of the enterprise. With a water conservancy enterprise as an example, portfolio man-agement is applied to the engineering projects awarded to the enterprise, and the combination of projects which may bring about the maximum benefits is selected. Through the example, the applicability and scientific values of project portfolio management for water conservancy enterprise are proved.%目前，多数水利企业为了获得更高的经济效益已不再仅仅对单个水利项目进行单独管理，而是在企业总体战略目标的指导下对多个相关项目进行组合管理。根据项目之间的相关性，利用整数规划算法构建了水利企业在采用项目组合管理时进行项目选择的数学模型，从而筛选出最优的项目组合，实现企业效益最大化的目标。以某水利企业为例，对其中标的若干个工程项目进行组合管理，选择使其获得最大利润的项目组合。由此阐明在水利企业中应用项目组合管理的适用性和科学性。
Institute of Scientific and Technical Information of China (English)
罗宗杰
2012-01-01
When the power grid blackout, making the power system restore normal operation quickly and efficiently can not only reduce the equipment damage of the power generation side, but also improve the load restoration speed of the power side. This paper focuses on the ability of the units which have not self-starting time limit, total system capacity constraints, start power limit, and the constraints of unit restoration priority, and gets the unit start sequence strategy for system restoration process through the mixed binary integer programming algorithm. It is concluded that: in a given recovery time, this strategy can get the optimal order of the system unit startup under the premise of ensuring the safe operation of the unit and the maximum generation capacity of system, and can reduce the post-reconstruction and load restoration time directly.%当电网大停电之后,运行人员快速高效地把电力系统恢复到正常运行状态,不仅可以降低发电侧的设备损害程度,还可提高用电侧负荷的恢复速度.重点分析了没有自启动能力的机组时间限制、系统总容量限制、启动功率限制、机组恢复优先权限制等条件,通过混合二元整数规划算法得到系统恢复过程中机组启动次序的策略.结论表明:在给定恢复时间内,采用这种策略能在保证机组的安全运行和系统的最大发电容量的前提下,得到系统机组启动的最优次序,可直接减少后期系统重构和负荷恢复的时间.
A new method of thermal network modeling - A nonlinear programming approach
Adachi, M.; Miyaoka, S.; Muramatsu, A.; Funabashi, M.; Nakajima, T.
A new method for correcting thermal network model coefficients is described. This method sharply reduces discrepancies obtained by the nonlinear programming approach in the conductance coefficients and radiation coefficients for determining the heat balance of a spacecraft. The method consists of an experimental design and a nonlinear parameter identification. An experimental design for obtaining useful data for the thermal network model correction is discussed. A simulation study has shown that the standard deviation of the estimated temperature and estimation error of the parameters are reduced by 50 percent and 70 percent respectively.
Giles, G. L.; Wallas, M.
1981-01-01
User documentation is presented for a computer program which considers the nonlinear properties of the strain isolator pad (SIP) in the static stress analysis of the shuttle thermal protection system. This program is generalized to handle an arbitrary SIP footprint including cutouts for instrumentation and filler bar. Multiple SIP surfaces are defined to model tiles in unique locations such as leading edges, intersections, and penetrations. The nonlinearity of the SIP is characterized by experimental stress displacement data for both normal and shear behavior. Stresses in the SIP are calculated using a Newton iteration procedure to determine the six rigid body displacements of the tile which develop reaction forces in the SIP to equilibrate the externally applied loads. This user documentation gives an overview of the analysis capabilities, a detailed description of required input data and an example to illustrate use of the program.
Slip and Slide Method of Factoring Trinomials with Integer Coefficients over the Integers
Donnell, William A.
2012-01-01
In intermediate and college algebra courses there are a number of methods for factoring quadratic trinomials with integer coefficients over the integers. Some of these methods have been given names, such as trial and error, reversing FOIL, AC method, middle term splitting method and slip and slide method. The purpose of this article is to discuss…
Elementary Theory of Factoring Trinomials with Integer Coefficients over the Integers
Donnell, William A.
2010-01-01
An important component of intermediate and college algebra courses involves teaching students methods to factor a trinomial with integer coefficients over the integers. The aim of this article is to present a theoretical justification of that which is often taught, but really never explained as to why it works. The theory is presented, and a…
Design of asymptotic estimators: an approach based on neural networks and nonlinear programming.
Alessandri, Angelo; Cervellera, Cristiano; Sanguineti, Marcello
2007-01-01
A methodology to design state estimators for a class of nonlinear continuous-time dynamic systems that is based on neural networks and nonlinear programming is proposed. The estimator has the structure of a Luenberger observer with a linear gain and a parameterized (in general, nonlinear) function, whose argument is an innovation term representing the difference between the current measurement and its prediction. The problem of the estimator design consists in finding the values of the gain and of the parameters that guarantee the asymptotic stability of the estimation error. Toward this end, if a neural network is used to take on this function, the parameters (i.e., the neural weights) are chosen, together with the gain, by constraining the derivative of a quadratic Lyapunov function for the estimation error to be negative definite on a given compact set. It is proved that it is sufficient to impose the negative definiteness of such a derivative only on a suitably dense grid of sampling points. The gain is determined by solving a Lyapunov equation. The neural weights are searched for via nonlinear programming by minimizing a cost penalizing grid-point constraints that are not satisfied. Techniques based on low-discrepancy sequences are applied to deal with a small number of sampling points, and, hence, to reduce the computational burden required to optimize the parameters. Numerical results are reported and comparisons with those obtained by the extended Kalman filter are made.
Nonlinear programming in design of control systems with specified handling qualities.
Schy, A. A.
1972-01-01
A method is described for using nonlinear programing in the computer-aided design of aircraft control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector, and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter aircraft, in which the requirements vector is chosen from the official handling-qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains.
Integer Discontinuity of Density Functional Theory
Mosquera, Martin A
2014-01-01
Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons.
Direct heuristic dynamic programming for nonlinear tracking control with filtered tracking error.
Yang, Lei; Si, Jennie; Tsakalis, Konstantinos S; Rodriguez, Armando A
2009-12-01
This paper makes use of the direct heuristic dynamic programming design in a nonlinear tracking control setting with filtered tracking error. A Lyapunov stability approach is used for the stability analysis of the tracking system. It is shown that the closed-loop tracking error and the approximating neural network weight estimates retain the property of uniformly ultimate boundedness under the presence of neural network approximation error and bounded unknown disturbances under certain conditions.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Nonlinear time series prediction is studied by using an improved least squares support vector machine (LSSVM) regression based on chaotic mutation evolutionary programming (CMEP) approach for parameter optimization.We analyze how the prediction error varies with different parameters (σ, γ) in LS-SVM. In order to select appropriate parameters for the prediction model, we employ CMEP algorithm. Finally, Nasdaq stock data are predicted by using this LS-SVM regression based on CMEP, and satisfactory results are obtained.
A nonlinear programming method for system design with results that have been implemented
Hauser, F.
1984-01-01
A general nonlinear programming algorithm (NICO) is discussed. An academic optimization example is given. The NICO multi-input, multi-output control system design is discussed. NICO applications relative to launch vehicle autopilot design, space shuttle static balance, transient response criteria in the design of a reentry vehicle control system, and waterjet propulsion and lift system components sized to a large surface effect ship are noted.
Nonlinear program based optimization of boost and buck-boost converter designs
Rahman, S.; Lee, F. C.
1981-01-01
The facility of an Augmented Lagrangian (ALAG) multiplier based nonlinear programming technique is demonstrated for minimum-weight design optimizations of boost and buck-boost power converters. Certain important features of ALAG are presented in the framework of a comprehensive design example for buck-boost power converter design optimization. The study provides refreshing design insight of power converters and presents such information as weight and loss profiles of various semiconductor components and magnetics as a function of the switching frequency.
Tilt stability in nonlinear programming under Mangasarian-Fromovitz constraint qualification
Mordukhovich, B. S.; Outrata, J. (Jiří)
2013-01-01
The paper concerns the study of tilt stability of local minimizers in standard problems of nonlinear programming. This notion plays an important role in both theoretical and numerical aspects of optimization and has drawn a lot of attention in optimization theory and its applications, especially in recent years. Under the classical Mangasarian–Fromovitz Constraint Qualification, we establish relationships between tilt stability and some other stability notions in constrained optimization. I...
Institute of Scientific and Technical Information of China (English)
陈晓华; 李春芝; 俞坚奇
2011-01-01
With the network storage technology development, how to improve transmission performance and expand storage capacity is problem to be resolved. This paper presents VCloud Storage, a cloud storage system based on virtual host. And it can improve file transmission performance, balance the load and expand storage capacity unlimitedly. It firstly abstracts running state mathematical model of the virtual hosts, then creates integer programming model on the running state mathematical model. By implicit enumeration algorithm, it allocates virtual host to the client storage request optimally. Finally client modules and virtual host modules finish file transmission collaboratively. The experimental result shows that the model and algorithm have optimization effect significantly. VCloud Storage total throughput and average transmission rate is superior to Microsoft's SkyDrive storage,Tencent QQ mailbox store and a single virtual host storage. The proposed model and algorithm enhance file transmission performance and stability, and are an effective method that improves the performance of storage system in WAN network.%随着网络存储技术的发展,如何提高广域网网络存储系统的传输性能和存储容量是亟待解决的同题.本文提出一个基于虚拟主机集群的云存储系统(VCloud Storage),具有良好的负载均衡能力,提高了文件传输性能,同时解决了存储容量无限扩展的问题.本文提出的云存储系统首先抽象虚拟主机运行状态数学模型,然后在虚拟主机运行状态数学模型的基础上建立整数规划模型,利用隐枚举算法,最优化分配虚拟主机给客户端模块的存储请求,最终客户端模块与虚拟主机接口协作完成文件传输.实验结果表明:采用本文提出的模型及算法具有明显的优化效果,VClDud Storage总吞吐量和平均传输率均优于微软SkyDrive存储、腾讯QQ邮箱存储和单虚拟主机存储.本文提出的模型及算法增强了文
Hermitian K-theory of the integers
Berrick, A. J.; Karoubi, M.
2005-01-01
The 2-primary torsion of the higher algebraic K-theory of the integers has been computed by Rognes and Weibel. In this paper we prove analogous results for the Hermitian K-theory of the integers with 2 inverted (denoted by Z'). We also prove in this case the analog of the Lichtenbaum conjecture for the hermitian K-theory of Z' : the homotopy fixed point set of a suitable Z/2 action on the classifying space of the algebraic K-theory of Z' is the hermitian K-theory of Z' after 2-adic completion.
NEW ALGORITHM FOR FAST INTEGER AMBIGUITY RESOLUTION
Institute of Scientific and Technical Information of China (English)
HEXiao-feng; HUXiao-ping
2005-01-01
Fast integer ambiguity resolution is referred as a key part in precision relative positioning of the GPS carrier phase. A new algorithm for fast integer ambiguity resolution based on LAMBDA and FASF methods is proposed. This algorithm integrates the LAMBDA method and the FASF method, thus improving the efficiency of the ambiguity resolution. Firstly, the ambiguity search space transformation in the LAMBDA method is used,and then the FASF method is used to search ambiguities. Experiments in the relative positioning of about 1 km static baseline demonstrate that the error is less than 1 cm.
A Binomial Integer-Valued ARCH Model.
Ristić, Miroslav M; Weiß, Christian H; Janjić, Ana D
2016-11-01
We present an integer-valued ARCH model which can be used for modeling time series of counts with under-, equi-, or overdispersion. The introduced model has a conditional binomial distribution, and it is shown to be strictly stationary and ergodic. The unknown parameters are estimated by three methods: conditional maximum likelihood, conditional least squares and maximum likelihood type penalty function estimation. The asymptotic distributions of the estimators are derived. A real application of the novel model to epidemic surveillance is briefly discussed. Finally, a generalization of the introduced model is considered by introducing an integer-valued GARCH model.
Trajectory optimization for vehicles using control vector parameterization and nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Spangelo, I.
1994-12-31
This thesis contains a study of optimal trajectories for vehicles. Highly constrained nonlinear optimal control problems have been solved numerically using control vector parameterization and nonlinear programming. Control vector parameterization with shooting has been described in detail to provide the reader with the theoretical background for the methods which have been implemented, and which are not available in standard text books. Theoretical contributions on accuracy analysis and gradient computations have also been presented. Optimal trajectories have been computed for underwater vehicles controlled in all six degrees of freedom by DC-motor driven thrusters. A class of nonlinear optimal control problems including energy-minimization, possibly combined with time minimization and obstacle avoidance, has been developed. A program system has been specially designed and written in the C language to solve this class of optimal control problems. Control vector parameterization with single shooting was used. This special implementation has made it possible to perform a detailed analysis, and to investigate numerical details of this class of optimization methods which would have been difficult using a general purpose CVP program system. The results show that this method for solving general optimal control problems is well suited for use in guidance and control of marine vehicles. Results from rocket trajectory optimization has been studied in this work to bring knowledge from this area into the new area of trajectory optimization of marine vehicles. 116 refs., 24 figs., 23 tabs.
Directory of Open Access Journals (Sweden)
Olav Slupphaug
2001-01-01
Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.
Institute of Scientific and Technical Information of China (English)
陈理; 王克峰; 徐霄羽; 姚平经
2004-01-01
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.
CONDITIONAL FACTORIZATION BASED ON LATTICE THEORY FOR -INTEGERS
Institute of Scientific and Technical Information of China (English)
Zheng Yonghui; Zhu Yuefei
2008-01-01
In this paper, the integer N = pkq is called a -integer, if p and q are odd primes with almost the same size and k is a positive integer. Such integers were previously proposed for various cryptographic applications. The conditional factorization based on lattice theory for n-bit -integers is considered, and there is an algorithm in time polynomial in n to factor these integers if the least significant |(2k-1)n/(3k-1)(k-1)| bits of p are given.
Energy Technology Data Exchange (ETDEWEB)
Raju, P. P.
1980-05-01
This report summarizes the results of the study program to assess the benefits of nonlinear analysis methods in Light Water Reactor (LWR) component designs. The current study reveals that despite its increased cost and other complexities, nonlinear analysis is a practical and valuable tool for the design of LWR components, especially under ASME Level D service conditions (faulted conditions) and it will greatly assist in the evaluation of ductile fracture potential of pressure boundary components. Since the nonlinear behavior is generally a local phenomenon, the design of complex components can be accomplished through substructuring isolated localized regions and evaluating them in detail using nonlinear analysis methods.
Quadratic forms representing all odd positive integers
Rouse, Jeremy
2011-01-01
We consider the problem of classifying all positive-definite integer-valued quadratic forms that represent all positive odd integers. Kaplansky considered this problem for ternary forms, giving a list of 23 candidates, and proving that 19 of those represent all positive odds. (Jagy later dealt with a 20th candidate.) Assuming that the remaining three forms represent all positive odds, we prove that an arbitrary, positive-definite quadratic form represents all positive odds if and only if it represents the odd numbers from 1 up to 451. This result is analogous to Bhargava and Hanke's celebrated 290-theorem. In addition, we prove that these three remaining ternaries represent all positive odd integers, assuming the generalized Riemann hypothesis. This result is made possible by a new analytic method for bounding the cusp constants of integer-valued quaternary quadratic forms $Q$ with fundamental discriminant. This method is based on the analytic properties of Rankin-Selberg $L$-functions, and we use it to prove...
Sums of Integer Squares: A New Look.
Sastry, K. R. S.; Pranesachar, C. R.; Venkatachala, B. J.
1998-01-01
Focuses on the study of the sum of two integer squares, neither of which is zero square. Develops some new interesting and nonstandard ideas that can be put to use in number theory class, mathematics club meetings, or popular lectures. (ASK)
Predecessor queries in dynamic integer sets
DEFF Research Database (Denmark)
Brodal, Gerth Stølting
1997-01-01
We consider the problem of maintaining a set of n integers in the range 0.2w–1 under the operations of insertion, deletion, predecessor queries, minimum queries and maximum queries on a unit cost RAM with word size w bits. Let f (n) be an arbitrary nondecreasing smooth function satisfying n...
Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.
Duarte, Belmiro P M; Wong, Weng Kee; Oliveira, Nuno M C
2016-02-15
We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for finding D-, A- and E-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficient D-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.
1979-01-01
A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.
Directory of Open Access Journals (Sweden)
Samir Dey
2015-07-01
Full Text Available This paper proposes a new multi-objective intuitionistic fuzzy goal programming approach to solve a multi-objective nonlinear programming problem in context of a structural design. Here we describe some basic properties of intuitionistic fuzzy optimization. We have considered a multi-objective structural optimization problem with several mutually conflicting objectives. The design objective is to minimize weight of the structure and minimize the vertical deflection at loading point of a statistically loaded three-bar planar truss subjected to stress constraints on each of the truss members. This approach is used to solve the above structural optimization model based on arithmetic mean and compare with the solution by intuitionistic fuzzy goal programming approach. A numerical solution is given to illustrate our approach.
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Integer least-squares theory for the GNSS compass
Teunissen, P.J.G.
2010-01-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategi
On the Delone property of (−β-integers
Directory of Open Access Journals (Sweden)
Wolfgang Steiner
2011-08-01
Full Text Available The (−β-integers are natural generalisations of the β-integers, and thus of the integers, for negative real bases. They can be described by infinite words which are fixed points of anti-morphisms. We show that they are not necessarily uniformly discrete and relatively dense in the real numbers.
Integer least-squares theory for the GNSS compass
Teunissen, P.J.G.
2010-01-01
Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search
Chen, Zhi; Yuan, Yuan; Zhang, Shu-Shen; Chen, Yu; Yang, Feng-Lin
2013-03-26
Critical environmental and human health concerns are associated with the rapidly growing fields of nanotechnology and manufactured nanomaterials (MNMs). The main risk arises from occupational exposure via chronic inhalation of nanoparticles. This research presents a chance-constrained nonlinear programming (CCNLP) optimization approach, which is developed to maximize the nanaomaterial production and minimize the risks of workplace exposure to MNMs. The CCNLP method integrates nonlinear programming (NLP) and chance-constrained programming (CCP), and handles uncertainties associated with both the nanomaterial production and workplace exposure control. The CCNLP method was examined through a single-walled carbon nanotube (SWNT) manufacturing process. The study results provide optimal production strategies and alternatives. It reveal that a high control measure guarantees that environmental health and safety (EHS) standards regulations are met, while a lower control level leads to increased risk of violating EHS regulations. The CCNLP optimization approach is a decision support tool for the optimization of the increasing MNMS manufacturing with workplace safety constraints under uncertainties.
The solution of singular optimal control problems using direct collocation and nonlinear programming
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
A Class of Semilocal E-Preinvex Functions and Its Applications in Nonlinear Programming
Directory of Open Access Journals (Sweden)
Hehua Jiao
2012-01-01
Full Text Available A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.
Fleming, P.
1983-01-01
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 nonlinear 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. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.
A NEW SQP-FILTER METHOD FOR SOLVING NONLINEAR PROGRAMMING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Duoquan Li
2006-01-01
In [4],Fletcher and Leyffer present a new method that solves nonlinear programming problems without a penalty function by SQP-Filter algorithm. It has attracted much attention due to its good numerical results. In this paper we propose a new SQP-Filter method which can overcome Maratos effect more effectively. We give stricter acceptant criteria when the iterative points are far from the optimal points and looser ones vice-versa. About this new method,the proof of global convergence is also presented under standard assumptions. Numerical results show that our method is efficient.
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
CAD of control systems: Application of nonlinear programming to a linear quadratic formulation
Fleming, P.
1983-01-01
The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a Computer Aided Design (CAD) package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, model following errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.
Institute of Scientific and Technical Information of China (English)
Qin Ni
2001-01-01
An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and possesses Q-quadratic convergence rate. The global convergence of this new method is proved,the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems.
Nonsingularity Conditions for FB System of Reformulating Nonlinear Second-Order Cone Programming
Directory of Open Access Journals (Sweden)
Shaohua Pan
2013-01-01
Full Text Available This paper is a counterpart of Bi et al., 2011. For a locally optimal solution to the nonlinear second-order cone programming (SOCP, specifically, under Robinson’s constraint qualification, we establish the equivalence among the following three conditions: the nonsingularity of Clarke’s Jacobian of Fischer-Burmeister (FB nonsmooth system for the Karush-Kuhn-Tucker conditions, the strong second-order sufficient condition and constraint nondegeneracy, and the strong regularity of the Karush-Kuhn-Tucker point.
Luo, Biao; Wu, Huai-Ning; Li, Han-Xiong
2015-04-01
Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2017-03-01
This paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton-Jacobi-Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.
Lu, Zhao; Sun, Jing; Butts, Kenneth
2014-05-01
Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
Discrete-time nonlinear HJB solution using approximate dynamic programming: convergence proof.
Al-Tamimi, Asma; Lewis, Frank L; Abu-Khalaf, Murad
2008-08-01
Convergence of the value-iteration-based heuristic dynamic programming (HDP) algorithm is proven in the case of general nonlinear systems. That is, it is shown that HDP converges to the optimal control and the optimal value function that solves the Hamilton-Jacobi-Bellman equation appearing in infinite-horizon discrete-time (DT) nonlinear optimal control. It is assumed that, at each iteration, the value and action update equations can be exactly solved. The following two standard neural networks (NN) are used: a critic NN is used to approximate the value function, whereas an action network is used to approximate the optimal control policy. It is stressed that this approach allows the implementation of HDP without knowing the internal dynamics of the system. The exact solution assumption holds for some classes of nonlinear systems and, specifically, in the specific case of the DT linear quadratic regulator (LQR), where the action is linear and the value quadratic in the states and NNs have zero approximation error. It is stressed that, for the LQR, HDP may be implemented without knowing the system A matrix by using two NNs. This fact is not generally appreciated in the folklore of HDP for the DT LQR, where only one critic NN is generally used.
PSLQ: An Algorithm to Discover Integer Relations
Energy Technology Data Exchange (ETDEWEB)
Bailey, David H.; Borwein, J. M.
2009-04-03
Let x = (x{sub 1}, x{sub 2} {hor_ellipsis}, x{sub n}) be a vector of real or complex numbers. x is said to possess an integer relation if there exist integers a{sub i}, not all zero, such that a{sub 1}x{sub 1} + a{sub 2}x{sub 2} + {hor_ellipsis} + a{sub n}x{sub n} = 0. By an integer relation algorithm, we mean a practical computational scheme that can recover the vector of integers ai, if it exists, or can produce bounds within which no integer relation exists. As we will see in the examples below, an integer relation algorithm can be used to recognize a computed constant in terms of a formula involving known constants, or to discover an underlying relation between quantities that can be computed to high precision. At the present time, the most effective algorithm for integer relation detection is the 'PSLQ' algorithm of mathematician-sculptor Helaman Ferguson [10, 4]. Some efficient 'multi-level' implementations of PSLQ, as well as a variant of PSLQ that is well-suited for highly parallel computer systems, are given in [4]. PSLQ constructs a sequence of integer-valued matrices B{sub n} that reduces the vector y = xB{sub n}, until either the relation is found (as one of the columns of B{sub n}), or else precision is exhausted. At the same time, PSLQ generates a steadily growing bound on the size of any possible relation. When a relation is found, the size of smallest entry of the vector y abruptly drops to roughly 'epsilon' (i.e. 10{sup -p}, where p is the number of digits of precision). The size of this drop can be viewed as a 'confidence level' that the relation is real and not merely a numerical artifact - a drop of 20 or more orders of magnitude almost always indicates a real relation. Very high precision arithmetic must be used in PSLQ. If one wishes to recover a relation of length n, with coefficients of maximum size d digits, then the input vector x must be specified to at least nd digits, and one must employ nd
Integer sparse distributed memory: analysis and results.
Snaider, Javier; Franklin, Stan; Strain, Steve; George, E Olusegun
2013-10-01
Sparse distributed memory is an auto-associative memory system that stores high dimensional Boolean vectors. Here we present an extension of the original SDM, the Integer SDM that uses modular arithmetic integer vectors rather than binary vectors. This extension preserves many of the desirable properties of the original SDM: auto-associativity, content addressability, distributed storage, and robustness over noisy inputs. In addition, it improves the representation capabilities of the memory and is more robust over normalization. It can also be extended to support forgetting and reliable sequence storage. We performed several simulations that test the noise robustness property and capacity of the memory. Theoretical analyses of the memory's fidelity and capacity are also presented.
D. Veestraeten
2015-01-01
Sums of the parabolic cylinder function for, in absolute value, growing half-integer and integer orders emerge in numerous fields such as time-series analysis, quantum optics and transmission in wireless channels. This paper derives recursion formulas for the parabolic cylinder function with integer
Energy Technology Data Exchange (ETDEWEB)
De la Torre Vega, Eli
1997-04-01
In the first chapter the deduction of the Benders cuts are presented, departing from the properties of duality. Also the properties of the Benders cuts are presented, as well as the initial algorithm of Benders to solve any problem of lineal integer-mixed programming are presented. In the second chapter, of the planning of the expansion of means of generation and transmission in an electric power system is presented and the different structures of the mathematical programming it gives rise to and how the method of Benders can be adapted to these. In the third chapter the theoretical contributions of this work are presented: a) How to initialize the master problem to take advantage of the acquired experience after having solved a similar problem, so that it can be solved more efficiently, the succession of integer-mixed problems of linear programming that arise when solving the problem of the planning of the expansion of generation and transmission means in an electric power system. b) How to generate a master problem whose continuous optimal solution corresponds to the optimal continuous one of the integer-mixed problem, so that the search of integer solutions is made in the vicinity of the optimum continuous. c) How to generate an integer solution, close to the optimum continuous of the integer-mixed problem, that has high probability of being feasible, and that is perhaps the optimal integer solution, in a smaller time than that required to solve it in exact form. In addition, other ideas are presented that can be incorporated to the Benders method. In order to show the effectiveness of the proposed ideas, in chapter 4 the results obtained when solving several problems are presented using: 1. The updated Benders method, 2. The branch and bound method, 3. The update of Benders when adding restrictions and 4. The update of Benders when considered as integer each time to more variables. Finally a summary is made of the achievements, of the conclusions obtained and
Asymptotic stabilisation for a class of feedforward input-delay systems with ratios of odd integers
Wu, Jian; Chen, Weisheng; Miao, Qiguang
2013-11-01
This article addresses the stabilisation problem by state-feedback for a class of feedforward input-delay nonlinear systems with ratios of odd integer powers. The designed controller achieves the global asymptotic stability. Based on the appropriate state transformation of time-delay systems and the Lyapunov method, the problem of controller design can be converted into the problem of finding a parameter which can be obtained by appraising the nonlinear terms of the systems. Finally, three simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this article.
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Zhu, Yuanheng; Zhao, Dongbin; Yang, Xiong; Zhang, Qichao
2017-01-10
Sum of squares (SOS) polynomials have provided a computationally tractable way to deal with inequality constraints appearing in many control problems. It can also act as an approximator in the framework of adaptive dynamic programming. In this paper, an approximate solution to the H∞ optimal control of polynomial nonlinear systems is proposed. Under a given attenuation coefficient, the Hamilton-Jacobi-Isaacs equation is relaxed to an optimization problem with a set of inequalities. After applying the policy iteration technique and constraining inequalities to SOS, the optimization problem is divided into a sequence of feasible semidefinite programming problems. With the converged solution, the attenuation coefficient is further minimized to a lower value. After iterations, approximate solutions to the smallest L₂-gain and the associated H∞ optimal controller are obtained. Four examples are employed to verify the effectiveness of the proposed algorithm.
A high performance neural network for solving nonlinear programming problems with hybrid constraints
Tao, Qing; Cao, Jinde; Xue, Meisheng; Qiao, Hong
2001-09-01
A continuous neural network is proposed in this Letter for solving optimization problems. It not only can solve nonlinear programming problems with the constraints of equality and inequality, but also has a higher performance. The main advantage of the network is that it is an extension of Newton's gradient method for constrained problems, the dynamic behavior of the network under special constraints and the convergence rate can be investigated. Furthermore, the proposed network is simpler than the existing networks even for solving positive definite quadratic programming problems. The network considered is constrained by a projection operator on a convex set. The advanced performance of the proposed network is demonstrated by means of simulation of several numerical examples.
On the convex hull of the simple integer recourse objective function
Klein Haneveld, Willem K.; Stougie, L.; van der Vlerk, Maarten H.
1995-01-01
We consider the objective function of a simple integer recourse problem with fixed technology matrix. Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program. We present an
On the expected value function of a simple integer recourse problem with random technology matrix
Klein Haneveld, Willem K.; van der Vlerk, Maarten H.
1994-01-01
In this paper we consider the expected value function of a stochastic simple recourse program with random technology matrix and integer variables in the second stage. Due to its separability the analysis is straightforward. Conditions for finiteness, continuity, Lipschitz continuity and
On the convex hull of the simple integer recourse objective function
Klein Haneveld, Willem K.; Stougie, L.; van der Vlerk, Maarten H.
1995-01-01
We consider the objective function of a simple integer recourse problem with fixed technology matrix. Using properties of the expected value function, we prove a relation between the convex hull of this function and the expected value function of a continuous simple recourse program. We present an a
Park, Y. C.; Chang, M. H.; Lee, T.-Y.
2007-06-01
A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.
FORTRAN programs for calculating nonlinear seismic ground response in two dimensions
Joyner, W.B.
1978-01-01
The programs described here were designed for calculating the nonlinear seismic response of a two-dimensional configuration of soil underlain by a semi-infinite elastic medium representing bedrock. There are two programs. One is for plane strain motions, that is, motions in the plane perpendicular to the long axis of the structure, and the other is for antiplane strain motions, that is motions parallel to the axis. The seismic input is provided by specifying what the motion of the rock-soil boundary would be if the soil were absent and the boundary were a free surface. This may be done by supplying a magnetic tape containing the values of particle velocity for every boundary point at every instant of time. Alternatively, a punch card deck may be supplied giving acceleration values at every instant of time. In the plane strain program it is assumed that the acceleration values apply simultaneously to every point on the boundary; in the antiplane strain program it is assumed that the acceleration values characterize a plane shear wave propagating upward in the underlying elastic medium at a specified angle with the vertical. The nonlinear hysteretic behavior of the soil is represented by a three-dimensional rheological model. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. Computations are done in terms of stress departures from an unspecified initial state. Source listings are provided here along with instructions for preparing the input. A more detailed discussion of the method is presented elsewhere.
Xu, Hao; Jagannathan, Sarangapani
2013-03-01
The stochastic optimal controller design for the nonlinear networked control system (NNCS) with uncertain system dynamics is a challenging problem due to the presence of both system nonlinearities and communication network imperfections, such as random delays and packet losses, which are not unknown a priori. In the recent literature, neuro dynamic programming (NDP) techniques, based on value and policy iterations, have been widely reported to solve the optimal control of general affine nonlinear systems. However, for realtime control, value and policy iterations-based methodology are not suitable and time-based NDP techniques are preferred. In addition, output feedback-based controller designs are preferred for implementation. Therefore, in this paper, a novel NNCS representation incorporating the system uncertainties and network imperfections is introduced first by using input and output measurements for facilitating output feedback. Then, an online neural network (NN) identifier is introduced to estimate the control coefficient matrix, which is subsequently utilized for the controller design. Subsequently, the critic and action NNs are employed along with the NN identifier to determine the forward-in-time, time-based stochastic optimal control of NNCS without using value and policy iterations. Here, the value function and control inputs are updated once a sampling instant. By using novel NN weight update laws, Lyapunov theory is used to show that all the closed-loop signals and NN weights are uniformly ultimately bounded in the mean while the approximated control input converges close to its target value with time. Simulation results are included to show the effectiveness of the proposed scheme.
Decimal Integer Multiplication based on Molecular Beacons
Directory of Open Access Journals (Sweden)
Jing Wang
2013-12-01
Full Text Available Due to the enhancement of circuit integration level, and the accelerating of working frequency of traditional computer, it requires components dimension must be constantly decreased. So encapsulation, etching and other problems of chip are becoming more and more difficult to solve, which causes its performance also become unstable. In order to overcome this problem, DNA computing as a new kind of molecular computing mode, with its high parallelism, huge amounts of storage capacity, low energy consumption advantages has received extensive attention. Being the same with traditional electronic computer, DNA computer is composed by arithmetic operations such as addition, subtraction, multiplication and dividing and basic logic units such as AND, OR, NON gate. This paper puts forward a new method to realize decimal integer multiplication based on molecular beacons. The algorithm firstly converts decimal integer to binary number, and then resolves the multiplication process into multiplication of current bit and addition of intermediate result after shifting two steps. Molecular beacon is used as multiplying unit, coding sequence is used as multiplier in this method. Based on the working principle of molecular beacon, multiplication operation of two one-bit binary is simulated. And by recording fluorescence status of molecular beacon to observe intermediate result and carry-bit situation, the final result can be obtained through addition after shifting. Examples prove that this method can realize decimal integer multiplication rapidly and accurately. This method is similar to multiplication system in traditional electronic computer, and it provides a simple, easier operation method for DNA computer to realize arithmetic operation.
Integer Set Compression and Statistical Modeling
DEFF Research Database (Denmark)
Larsson, N. Jesper
2014-01-01
Compression of integer sets and sequences has been extensively studied for settings where elements follow a uniform probability distribution. In addition, methods exist that exploit clustering of elements in order to achieve higher compression performance. In this work, we address the case where...... enumeration of elements may be arbitrary or random, but where statistics is kept in order to estimate probabilities of elements. We present a recursive subset-size encoding method that is able to benefit from statistics, explore the effects of permuting the enumeration order based on element probabilities...
Division Unit for Binary Integer Decimals
DEFF Research Database (Denmark)
Lang, Tomas; Nannarelli, Alberto
2009-01-01
-recurrence algorithm to BID representation and implement the division unit in standard cell technology. The implementation of the proposed BID division unit is compared to that of a BCD based unit implementing the same algorithm. The comparison shows that for normalized operands the BID unit has the same latency......In this work, we present a radix-10 division unit that is based on the digit-recurrence algorithm and implements binary encodings (binary integer decimal or BID) for significands. Recent decimal division designs are all based on the binary coded decimal (BCD) encoding. We adapt the radix-10 digit...
On large-scale nonlinear programming techniques for solving optimal control problems
Energy Technology Data Exchange (ETDEWEB)
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
Finding Bayesian Optimal Designs for Nonlinear Models: A Semidefinite Programming-Based Approach.
Duarte, Belmiro P M; Wong, Weng Kee
2015-08-01
This paper uses semidefinite programming (SDP) to construct Bayesian optimal design for nonlinear regression models. The setup here extends the formulation of the optimal designs problem as an SDP problem from linear to nonlinear models. Gaussian quadrature formulas (GQF) are used to compute the expectation in the Bayesian design criterion, such as D-, A- or E-optimality. As an illustrative example, we demonstrate the approach using the power-logistic model and compare results in the literature. Additionally, we investigate how the optimal design is impacted by different discretising schemes for the design space, different amounts of uncertainty in the parameter values, different choices of GQF and different prior distributions for the vector of model parameters, including normal priors with and without correlated components. Further applications to find Bayesian D-optimal designs with two regressors for a logistic model and a two-variable generalised linear model with a gamma distributed response are discussed, and some limitations of our approach are noted.
Zhu, Yuanheng; Zhao, Dongbin; Li, Xiangjun
2017-03-01
H∞ control is a powerful method to solve the disturbance attenuation problems that occur in some control systems. The design of such controllers relies on solving the zero-sum game (ZSG). But in practical applications, the exact dynamics is mostly unknown. Identification of dynamics also produces errors that are detrimental to the control performance. To overcome this problem, an iterative adaptive dynamic programming algorithm is proposed in this paper to solve the continuous-time, unknown nonlinear ZSG with only online data. A model-free approach to the Hamilton-Jacobi-Isaacs equation is developed based on the policy iteration method. Control and disturbance policies and value are approximated by neural networks (NNs) under the critic-actor-disturber structure. The NN weights are solved by the least-squares method. According to the theoretical analysis, our algorithm is equivalent to a Gauss-Newton method solving an optimization problem, and it converges uniformly to the optimal solution. The online data can also be used repeatedly, which is highly efficient. Simulation results demonstrate its feasibility to solve the unknown nonlinear ZSG. When compared with other algorithms, it saves a significant amount of online measurement time.
Pavarini, C.
1974-01-01
Work in two somewhat distinct areas is presented. First, the optimal system design problem for a Mars-roving vehicle is attacked by creating static system models and a system evaluation function and optimizing via nonlinear programming techniques. The second area concerns the problem of perturbed-optimal solutions. Given an initial perturbation in an element of the solution to a nonlinear programming problem, a linear method is determined to approximate the optimal readjustments of the other elements of the solution. Then, the sensitivity of the Mars rover designs is described by application of this method.
Institute of Scientific and Technical Information of China (English)
Wan Zhongping; Wang Guangrain; Lv Yibing
2011-01-01
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems
Energy Technology Data Exchange (ETDEWEB)
Lee, Se Jung; Park, Gyung Jin [Hanyang University, Seoul (Korea, Republic of)
2014-05-15
In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency.
Hamiltonian-Driven Adaptive Dynamic Programming for Continuous Nonlinear Dynamical Systems.
Yang, Yongliang; Wunsch, Donald; Yin, Yixin
2017-02-01
This paper presents a Hamiltonian-driven framework of adaptive dynamic programming (ADP) for continuous time nonlinear systems, which consists of evaluation of an admissible control, comparison between two different admissible policies with respect to the corresponding the performance function, and the performance improvement of an admissible control. It is showed that the Hamiltonian can serve as the temporal difference for continuous-time systems. In the Hamiltonian-driven ADP, the critic network is trained to output the value gradient. Then, the inner product between the critic and the system dynamics produces the value derivative. Under some conditions, the minimization of the Hamiltonian functional is equivalent to the value function approximation. An iterative algorithm starting from an arbitrary admissible control is presented for the optimal control approximation with its convergence proof. The implementation is accomplished by a neural network approximation. Two simulation studies demonstrate the effectiveness of Hamiltonian-driven ADP.
Lewis, Robert Michael
1997-01-01
This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.
Assimilation of ERBE data with a nonlinear programming technique to improve cloud-cover diagnosis
Wu, Xiangqian; Smith, William L.
1992-01-01
A method is developed to assimilate satellite data for the purpose of improving the diagnosis of fractional cloud cover within a numerical weather prediction model. The method makes use of a nonlinear programming technique to find a set of parameters for the cloud diagnosis that minimizes the difference between the observed and model-produced outgoing longwave radiation (OLR). The algorithm and theoretical basis of the method are presented. The method has been applied in two forecast experiments using a numerical weather prediction model. The results from a winter case demonstrate that the root-mean-square (rms) difference between the observed and forecasted OLR can be reduced by 50 percent when the optimized cloud diagnosis is used, with the remaining rms difference within the background noise.
An inner-outer nonlinear programming approach for constrained quadratic matrix model updating
Andretta, M.; Birgin, E. G.; Raydan, M.
2016-01-01
The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns with updating a symmetric second-order finite element model so that it remains symmetric and the updated model reproduces a given set of desired eigenvalues and eigenvectors by replacing the corresponding ones from the original model. Taking advantage of the special structure of the constraint set, it is first shown that the QFEMUP can be formulated as a suitable constrained nonlinear programming problem. Using this formulation, a method based on successive optimizations is then proposed and analyzed. To avoid that spurious modes (eigenvectors) appear in the frequency range of interest (eigenvalues) after the model has been updated, additional constraints based on a quadratic Rayleigh quotient are dynamically included in the constraint set. A distinct practical feature of the proposed method is that it can be implemented by computing only a few eigenvalues and eigenvectors of the associated quadratic matrix pencil.
EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
DU Xue-wu; ZHANG Lian-sheng; SHANG You-lin; LI Ming-ming
2005-01-01
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, from the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
User's guide to the Fault Inferring Nonlinear Detection System (FINDS) computer program
Caglayan, A. K.; Godiwala, P. M.; Satz, H. S.
1988-01-01
Described are the operation and internal structure of the computer program FINDS (Fault Inferring Nonlinear Detection System). The FINDS algorithm is designed to provide reliable estimates for aircraft position, velocity, attitude, and horizontal winds to be used for guidance and control laws in the presence of possible failures in the avionics sensors. The FINDS algorithm was developed with the use of a digital simulation of a commercial transport aircraft and tested with flight recorded data. The algorithm was then modified to meet the size constraints and real-time execution requirements on a flight computer. For the real-time operation, a multi-rate implementation of the FINDS algorithm has been partitioned to execute on a dual parallel processor configuration: one based on the translational dynamics and the other on the rotational kinematics. The report presents an overview of the FINDS algorithm, the implemented equations, the flow charts for the key subprograms, the input and output files, program variable indexing convention, subprogram descriptions, and the common block descriptions used in the program.
Institute of Scientific and Technical Information of China (English)
陈理; 王克峰; 徐霄羽; 姚平经
2004-01-01
In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant.The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.
Horizontal visibility graphs from integer sequences
Lacasa, Lucas
2016-09-01
The horizontal visibility graph (HVG) is a graph-theoretical representation of a time series and builds a bridge between dynamical systems and graph theory. In recent years this representation has been used to describe and theoretically compare different types of dynamics and has been applied to characterize empirical signals, by extracting topological features from the associated HVGs which have shown to be informative on the class of dynamics. Among some other measures, it has been shown that the degree distribution of these graphs is a very informative feature that encapsulates nontrivial information of the series's generative dynamics. In particular, the HVG associated to a bi-infinite real-valued series of independent and identically distributed random variables is a universal exponential law P(k)=(1/3){(2/3)}k-2, independent of the series marginal distribution. Most of the current applications have however only addressed real-valued time series, as no exact results are known for the topological properties of HVGs associated to integer-valued series. In this paper we explore this latter situation and address univariate time series where each variable can only take a finite number n of consecutive integer values. We are able to construct an explicit formula for the parametric degree distribution {P}n(k), which we prove to converge to the continuous case for large n and deviates otherwise. A few applications are then considered.
An experiment on Lowest Unique Integer Games
Yamada, Takashi; Hanaki, Nobuyuki
2016-12-01
We experimentally study Lowest Unique Integer Games (LUIGs) to determine if and how subjects self-organize into different behavioral classes. In a LUIG, N(≥ 3) players submit a positive integer up to M and the player choosing the smallest number not chosen by anyone else wins. LUIGs are simplified versions of real systems such as Lowest/Highest Unique Bid Auctions that have been attracting attention from scholars, yet experimental studies are scarce. Furthermore, LUIGs offer insights into choice patterns that can shed light on the alleviation of congestion problems. Here, we consider four LUIGs with N = { 3 , 4 } and M = { 3 , 4 } . We find that (a) choices made by more than 1/3 of subjects were not significantly different from what a symmetric mixed-strategy Nash equilibrium (MSE) predicts; however, (b) subjects who behaved significantly differently from what the MSE predicts won the game more frequently. What distinguishes subjects was their tendencies to change their choices following losses.
Prime labeling of families of trees with Gaussian integers
Directory of Open Access Journals (Sweden)
Steven Klee
2016-08-01
Full Text Available A graph on n vertices is said to admit a prime labeling if we can label its vertices with the first n natural numbers such that any two adjacent vertices have relatively prime labels. Here we extend the idea of prime labeling to the Gaussian integers, which are the complex numbers whose real and imaginary parts are both integers. We begin by defining an order on the Gaussian integers that lie in the first quadrant. Using this ordering, we show that several families of trees admit a prime labeling with the Gaussian integers.
Nonlinear FOPDT Model Identification for the Superheat Dynamic in a Refrigeration System
DEFF Research Database (Denmark)
Yang, Zhenyu; Sun, Zhen; Andersen, Casper
2011-01-01
An on-line nonlinear FOPDT system identification method is proposed and applied to model the superheat dynamic in a supermarket refrigeration system. The considered nonlinear FOPDT model is an extension of the standard FOPDT model by means that its parameters are time dependent. After......-dependent parameters. The proposed method is firstly tested through a number of numerical examples, and then applied to model the superheat dynamic in a supermarket refrigeration system based on experimental data. As shown in these studies, the proposed method is quite promising in terms of reasonable accuracy, large...... the considered system is discretized, the nonlinear FOPDT identification problem is formulated as a Mixed Integer Non-Linear Programming problem, and then an identification algorithm is proposed by combining the Branch-and-Bound method and Least Square technique, in order to on-line identify these time...
Integer wavelet transform for embedded lossy to lossless image compression.
Reichel, J; Menegaz, G; Nadenau, M J; Kunt, M
2001-01-01
The use of the discrete wavelet transform (DWT) for embedded lossy image compression is now well established. One of the possible implementations of the DWT is the lifting scheme (LS). Because perfect reconstruction is granted by the structure of the LS, nonlinear transforms can be used, allowing efficient lossless compression as well. The integer wavelet transform (IWT) is one of them. This is an interesting alternative to the DWT because its rate-distortion performance is similar and the differences can be predicted. This topic is investigated in a theoretical framework. A model of the degradations caused by the use of the IWT instead of the DWT for lossy compression is presented. The rounding operations are modeled as additive noise. The noise are then propagated through the LS structure to measure their impact on the reconstructed pixels. This methodology is verified using simulations with random noise as input. It predicts accurately the results obtained using images compressed by the well-known EZW algorithm. Experiment are also performed to measure the difference in terms of bit rate and visual quality. This allows to a better understanding of the impact of the IWT when applied to lossy image compression.
Detection of gross errors using mixed integer optimization approach in process industry
Institute of Scientific and Technical Information of China (English)
MEI Cong-li; SU Hong-ye; CHU Jian
2007-01-01
A novel mixed integer linear programming (NMILP) model for detection of gross errors is presented in this paper.Yamamura et al.(1988) designed a model for detection of gross errors and data reconciliation based on Akaike information criterion (AIC). But much computational cost is needed due to its combinational nature. A mixed integer linear programming (MILP)approach was performed to reduce the computational cost and enhance the robustness. But it loses the super performance of maximum likelihood estimation. To reduce the computational cost and have the merit of maximum likelihood estimation, the simultaneous data reconciliation method in an MILP framework is decomposed and replaced by an NMILP subproblem and a quadratic programming (QP) or a least squares estimation (LSE) subproblem. Simulation result of an industrial case shows the high efficiency of the method.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function,constraint functions and their first-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.
Energy Technology Data Exchange (ETDEWEB)
Glass, Micheal W.; Hogan, Roy E., Jr.; Gartling, David K.
2010-03-01
The need for the engineering analysis of systems in which the transport of thermal energy occurs primarily through a conduction process is a common situation. For all but the simplest geometries and boundary conditions, analytic solutions to heat conduction problems are unavailable, thus forcing the analyst to call upon some type of approximate numerical procedure. A wide variety of numerical packages currently exist for such applications, ranging in sophistication from the large, general purpose, commercial codes, such as COMSOL, COSMOSWorks, ABAQUS and TSS to codes written by individuals for specific problem applications. The original purpose for developing the finite element code described here, COYOTE, was to bridge the gap between the complex commercial codes and the more simplistic, individual application programs. COYOTE was designed to treat most of the standard conduction problems of interest with a user-oriented input structure and format that was easily learned and remembered. Because of its architecture, the code has also proved useful for research in numerical algorithms and development of thermal analysis capabilities. This general philosophy has been retained in the current version of the program, COYOTE, Version 5.0, though the capabilities of the code have been significantly expanded. A major change in the code is its availability on parallel computer architectures and the increase in problem complexity and size that this implies. The present document describes the theoretical and numerical background for the COYOTE program. This volume is intended as a background document for the user's manual. Potential users of COYOTE are encouraged to become familiar with the present report and the simple example analyses reported in before using the program. The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction
On Secure Two-Party Integer Division
DEFF Research Database (Denmark)
Dahl, Morten; Ning, Chao; Toft, Tomas
2012-01-01
We consider the problem of secure integer division: given two Paillier encryptions of ℓ-bit values n and d, determine an encryption of $\\lfloor \\frac{n}{d}\\rfloor$ without leaking any information about n or d. We propose two new protocols solving this problem. The first requires $\\ensuremath......{\\mathcal{O}}(\\ell)$ arithmetic operations on encrypted values (secure addition and multiplication) in $\\ensuremath{\\mathcal{O}}(1)$ rounds. This is the most efficient constant-rounds solution to date. The second protocol requires only $\\ensuremath{\\mathcal{O}} \\left( (\\log^2 \\ell)(\\kappa + \\operatorname{loglog} \\ell) \\right......)$ arithmetic operations in $\\ensuremath{\\mathcal{O}}(\\log^2 \\ell)$ rounds, where κ is a correctness parameter. Theoretically, this is the most efficient solution to date as all previous solutions have required Ω(ℓ) operations. Indeed, the fact that an o(ℓ) solution is possible at all is highly surprising....
Statistical Mechanical Models of Integer Factorization Problem
Nakajima, Chihiro H.; Ohzeki, Masayuki
2017-01-01
We formulate the integer factorization problem via a formulation of the searching problem for the ground state of a statistical mechanical Hamiltonian. The first passage time required to find a correct divisor of a composite number signifies the exponential computational hardness. The analysis of the density of states of two macroscopic quantities, i.e., the energy and the Hamming distance from the correct solutions, leads to the conclusion that the ground state (correct solution) is completely isolated from the other low-energy states, with the distance being proportional to the system size. In addition, the profile of the microcanonical entropy of the model has two peculiar features that are each related to two marked changes in the energy region sampled via Monte Carlo simulation or simulated annealing. Hence, we find a peculiar first-order phase transition in our model.
Directory of Open Access Journals (Sweden)
Veli ULUÇAM
2010-07-01
Full Text Available Abstract:This work presents a mixed integer linearprogramming method developed by using 0-1 variables forsolving aggregate production planning problem with thefollowing performance criteria: (1 maximize profit, (2minimize costs. The production planning activities are calledas aggregate production planning when both it is producedmore than one goods and the demand changes period byperiod. The purpose of aggregate production planning is not toprepare detailed plans for each goods, it is to do plans forwhole goods produced in the firm together to take in hand.Aggregate production planning is probably one of the mostimportant, yet least understood, jobs that a manager performs.However, all parts of the organization, operations, marketing,finance, and so on, must work together in the planning processto ensure that they are moving in harmony with one another.Aggregate production planning is such a method that canmove all parts of the organizations in same harmony.Özet:Bu çalışmada; kazançların maksimize edilirkenmaliyetlerin minimize edilebileceği bir bütünleşik üretimplanlama probleminin, 0–1 değişkenleri kullanılarakgeliştirilmiş karma tamsayılı doğrusal programlama tekniği ileçözümü anlatılmaktadır. Birden fazla çeşitte ürünün bir aradaüretildiği ve talebin dönemlere göre değişiklik gösterdiğidurumlarda üretim planlama faaliyetleri bütünleşik üretimplanlama olarak tanımlanır. Planlama çalışmalarınınbütünleşik olma niteliği, bu yöntemin tek tek ürünlerin detaylıplanlarının hazırlanması amacıyla değil, işletme tarafındanüretilen tüm ürünlerin bir arada ele alınarak planlamaçalışmalarının yapılmasıdır. Son yıllarda daha iyi anlaşıldığıüzere, bütünleşik üretim planlaması bir yöneticininperformansını etkileyen en önemli kriterdir. Bununla beraberbir işletmenin tüm bölümleri, üretim, pazarlama, finans vediğerleri aynı ahenk içersinde ve uyumlu olarak
Superposition of two optical vortices with opposite integer or non-integer orbital angular momentum
Directory of Open Access Journals (Sweden)
Carlos Fernando Díaz Meza
2016-04-01
Full Text Available This work develops a brief proposal to achieve the superposition of two opposite vortex beams, both with integer or non-integer mean value of the orbital angular momentum. The first part is about the generation of this kind of spatial light distributions through a modified Brown and Lohmann’s hologram. The inclusion of a simple mathematical expression into the pixelated grid’s transmittance function, based in Fourier domain properties, shifts the diffraction orders counterclockwise and clockwise to the same point and allows the addition of different modes. The strategy is theoretically and experimentally validated for the case of two opposite rotation helical wavefronts.
Garbage-free reversible constant multipliers for arbitrary integers
DEFF Research Database (Denmark)
Mogensen, Torben Ægidius
2013-01-01
We present a method for constructing reversible circuitry for multiplying integers by arbitrary integer constants. The method is based on Mealy machines and gives circuits whose size are (in the worst case) linear in the size of the constant. This makes the method unsuitable for large constants......, but gives quite compact circuits for small constants. The circuits use no garbage or ancillary lines....
On the Relationship between Integer Lifting and Rounding Transform
Directory of Open Access Journals (Sweden)
R. Vargic
2007-12-01
Full Text Available In this paper we analyze the relationship between integer Lifting scheme and Rounding transform as means to compute the wavelet transform in signal processing area. We bring some new results which better describe relationship, reversibility and equivalence of integer lifting scheme and rounding transform concept.
A Paper-and-Pencil gcd Algorithm for Gaussian Integers
Szabo, Sandor
2005-01-01
As with natural numbers, a greatest common divisor of two Gaussian (complex) integers "a" and "b" is a Gaussian integer "d" that is a common divisor of both "a" and "b". This article explores an algorithm for such gcds that is easy to do by hand.
Discrete Dirac equation on a finite half-integer lattice
Smalley, L. L.
1986-01-01
The formulation of the Dirac equation on a discrete lattice with half-integer spacing and periodic boundary conditions is investigated analytically. The importance of lattice formulations for problems in field theory and quantum mechanics is explained; the concept of half-integer Fourier representation is introduced; the discrete Dirac equation for the two-dimensional case is derived; dispersion relations for the four-dimensional case are developed; and the spinor formulation for the Dirac fields on the half-integer lattice and the discrete time variable for the four-dimensional time-dependent Dirac equation are obtained. It is argued that the half-integer lattice, because it takes the Dirac Lagrangian into account, is more than a mere relabeling of the integer lattice and may have fundamental physical meaning (e.g., for the statistics of fermions). It is noted that the present formulation does not lead to species doubling, except in the continuum limit.
Gorelick, S.M.; Voss, C.I.; Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.
1984-01-01
A simulation-management methodology is demonstrated for the rehabilitation of aquifers that have been subjected to chemical contamination. Finite element groundwater flow and contaminant transport simulation are combined with nonlinear optimization. The model is capable of determining well locations plus pumping and injection rates for groundwater quality control. Examples demonstrate linear or nonlinear objective functions subject to linear and nonlinear simulation and water management constraints. -from Authors
Optimal bipedal interactions with dynamic terrain: synthesis and analysis via nonlinear programming
Hubicki, Christian; Goldman, Daniel; Ames, Aaron
In terrestrial locomotion, gait dynamics and motor control behaviors are tuned to interact efficiently and stably with the dynamics of the terrain (i.e. terradynamics). This controlled interaction must be particularly thoughtful in bipeds, as their reduced contact points render them highly susceptible to falls. While bipedalism under rigid terrain assumptions is well-studied, insights for two-legged locomotion on soft terrain, such as sand and dirt, are comparatively sparse. We seek an understanding of how biological bipeds stably and economically negotiate granular media, with an eye toward imbuing those abilities in bipedal robots. We present a trajectory optimization method for controlled systems subject to granular intrusion. By formulating a large-scale nonlinear program (NLP) with reduced-order resistive force theory (RFT) models and jamming cone dynamics, the optimized motions are informed and shaped by the dynamics of the terrain. Using a variant of direct collocation methods, we can express all optimization objectives and constraints in closed-form, resulting in rapid solving by standard NLP solvers, such as IPOPT. We employ this tool to analyze emergent features of bipedal locomotion in granular media, with an eye toward robotic implementation.
Value Iteration Adaptive Dynamic Programming for Optimal Control of Discrete-Time Nonlinear Systems.
Wei, Qinglai; Liu, Derong; Lin, Hanquan
2016-03-01
In this paper, a value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon undiscounted optimal control problems for discrete-time nonlinear systems. The present value iteration ADP algorithm permits an arbitrary positive semi-definite function to initialize the algorithm. A novel convergence analysis is developed to guarantee that the iterative value function converges to the optimal performance index function. Initialized by different initial functions, it is proven that the iterative value function will be monotonically nonincreasing, monotonically nondecreasing, or nonmonotonic and will converge to the optimum. In this paper, for the first time, the admissibility properties of the iterative control laws are developed for value iteration algorithms. It is emphasized that new termination criteria are established to guarantee the effectiveness of the iterative control laws. Neural networks are used to approximate the iterative value function and compute the iterative control law, respectively, for facilitating the implementation of the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the present method.
Event-Based Robust Control for Uncertain Nonlinear Systems Using Adaptive Dynamic Programming.
Zhang, Qichao; Zhao, Dongbin; Wang, Ding
2016-10-18
In this paper, the robust control problem for a class of continuous-time nonlinear system with unmatched uncertainties is investigated using an event-based control method. First, the robust control problem is transformed into a corresponding optimal control problem with an augmented control and an appropriate cost function. Under the event-based mechanism, we prove that the solution of the optimal control problem can asymptotically stabilize the uncertain system with an adaptive triggering condition. That is, the designed event-based controller is robust to the original uncertain system. Note that the event-based controller is updated only when the triggering condition is satisfied, which can save the communication resources between the plant and the controller. Then, a single network adaptive dynamic programming structure with experience replay technique is constructed to approach the optimal control policies. The stability of the closed-loop system with the event-based control policy and the augmented control policy is analyzed using the Lyapunov approach. Furthermore, we prove that the minimal intersample time is bounded by a nonzero positive constant, which excludes Zeno behavior during the learning process. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed control scheme.
Sahoo, Avimanyu; Xu, Hao; Jagannathan, Sarangapani
2016-09-01
This paper presents an event-triggered near optimal control of uncertain nonlinear discrete-time systems. Event-driven neurodynamic programming (NDP) is utilized to design the control policy. A neural network (NN)-based identifier, with event-based state and input vectors, is utilized to learn the system dynamics. An actor-critic framework is used to learn the cost function and the optimal control input. The NN weights of the identifier, the critic, and the actor NNs are tuned aperiodically once every triggered instant. An adaptive event-trigger condition to decide the trigger instants is derived. Thus, a suitable number of events are generated to ensure a desired accuracy of approximation. A near optimal performance is achieved without using value and/or policy iterations. A detailed analysis of nontrivial inter-event times with an explicit formula to show the reduction in computation is also derived. The Lyapunov technique is used in conjunction with the event-trigger condition to guarantee the ultimate boundedness of the closed-loop system. The simulation results are included to verify the performance of the controller. The net result is the development of event-driven NDP.
Sahoo, Avimanyu; Jagannathan, Sarangapani
2017-02-01
In this paper, an event-driven stochastic adaptive dynamic programming (ADP)-based technique is introduced for nonlinear systems with a communication network within its feedback loop. A near optimal control policy is designed using an actor-critic framework and ADP with event sampled state vector. First, the system dynamics are approximated by using a novel neural network (NN) identifier with event sampled state vector. The optimal control policy is generated via an actor NN by using the NN identifier and value function approximated by a critic NN through ADP. The stochastic NN identifier, actor, and critic NN weights are tuned at the event sampled instants leading to aperiodic weight tuning laws. Above all, an adaptive event sampling condition based on estimated NN weights is designed by using the Lyapunov technique to ensure ultimate boundedness of all the closed-loop signals along with the approximation accuracy. The net result is event-driven stochastic ADP technique that can significantly reduce the computation and network transmissions. Finally, the analytical design is substantiated with simulation results.
The nurse scheduling problem: a goal programming and nonlinear optimization approaches
Hakim, L.; Bakhtiar, T.; Jaharuddin
2017-01-01
Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.
Optimal aeroassisted orbital transfer with plane change using collocation and nonlinear programming
Shi, Yun. Y.; Nelson, R. L.; Young, D. H.
1990-01-01
The fuel optimal control problem arising in the non-planar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) with orbital plane change. The basic strategy here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the aeroassisted HEO to LEO transfer consists of three phases. In the first phase, the orbital transfer begins with a deorbit impulse at HEO which injects the vehicle into an elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and bank angle modulations to perform the desired orbital plane change and to satisfy heating constraints. Because of the energy loss during the turn, an impulse is required to initiate the third phase to boost the vehicle back to the desired LEO orbital altitude. The third impulse is then used to circularize the orbit at LEO. The problem is solved by a direct optimization technique which uses piecewise polynomial representation for the state and control variables and collocation to satisfy the differential equations. This technique converts the optimal control problem into a nonlinear programming problem which is solved numerically. Solutions were obtained for cases with and without heat constraints and for cases of different orbital inclination changes. The method appears to be more powerful and robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Optimal Reservoir Operation for Hydropower Generation using Non-linear Programming Model
Arunkumar, R.; Jothiprakash, V.
2012-05-01
Hydropower generation is one of the vital components of reservoir operation, especially for a large multi-purpose reservoir. Deriving optimal operational rules for such a large multi-purpose reservoir serving various purposes like irrigation, hydropower and flood control are complex, because of the large dimension of the problem and the complexity is more if the hydropower production is not an incidental. Thus optimizing the operations of a reservoir serving various purposes requires a systematic study. In the present study such a large multi-purpose reservoir, namely, Koyna reservoir operations are optimized for maximizing the hydropower production subject to the condition of satisfying the irrigation demands using a non-linear programming model. The hydropower production from the reservoir is analysed for three different dependable inflow conditions, representing wet, normal and dry years. For each dependable inflow conditions, various scenarios have been analyzed based on the constraints on the releases and the results are compared. The annual power production, combined monthly power production from all the powerhouses, end of month storage levels, evaporation losses and surplus are discussed. From different scenarios, it is observed that more hydropower can be generated for various dependable inflow conditions, if the restrictions on releases are slightly relaxed. The study shows that Koyna dam is having potential to generate more hydropower.
Sumin, M. I.
2015-06-01
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
Integer lattice dynamics for Vlasov-Poisson
Mocz, Philip; Succi, Sauro
2017-03-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving-mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.
Integer Lattice Dynamics for Vlasov-Poisson
Mocz, Philip
2016-01-01
We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, ...
The integer quantum hall effect revisited
Energy Technology Data Exchange (ETDEWEB)
Michalakis, Spyridon [Los Alamos National Laboratory; Hastings, Matthew [Q STATION, CALIFORNIA
2009-01-01
For T - L x L a finite subset of Z{sup 2}, let H{sub o} denote a Hamiltonian on T with periodic boundary conditions and finite range, finite strength intetactions and a unique ground state with a nonvanishing spectral gap. For S {element_of} T, let q{sub s} denote the charge at site s and assume that the total charge Q = {Sigma}{sub s {element_of} T} q{sub s} is conserved. Using the local charge operators q{sub s}, we introduce a boundary magnetic flux in the horizontal and vertical direction and allow the ground state to evolve quasiadiabatically around a square of size one magnetic flux, in flux space. At the end of the evolution we obtain a trivial Berry phase, which we compare, via a method reminiscent of Stokes Theorem. to the Berry phase obtained from an evolution around an exponentially small loop near the origin. As a result, we show, without any averaging assumption, that the Hall conductance is quantized in integer multiples of e{sup 2}/h up to exponentially small corrections of order e{sup -L/{zeta}}, where {zeta}, is a correlation length that depends only on the gap and the range and strength of the interactions.
Directory of Open Access Journals (Sweden)
Zhong Wan
2013-01-01
Full Text Available In accord with the practical engineering design conditions, a nonlinear programming model is constructed for maximizing the fatigue life of V-belt drive in which some polymorphic uncertainties are incorporated. For a given satisfaction level and a confidence level, an equivalent formulation of this uncertain optimization model is obtained where only interval parameters are involved. Based on the concepts of maximal and minimal range inequalities for describing interval inequality, the interval parameter model is decomposed into two standard nonlinear programming problems, and an algorithm, called two-step based sampling algorithm, is developed to find an interval optimal solution for the original problem. Case study is employed to demonstrate the validity and practicability of the constructed model and the algorithm.
Directory of Open Access Journals (Sweden)
Yonghwan Kim
2011-03-01
Full Text Available The present paper introduced a computer program, called WISH, which is based on a time-domain Rankine panel method. The WISH has been developed for practical use to predict the linear and nonlinear ship motion and structural loads in waves. The WISH adopts three different levels of seakeeping analysis: linear, weakly-nonlinear and weak-scatterer approaches. Later, WISH-FLEX has been developed to consider hydroelasticity effects on hull-girder structure. This program can solve the springing and whipping problems by coupling between the hydrodynamic and structural problems. More recently this development has been continued to more diverse problems, including the motion responses of multiple adjacent bodies, the effects of seakeeping in ship maneuvering, and the floating-body motion in finite-depth domain with varying bathymetry. This paper introduces a brief theoretical and numerical background of the WISH package, and some validation results. Also several applications to real ships and offshore structures are shown.
Diversity and non-integer differentiation for system dynamics
Oustaloup, Alain
2014-01-01
Based on a structured approach to diversity, notably inspired by various forms of diversity of natural origins, Diversity and Non-integer Derivation Applied to System Dynamics provides a study framework to the introduction of the non-integer derivative as a modeling tool. Modeling tools that highlight unsuspected dynamical performances (notably damping performances) in an ""integer"" approach of mechanics and automation are also included. Written to enable a two-tier reading, this is an essential resource for scientists, researchers, and industrial engineers interested in this subject area. Ta
Generalization of a few results in Integer Partitions
Dastidar, Manosij Ghosh
2011-01-01
In this paper, we generalize a few important results in Integer Partitions; namely the results known as Stanley's theorem and Elder's theorem, and the congruence results proposed by Ramanujan for the partition function. We generalize the results of Stanley and Elder from a fixed integer to an array of subsequent integers, and propose an analogue of Ramanujan's congruence relations for the `number of parts' function instead of the partition function. We also deduce the generating function for the `number of parts', and relate the technical results with their graphical interpretations through a novel use of the Ferrer's diagrams.
Poole, L. R.
1972-01-01
A computer program is presented by which the effects of nonlinear suspension-system elastic characteristics on parachute inflation loads and motions can be investigated. A mathematical elastic model of suspension-system geometry is coupled to the planar equations of motion of a general vehicle and canopy. Canopy geometry and aerodynamic drag characteristics and suspension-system elastic properties are tabular inputs. The equations of motion are numerically integrated by use of an equivalent fifth-order Runge-Kutta technique.
A nonlinear programming optimization model to maximize net revenue in cheese manufacture.
Papadatos, A; Berger, A M; Pratt, J E; Barbano, D M
2002-11-01
A nonlinear programming optimization model was developed to maximize net revenue in cheese manufacture and is described in this paper. The model identifies the optimal mix of milk resources together with the types of cheeses and co-products that maximize net revenue. It works in Excel while it takes the data specified by the user from a user-friendly interface created in Access. The user can specify any number of resources, cheese types, and co-products. To demonstrate the capabilities of the model, we determined the impact of variation in milk price and composition in the period 1998 to 2000 on the optimal mix of resources and optimal type of co-product for Cheddar and low-moisture, part-skim Mozzarella. It was also desired to determine the impact of variation in protein content of nonfat dry milk (NDM) on net revenue, and examine the effect of reconstitution of NDM with water versus milk on net revenue. The optimal mix of resources and the net revenue markedly varied as milk resource prices and composition varied. The net revenue for Mozzarella was much higher than for Cheddar when the price of cream was high. Cheese plants that did not optimize the use of resources in response to variations in prices and composition missed a significant profit opportunity. Whey powder was more profitable than 34% whey protein concentrate and lactose in most months. The use of high-protein NDM led to an appreciable increase in net revenue. When the value of the nonfat portion of raw milk was high, reconstitution of NDM with water rather than milk markedly raised net revenue.
Compiler for Fast, Accurate Mathematical Computing on Integer Processors Project
National Aeronautics and Space Administration — The proposers will develop a computer language compiler to enable inexpensive, low-power, integer-only processors to carry our mathematically-intensive comptutations...
Research on an augmented Lagrangian penalty function algorithm for nonlinear programming
Frair, L.
1978-01-01
The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.
Mixed-integer vertex covers on bipartite graphs
Gerards, A.M.H.; Conforti, M.; Zambelli, G.; Fischetti, M.; Williamson, D.P.
2007-01-01
Let $A$ be the edge-node incidence matrix of a bipartite graph $G = (U, V ; E)$, $I$ be a subset of the nodes of $G$, and $b$ be a vector such that $2b$ is integral. We consider the following mixed-integer set: $X(G, b, I) = {x : Ax ≥ b, x ≥ 0, x_i$ integer for all $i ∈ I}$
Abrashkevich, Alexander; Puzynin, I. V.
2004-01-01
A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program. Program summaryTitle of program: CANM Catalogue number: ADSN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSN Program available from: CPC Program Library, Queen's University of Belfast, Northern Ireland Licensing provisions: none Computer for which the program is designed and others on which it has been tested: Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PC Installation: Department of Chemistry, University of Toronto, Toronto, Canada Operating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7 Programming language used: FORTRAN 90 Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KB No. of bits in distributed program including test data, etc.: 15283 Distribution format: tar gz format No. of lines in distributed program, including test data, etc.: 1794 Peripherals used: line printer, scratch disc store External subprograms used: DGECO and DGESL [1] Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's method Nature of physical problem: System of nonlinear simultaneous equations F i(x 1,x 2,…,x n)=0,1⩽i⩽n, is numerically solved. It can be written in vector form as F( X)= 0, X∈ Rn, where F : Rn→ Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of
Wang, Fei-Yue; Jin, Ning; Liu, Derong; Wei, Qinglai
2011-01-01
In this paper, we study the finite-horizon optimal control problem for discrete-time nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an ε-error bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method.
Minimum fuel coplanar aeroassisted orbital transfer using collocation and nonlinear programming
Shi, Yun Yuan; Young, D. H.
1991-01-01
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem
Tiffany, Sherwood H.; Adams, William M., Jr.
1988-01-01
The approximation of unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft are discussed. Two methods of formulating these approximations are extended to include the same flexibility in constraining the approximations and the same methodology in optimizing nonlinear parameters as another currently used extended least-squares method. Optimal selection of nonlinear parameters is made in each of the three methods by use of the same nonlinear, nongradient optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is lower order than that required when no optimization of the nonlinear terms is performed. The free linear parameters are determined using the least-squares matrix techniques of a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from different approaches are described and results are presented that show comparative evaluations from application of each of the extended methods to a numerical example.
Minimizing the Integer Ambiguity Search Space for RTK
Institute of Scientific and Technical Information of China (English)
Yang Yun-chun; R. R. Hatch; R. T. Sharpe
2003-01-01
Differential GPS carrier phase measurements have much lower noise and multipath error than that of pseudorange measurements.The result is centimeter accuracy for Real-Time Kinematic (RTK).However, the measurement of the carrier phase has a constant unknown integer ambiguity. Several technical issues are related to solving the integer ambiguity correctly. They are: proper stochastic model, search space definition and initialization, search space reduction, state and standard deviation calculation, validation and rejection criteria for the unique and correct candidate. Search space reduction is critically important. It not only affects the ambiguity resolution speed, but also defines the ambiguity resolution success rate. The smaller the search space, the easier it is to find the unique and correct candidate set. The paper analyzes the integer ambiguity search space in its residual domain.The search space is minimized by: Analyzing the maximum independent integer ambiguity measurement set theoretically; Selecting the best initial measurement set that minimizes the search range of each satellite in the set and reduces the error effects from noise that may cause the wrong integer ambiguity solution for the remaining satellites not contained in the initial measurement set.Since the Residual Sensitive Matrix (S-Matrix) relates the integer ambiguity candidate set directly to post-fix residuals, it is not necessary to compute a fix for each candidate set thus making the integ erambiguity search process much more efficient. Also, minimizing the search space in the residual domain improves the search efficiency significantly and at the same time improves its reliability. Performance issues, such as recursive and weighted search techniques as well as methods for improving reliability, are also discussed in the article.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Solution of transient optimization problems by using an algorithm based on nonlinear programming
Teren, F.
1977-01-01
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Directory of Open Access Journals (Sweden)
Deisemara Ferreira
2008-01-01
Full Text Available Neste artigo propomos um modelo de otimização inteira mista para o problema de dimensionamento e seqüenciamento dos lotes de produção em fábricas de refrigerantes de pequeno porte, com tempos e custos de set up de produção dependentes do seqüenciamento dos lotes. O modelo considera o estágio de envase como sendo o gargalo da produção da planta, o que é comum em fábricas de pequeno porte com uma única linha de envase, e restrições de lote mínimo do estágio de xaroparia. Variações da heurística relax and fix são propostas e comparadas na solução de exemplares do modelo, gerados com dados reais de uma fábrica localizada no interior do Estado de São Paulo. Os resultados mostram que as abordagens são capazes de gerar soluções melhores do que as utilizadas pela empresa.In this paper we propose a mixed integer programming model to the lot sizing and sequencing problem of a soft drink plant with sequence-dependent set up costs and times. The model considers that the bottling stage is the production bottleneck, which is common in small plants with only one production line, and minimum lot size constrains of the syrup stage. Variations of the relax and fix heuristic are proposed and compared. A computational study with instances generated based on real data from a plant situated in the State of São Paulo-Brazil is also presented. The results show that the approaches are capable to produce better solutions than the ones from the company.
Modeling of non-linear CHP efficiency curves in distributed energy systems
DEFF Research Database (Denmark)
Milan, Christian; Stadler, Michael; Cardoso, Gonçalo
2015-01-01
Distributed energy resources gain an increased importance in commercial and industrial building design. Combined heat and power (CHP) units are considered as one of the key technologies for cost and emission reduction in buildings. In order to make optimal decisions on investment and operation...... for these technologies, detailed system models are needed. These models are often formulated as linear programming problems to keep computational costs and complexity in a reasonable range. However, CHP systems involve variations of the efficiency for large nameplate capacity ranges and in case of part load operation......, which can be even of non-linear nature. Since considering these characteristics would turn the models into non-linear problems, in most cases only constant efficiencies are assumed. This paper proposes possible solutions to address this issue. For a mixed integer linear programming problem two...
Directory of Open Access Journals (Sweden)
Toly Chen
2013-01-01
Full Text Available This study proposes a multiobjective fuzzy nonlinear programming (MOFNP approach to enhance the long-term yield competitiveness of a semiconductor manufacturing factory. By modeling the long-term competitiveness of every product in a semiconductor manufacturing plant with the fuzzy correlation coefficient (FCC between time and instantaneous competitiveness, the proposed model considers the various viewpoints when interpreting the overall competitiveness of the semiconductor manufacturing plant in the long-term. All noninferior solutions of the MOFNP solutions are then derived using a systematic procedure. A real example is employed to illustrate the applicability of the proposed methodology.
Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan
2011-12-01
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
Institute of Scientific and Technical Information of China (English)
2013-01-01
In this paper, a numerical method based on a coupling between a mathematical model of nonlinear transient ship manoeu-vring motion in the horizontal plane and Mathematical Programming (MP) techniques is proposed. The aim of the proposed proce-dure is an efficient estimation of optimal ship hydrodynamic parameters in a dynamic model at the early design stage. The proposed procedure has been validated through turning circle and zigzag manoeuvres based on experimental data of sea trials of the 190 000-dwt oil tanker. Comparisons between experimental and computed data show a good agreement of overall tendency in manoeuvring trajectories.
Fractal electrodynamics via non-integer dimensional space approach
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2015-09-25
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested. - Highlights: • Electrodynamics of fractal media is described by non-integer dimensional spaces. • Applications of the fractal Gauss's and Ampere's laws are suggested. • Fractal Poisson equation, equation for fractal stream of charges are considered.
Non-integer expansion embedding techniques for reversible image watermarking
Xiang, Shijun; Wang, Yi
2015-12-01
This work aims at reducing the embedding distortion of prediction-error expansion (PE)-based reversible watermarking. In the classical PE embedding method proposed by Thodi and Rodriguez, the predicted value is rounded to integer number for integer prediction-error expansion (IPE) embedding. The rounding operation makes a constraint on a predictor's performance. In this paper, we propose a non-integer PE (NIPE) embedding approach, which can proceed non-integer prediction errors for embedding data into an audio or image file by only expanding integer element of a prediction error while keeping its fractional element unchanged. The advantage of the NIPE embedding technique is that the NIPE technique can really bring a predictor into full play by estimating a sample/pixel in a noncausal way in a single pass since there is no rounding operation. A new noncausal image prediction method to estimate a pixel with four immediate pixels in a single pass is included in the proposed scheme. The proposed noncausal image predictor can provide better performance than Sachnev et al.'s noncausal double-set prediction method (where data prediction in two passes brings a distortion problem due to the fact that half of the pixels were predicted with the watermarked pixels). In comparison with existing several state-of-the-art works, experimental results have shown that the NIPE technique with the new noncausal prediction strategy can reduce the embedding distortion for the same embedding payload.
Integer programming for the generalized high school timetabling problem
DEFF Research Database (Denmark)
Kristiansen, Simon; Sørensen, Matias; Stidsen, Thomas Riis
2015-01-01
Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby...
Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks
Lee, Charles H.; Cheung, Kar-Ming
2012-01-01
In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.
Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks
Lee, Charles H.; Cheung, Kar-Ming
2012-01-01
In this paper, we propose to solve the constrained optimization problem in two phases. The first phase uses heuristic methods such as the ant colony method, particle swarming optimization, and genetic algorithm to seek a near optimal solution among a list of feasible initial populations. The final optimal solution can be found by using the solution of the first phase as the initial condition to the SQP algorithm. We demonstrate the above problem formulation and optimization schemes with a large-scale network that includes the DSN ground stations and a number of spacecraft of deep space missions.
An integer linear programming model for an Ecovat buffer
Goeijen, de Gijs J.; Smit, Gerard J.M.; Hurink, Johann L.
2016-01-01
An increase in the number of volatile renewables in the electricity grid enhances the imbalance of supply and demand. One promising candidate to solve this problem is to improve the energy storage. The Ecovat system is a new seasonal thermal energy storage system currently under development. In this
New Approaches for Very Large-Scale Integer Programming
2016-06-24
problems. In the context of MIP, some recent works propose ML techniques for constructing a portfolio of good parameter configurations for a MIP solver... benefit of being instance-specific and of continuing the branch-and-bound seamlessly, without losing work when switching between learning and prediction...computational results on instances from MIPLIB 2010 illustrating the benefits of this framework. DISTRIBUTION A: Distribution approved for public release
Heuristic Procedures for 0-1 Integer Programming.
1987-03-01
A 30 60 0.021 0 ST B 30 60 0.010 0 ie 40 Chapter 4 Conclusions A heuristic algorithm aims at obtaining a very good feasible solution relatively...Department of Operations Research, Stanford University, February, 1977. 19. Ibaraki, T., Ohashi, T., and Mine, H. " A Heuristic Algorithm for Mixed
Stochastic Dynamic Mixed-Integer Programming (SD-MIP)
2015-05-05
et al (2009), there is continuing interest in using SA methods for SP problems. This genre of methods creates a sequence of sampled subgradients...Phone Number Contact phone number if there is a problem with the report 213-740-6810 Organization / Institution name University of Southern California
Vertical partitioning of relational OLTP databases using integer programming
DEFF Research Database (Denmark)
Amossen, Rasmus Resen
2010-01-01
A way to optimize performance of relational row store databases is to reduce the row widths by vertically partition- ing tables into table fractions in order to minimize the number of irrelevant columns/attributes read by each transaction. This pa- per considers vertical partitioning algorithms...... for relational row- store OLTP databases with an H-store-like architecture, meaning that we would like to maximize the number of single-sited transactions. We present a model for the vertical partitioning problem that, given a schema together with a vertical partitioning and a workload, estimates the costs...... (bytes read/written by storage layer access methods and bytes transferred between sites) of evaluating the workload on the given partitioning. The cost model allows for arbitrarily prioritizing load balancing of sites vs. total cost minimization. We show that finding a minimum-cost vertical partitioning...
Gap solitons in periodic Schrodinger lattice system with nonlinear hopping
Directory of Open Access Journals (Sweden)
Ming Cheng
2016-10-01
Full Text Available This article concerns the periodic discrete Schrodinger equation with nonlinear hopping on the infinite integer lattice. We obtain the existence of gap solitons by the linking theorem and concentration compactness method together with a periodic approximation technique. In addition, the behavior of such solutions is studied as $\\alpha\\to 0$. Notice that the nonlinear hopping can be sign changing.
Institute of Scientific and Technical Information of China (English)
张慧妍; 李爽; 于家斌; 王小艺; 许继平
2015-01-01
, temperature and relative humidity, and its output was daily generating capacity of photovoltaic power. When the daily generating capacity was less than zero, it was the rainy day without electricity output. And so the maximum continuous rainy days of poor photovoltaic power generation were effectively set by the historical meteorological data of the buoy operation place. Then, for the possible size deviations between the expected and the practical values, a fuzzy integer programming algorithm was proposed. The advocated solution fused the characteristics of Werners algorithm and cutting-plane method. It transformed the objective function and fuzzy constraints into the general constraints, and the Werners symmetric model was obtained. The cutting-plane method was used to get the integer solution of the model, which would optimize the design parameter configuration of PV-battery power source with the fluctuation tolerance. Later, the sensitivity analysis of the maximum consecutive rainy days was carried out to investigate the fluctuating effect of weather factor on the system stability. Finally, the simulation examples indicated that the maximum continuous rainy days could be reduced by 5 d, which meant to reduce 33.3% margin requirements of the storage battery. By the proposed fuzzy integer programming method, the parameters of electric power supply for the water quality monitoring buoy were obtained with the minimum construction cost and maximum fuzzy membership degree. It was helpful to overcome the fluctuation of the size of the buoy body in practice, which would improve the feasibility and effectiveness of the theoretical method applied. Sensitivity analysis showed that when the maximum continuous rainy days extended occasionally to 1 d, the power source still could support the running of water quality monitoring buoy. This research provides a feasible solution to the problems of the renewable stand-alone energy power generation system of water quality monitoring buoy. The
Theoretical and algorithmic advances in multi-parametric programming and control
Pistikopoulos, Efstratios N.
2012-04-21
This paper presents an overview of recent theoretical and algorithmic advances, and applications in the areas of multi-parametric programming and explicit/multi-parametric model predictive control (mp-MPC). In multi-parametric programming, advances include areas such as nonlinear multi-parametric programming (mp-NLP), bi-level programming, dynamic programming and global optimization for multi-parametric mixed-integer linear programming problems (mp-MILPs). In multi-parametric/explicit MPC (mp-MPC), advances include areas such as robust multi-parametric control, multi-parametric nonlinear MPC (mp-NMPC) and model reduction in mp-MPC. A comprehensive framework for multi-parametric programming and control is also presented. Recent applications include a hydrogen storage device, a fuel cell power generation system, an unmanned autonomous vehicle (UAV) and a hybrid pressure swing adsorption (PSA) system. © 2012 Springer-Verlag.
Multiplicity of Summands in the Random Partitions of an Integer
Indian Academy of Sciences (India)
Ghurumuruhan Ganesan
2013-02-01
In this paper, we prove a conjecture of Yakubovich regarding limit shapes of `slices’ of two-dimensional (2D) integer partitions and compositions of when the number of summands $m\\sim An^$ for some >0 and $ < \\frac{1}{2}$. We prove that the probability that there is a summand of multiplicity in any randomly chosen partition or composition of an integer goes to zero asymptotically with provided is larger than a critical value. As a corollary, we strengthen a result due to Erdös and Lehner (Duke Math. J. 8(1941) 335–345) that concerns the relation between the number of integer partitions and compositions when $=\\frac{1}{3}$.
The lattice of integer flows of a regular matroid
Su, Yi
2009-01-01
For a finite multigraph G, let \\Lambda(G) denote the lattice of integer flows of G -- this is a finitely generated free abelian group with an integer-valued positive definite bilinear form. Bacher, de la Harpe, and Nagnibeda show that if G and H are 2-isomorphic graphs then \\Lambda(G) and \\Lambda(H) are isometric, and remark that they were unable to find a pair of nonisomorphic 3-connected graphs for which the corresponding lattices are isometric. We explain this by examining the lattice \\Lambda(M) of integer flows of any regular matroid M. Let M_\\bullet be the minor of M obtained by contracting all co-loops. We show that \\Lambda(M) and \\Lambda(N) are isometric if and only if M_\\bullet and N_\\bullet are isomorphic.
Institute of Scientific and Technical Information of China (English)
孙效玉; 张维国; 陈毓; 王侠; 孙梦红
2012-01-01
针对露天矿生产不均衡产生的长期计划与短期计划严重脱节问题,通过对露天矿时空发展关系的分析,分时段建立露天矿短期计划的0-1整数规划模型,提出了超级组合块的概念,论述了短期计划优化处理逻辑。并在Surpac平台上采用TCL语言二次开发完成长期计划制作、台阶条块划分与动态显示功能,在VC＋＋环境下通过调用LindoAPI数学软件自动优化形成短期计划。结果只需十几分钟到几小时的时间,即可实现传统方法根本无力解决的根据长期计划自动形成短期计划、进而验证长期计划的难题,实践证明这种方法稳定性强、工作效率高。%To solve the confliction between long-term and short-term production plan on open-pit mine, established a 0- 1 integer programming model of short-term plans by time period applying with space-time development, and a new con- cept of ＂super combo blocks＂ was proposed and the progress logic of short-term plan was dealt with. It implemented the design of long-term plan, dividing blocks from strip benches and dynamic displaying by secondary development using the TCL language on the Surpac software platform. The short-term plan could be automatically optimized by call- ing LindoAPI mathematical software under Visual C ＋ ＋ environment. It solved the problem that the short-term plan cannot be drawn out from automatic optimization based on long-term plan, but the program running time could be mi- nutes or few hours. The reliability and efficiency of the method is proved in the work field.
Generalized Equations and Their Solutions. Part 2. Applications to Nonlinear Programming
1980-03-01
Bolivar, Caracas, Venezuela, with support from the United Nations Educational, Scientific and Cultural Organization under Proyecto UNESCO VEN-77-002. The...tional, Scientific and Cultural Crganization under Proyecto UNESCO VEN-77-0 02. Vhe author greatly appreciates the hospitality and support extended...condition is satisfied by the linearizations of the nonlinear problem, then the latter has, at least locally, an upper Lipschitzian inverse (which, of
FPGA Implementation of Optimal 3D-Integer DCT Structure for Video Compression.
Jacob, J Augustin; Kumar, N Senthil
2015-01-01
A novel optimal structure for implementing 3D-integer discrete cosine transform (DCT) is presented by analyzing various integer approximation methods. The integer set with reduced mean squared error (MSE) and high coding efficiency are considered for implementation in FPGA. The proposed method proves that the least resources are utilized for the integer set that has shorter bit values. Optimal 3D-integer DCT structure is determined by analyzing the MSE, power dissipation, coding efficiency, and hardware complexity of different integer sets. The experimental results reveal that direct method of computing the 3D-integer DCT using the integer set [10, 9, 6, 2, 3, 1, 1] performs better when compared to other integer sets in terms of resource utilization and power dissipation.
Arithmetic progressions in Salem-type subsets of the integers
Potgieter, Paul
2010-01-01
Given a subset of the integers of zero density, we define the weaker notion of fractional density of such a set. It is shown how this notion corresponds to that of the Hausdorff dimension of a compact subset of the reals. We then show that a version of a theorem of {\\L}aba and Pramanik on 3-term arithmetic progressions in subsets of the unit interval also holds for subsets of the integers with fractional density and satisfying certain Fourier-decay conditions.
Sharqawy, Mostafa H.
2016-12-01
Pore network models (PNM) of Berea and Fontainebleau sandstones were constructed using nonlinear programming (NLP) and optimization methods. The constructed PNMs are considered as a digital representation of the rock samples which were based on matching the macroscopic properties of the porous media and used to conduct fluid transport simulations including single and two-phase flow. The PNMs consisted of cubic networks of randomly distributed pores and throats sizes and with various connectivity levels. The networks were optimized such that the upper and lower bounds of the pore sizes are determined using the capillary tube bundle model and the Nelder-Mead method instead of guessing them, which reduces the optimization computational time significantly. An open-source PNM framework was employed to conduct transport and percolation simulations such as invasion percolation and Darcian flow. The PNM model was subsequently used to compute the macroscopic properties; porosity, absolute permeability, specific surface area, breakthrough capillary pressure, and primary drainage curve. The pore networks were optimized to allow for the simulation results of the macroscopic properties to be in excellent agreement with the experimental measurements. This study demonstrates that non-linear programming and optimization methods provide a promising method for pore network modeling when computed tomography imaging may not be readily available.
Modeling an integrated hospital management planning problem using integer optimization approach
Sitepu, Suryati; Mawengkang, Herman; Irvan
2017-09-01
Hospital is a very important institution to provide health care for people. It is not surprising that nowadays the people’s demands for hospital is increasing. However, due to the rising cost of healthcare services, hospitals need to consider efficiencies in order to overcome these two problems. This paper deals with an integrated strategy of staff capacity management and bed allocation planning to tackle these problems. Mathematically, the strategy can be modeled as an integer linear programming problem. We solve the model using a direct neighborhood search approach, based on the notion of superbasic variables.
A two-phase linear programming approach for redundancy allocation problems
Directory of Open Access Journals (Sweden)
Hsieh Yi-Chih
2002-01-01
Full Text Available Provision of redundant components in parallel is an efficient way to increase the system reliability, however, the weight, volume and cost of the system will increase simultaneously. This paper proposes a new two-phase linear programming approach for solving the nonlinear redundancy allocation problems subject to multiple linear constraints. The first phase is used to approximately allocate the resource by using a general linear programming, while the second phase is used to re-allocate the slacks of resource by using a 0-1 integer linear programming. Numerical results demonstrate the effectiveness and efficiency of the proposed approach.
Interactions, disorder and spin waves in quantum Hall ferromagnets near integer filling
Rapsch, S
2001-01-01
dynamics is discussed in chapter 5 and employed to study spin waves in a domain wall structure. A hydrodynamic theory of spin waves is used to treat long-wavelength excitations of randomly disordered quantum Hall ferromagnets. Finally, the contribution of spin waves to the optical conductivity is studied in chapter 6. Predictions are made for the experimental signatures of spin waves in disordered quantum Hall systems. The observability of these signatures is discussed both for transport measurements and NMR experiments. The interplay between exchange interactions and disorder is studied in quantum Hall ferromagnets near integer filling. Both analytical and numerical methods are used to investigate a non-linear sigma model of these systems in the limit of vanishing Zeeman coupling and at zero temperature. Chapter 1 gives an introduction to the quantum Hall effect and to quantum Hall ferromagnets in particular. A brief review of existing work on disordered quantum Hall systems is included. In chapters 2-4, the...
Institute of Scientific and Technical Information of China (English)
杨轶华; 吕显瑞; 刘庆怀
2006-01-01
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method (CHIIP)for convex nonlinear programming problems. For any convex nonlinear programming,without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method.
An introduction to nonlinear programming. IV - Numerical methods for constrained minimization
Sorenson, H. W.; Koble, H. M.
1976-01-01
An overview is presented of the numerical solution of constrained minimization problems. Attention is given to both primal and indirect (linear programs and unconstrained minimizations) methods of solution.
Quantum recurrence and integer ratios in neutron resonances
Energy Technology Data Exchange (ETDEWEB)
Ohkubo, Makio
1998-03-01
Quantum recurrence of the compound nucleus in neutron resonance reactions are described for normal modes which are excited on the compound nucleus simultaneously. In the structure of the recurrence time, integer relations among dominant level spacings are derived. The `base modes` are assumed as stable combinations of the normal modes, preferably excited in many nuclei. (author)
Unique Factorization in Cyclotomic Integers of Degree Seven
Duckworth, W. Ethan
2008-01-01
This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
Limit theorems for bifurcating integer-valued autoregressive processes
Blandin, Vassili
2012-01-01
We study the asymptotic behavior of the weighted least squares estimators of the unknown parameters of bifurcating integer-valued autoregressive processes. Under suitable assumptions on the immigration, we establish the almost sure convergence of our estimators, together with the quadratic strong law and central limit theorems. All our investigation relies on asymptotic results for vector-valued martingales.
Happy and Sad Thoughts: An Exploration of Children's Integer Reasoning
Whitacre, Ian; Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Lewis, Melinda L.
2012-01-01
The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…
Automorphisms of semigroups of invertible matrices with nonnegative integer elements
Energy Technology Data Exchange (ETDEWEB)
Semenov, Pavel P [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2012-09-30
Let G{sub n}(Z) be the subsemigroup of GL{sub n}(Z) consisting of the matrices with nonnegative integer coefficients. In the paper, the automorphisms of this semigroup are described for n{>=}2. Bibliography: 5 titles.
A fast DFT algorithm using complex integer transforms
Reed, I. S.; Truong, T. K.
1978-01-01
Winograd's algorithm for computing the discrete Fourier transform is extended considerably for certain large transform lengths. This is accomplished by performing the cyclic convolution, required by Winograd's method, by a fast transform over certain complex integer fields. This algorithm requires fewer multiplications than either the standard fast Fourier transform or Winograd's more conventional algorithms.
Triangular Numbers, Gaussian Integers, and KenKen
Watkins, John J.
2012-01-01
Latin squares form the basis for the recreational puzzles sudoku and KenKen. In this article we show how useful several ideas from number theory are in solving a KenKen puzzle. For example, the simple notion of triangular number is surprisingly effective. We also introduce a variation of KenKen that uses the Gaussian integers in order to…
Algorithms and Data Structures for Strings, Points and Integers
DEFF Research Database (Denmark)
Vind, Søren Juhl
This dissertation presents our research in the broad area of algorithms and data structures. More specifically, we show solutions for the following problems related to strings, points and integers. Results hold on the Word RAM and we measure space in w-bit words. Compressed Fingerprints. The Karp...
Negative Integer Understanding: Characterizing First Graders' Mental Models
Bofferding, Laura
2014-01-01
This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…
Happy and Sad Thoughts: An Exploration of Children's Integer Reasoning
Whitacre, Ian; Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Lewis, Melinda L.
2012-01-01
The purpose of this study was to investigate elementary children's conceptions that might serve as foundations for integer reasoning. Working from an abstract algebraic perspective and using an opposite-magnitudes context that is relevant to children, we analyzed the reasoning of 33 children in grades K-5. We focus our report on three prominent…
Simple integer recourse models : convexity and convex approximations
Klein Haneveld, W.K.; Stougie, L.; van der Vlerk, M.H.
We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a
Simple Integer Recourse Models : Convexity and Convex Approximations
Klein Haneveld, Willem K.; Stougie, L; van der Vlerk, Maarten H.
2004-01-01
We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead. Based on an explicit formula for the objective function, we derive a
Directory of Open Access Journals (Sweden)
Alexander Abuabara
2008-12-01
Full Text Available Este trabalho busca otimizar o planejamento do processo de corte unidimensional de tubos estruturais metálicos utilizados na fabricação de aeronaves leves agrícolas. Dois modelos de programação linear inteira mista são apresentados com o objetivo de minimizar as perdas do material cortado e considerando a possibilidade de gerar sobras com tamanhos suficientes para reaproveitamento (retalhos. Os modelos são resolvidos por meio de uma linguagem de modelagem usando um software de otimização. Para a validação dos modelos, dois experimentos computacionais foram realizados com dados reais de uma carteira de pedidos de uma aeronave leve voltada para o segmento do mercado agrícola, o Ipanema, produzido pela empresa brasileira Neiva/Embraer. As soluções dos modelos são comparadas com as soluções de uma heurística residual de arredondamento guloso da literatura e também com as soluções utilizadas pela empresa. Os resultados mostram que os modelos são úteis para apoiar as decisões envolvidas no planejamento deste processo de corte.This study aims to optimize the one-dimensional cutting process planning of structural metallic tubes used to build agricultural light aircrafts. Two mixed integer linear programming models are presented to minimize the waste of material cut and considering the possibility of generating surpluses with sizes sufficiently large for reuse (leftovers. The models are solved using a commercial modeling language and an optimization solver. For the validation of the models, two computational experiments were performed with actual data from the portfolio of a light aircraft designed for agricultural purposes, the Ipanema, produced by the Brazilian company Neiva/Embraer. The solutions of the models are compared with the solutions of a constructive heuristic of the literature and the solutions used by the company. The results show that the models are useful for being used in the planning of this cutting process.
Directory of Open Access Journals (Sweden)
Sílvia Maria Santana Mapa
2012-01-01
Full Text Available O objetivo do trabalho é avaliar a qualidade das soluções para o problema de localização-alocação de instalações geradas por um SIG-T (Sistema de Informação Geográfica para Transportes, obtidas após a utilização combinada das rotinas Localização de Facilidades e Problema do Transporte, quando comparadas com as soluções ótimas obtidas a partir de modelo matemático exato baseado em Programação Linear Inteira Mista (PLIM, desenvolvido externamente ao SIG. Os modelos foram aplicados a três simulações: a primeira propõe a abertura de fábricas e alocação de clientes no Estado de São Paulo; a segunda envolve um atacadista e um estudo de localização de centros de distribuição e alocação dos clientes varejistas; a terceira localiza creches em um contexto urbano, alocando a demanda. Os resultados mostraram que, quando se considera a capacidade das instalações, o modelo otimizante PLIM chegou a apresentar, em um dos cenários simulados, resultados até 37% melhores do que o SIG, além de propor locais diferentes para abertura de novas instalações. Quando não se considera a capacidade, o modelo SIG se mostrou tão eficiente quanto o modelo exato PLIM, chegando exatamente às mesmas soluções.This study aims to evaluate the quality of the solutions for facility location-allocation problems generated by a GIS-T (Geographic Information System for Transportation software. These solutions were obtained from combining the Facility Location and Transportation Problem routines, when compared with the optimal solutions, which were obtained using the exact mathematical model based on the Mixed Integer Linear Programming (MILP developed externally to the GIS. The models were applied to three simulations: the first one proposes set up businesses and customers' allocation in the state of São Paulo; the second involves a wholesaler and an investigation of distribution center location and retailers' allocation; and the third one
Word, Daniel P; Cummings, Derek A T; Burke, Donald S; Iamsirithaworn, Sopon; Laird, Carl D
2012-08-07
Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.
Jamali, A.; Khaleghi, E.; Gholaminezhad, I.; Nariman-zadeh, N.
2016-05-01
In this paper, a new multi-objective genetic programming (GP) with a diversity preserving mechanism and a real number alteration operator is presented and successfully used for Pareto optimal modelling of some complex non-linear systems using some input-output data. In this study, two different input-output data-sets of a non-linear mathematical model and of an explosive cutting process are considered separately in three-objective optimisation processes. The pertinent conflicting objective functions that have been considered for such Pareto optimisations are namely, training error (TE), prediction error (PE), and the length of tree (complexity of the network) (TL) of the GP models. Such three-objective optimisation implementations leads to some non-dominated choices of GP-type models for both cases representing the trade-offs among those objective functions. Therefore, optimal Pareto fronts of such GP models exhibit the trade-off among the corresponding conflicting objectives and, thus, provide different non-dominated optimal choices of GP-type models. Moreover, the results show that no significant optimality in TE and PE may occur when the TL of the corresponding GP model exceeds some values.
Designing a Fresh Food Supply Chain Network: An Application of Nonlinear Programming
Directory of Open Access Journals (Sweden)
Yu-Chung Tsao
2013-01-01
Full Text Available In today’s business environment, many fresh food companies have complex supply networks to distribute their products. For example, agricultural products are distributed through a multiechelon supply chain which includes agricultural association, agricultural produce marketing corporations (APMCs, markets, and so forth. In this paper a fresh produce supply network model is designed to determine the optimal service area for APMCs, the replenishment cycle time of APMCs, and the freshness-keeping effort, while maximizing the total profit. The objective is to address the integrated facility location, inventory allocation, and freshness-keeping effort problems. This paper develops an algorithm to solve the nonlinear problem, provides numerical analysis to illustrate the proposed solution procedure, and discusses the effects of various system parameters on the decisions and total profits. A real case of an agricultural product supply chain in Taiwan is used to verify the model. Results of this study can serve as a reference for business managers and administrators.
An inertia-free filter line-search algorithm for large-scale nonlinear programming
Energy Technology Data Exchange (ETDEWEB)
Chiang, Nai-Yuan; Zavala, Victor M.
2016-02-15
We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.
Directory of Open Access Journals (Sweden)
Zhi-yuan Li
2014-01-01
Full Text Available As the core of the effective financial crisis prevention, enterprise finance crisis prediction has been the focal attention of both theorists and businessmen. Financial crisis predictions need to apply a variety of financial and operating indicators for its analysis. Therefore, a new evaluation model based on nonlinear programming is established, the nature of the model is proved, the detailed solution steps of the model are given, and the significance and algorithm of the model are thoroughly discussed in this study. The proposed model can deal with the case of missing data, and has the good isotonic property and profound theoretical background. In the empirical analysis to predict the financial crisis and through the comparison of the analysis of historical data and the real enterprises with financial crisis, we find that the results are in accordance with the real enterprise financial conditions and the proposed model has a good predictive ability.
Directory of Open Access Journals (Sweden)
Seyed Abolghasem Mortazavi
2014-03-01
Full Text Available Water resources sustainability is one of the major issues in the agricultural sustainability. In this study sustainability of water resources has been investigated by use of linear and non-linear models in six models based on optimal utilization of water resources in the north parts farms of Iran because of incorrect use of agricultural water resources, from 2011 to 2012. Also “gross margin per a unit of water consumption” and “employment per a unit of water consumption” are used as indicators for assessing the sustainability of cropping patterns. The results show that cropping pattern of fractional goal programming (FGP model has been near to current situation and has shown realistic conditions according to expertise and advantage of this area in cultivation of certain crops. So the FGP model has desirability in each of indicators than other five models.
Huang, Y L; Huang, G H; Liu, D F; Zhu, H; Sun, W
2012-10-15
Although integrated simulation and optimization approaches under stochastic uncertainty have been applied to eutrophication management problems, few studies are reported in eutrophication control planning where multiple formats of uncertainties and nonlinearities are addressed in forms of intervals and probabilistic distributions within an integrated framework. Since the impounding of Three Gorges Reservoir (TGR), China in 2003, the hydraulic conditions and aquatic environment of the Xiangxi Bay (XXB) have changed significantly. The resulting emergence of eutrophication and algal blooms leads to its deteriorated water quality. The XXB becomes an ideal case study area. Thus, a simulation-based inexact chance-constrained nonlinear programming (SICNP) model is developed and applied to eutrophication control planning in the XXB of the TGR under uncertainties. In the SICNP, the wastewater treatment costs for removing total phosphorus (TP) are set as the objective function; effluent discharge standards, stream water quality standards and eutrophication control standards are considered in the constraints; a steady-state simulation model for phosphorus transport and fate is embedded in the environmental standards constraints; the interval programming and chance-constrained approaches are integrated to provide interval decision variables but also the associated risk levels in violating the system constraints. The model results indicate that changes in the violating level (q) will result in different strategy distributions at spatial and temporal scales; the optimal value of cost objective is from [2.74, 13.41] million RMB to [2.25, 13.08] million RMB when q equals from 0.01 to 0.25; the required TP treatment efficiency for the Baisha plant is the most stringent, which is followed by the Xiakou Town and the Zhaojun Town, while the requirement for the Pingyikou cement plant is the least stringent. The model results are useful for making optimal policies on eutrophication
Efficient Algorithms for gcd and Cubic Residuosity in the Ring of Eisenstein Integers
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Frandsen, Gudmund Skovbjerg
2003-01-01
We present simple and efficient algorithms for computing gcd and cubic residuosity in the ring of Eisenstein integers, bf Z[ ]i.e. the integers extended with , a complex primitive third root of unity. The algorithms are similar and may be seen as generalisations of the binary integer gcd and deri...... primality tests and the implementation of cryptographic protocols....
GNSS integer ambiguity estimation and evaluation: LAMBDA and Ps-LAMBDA
Li, B.; Verhagen, A.A.; Teunissen, P.J.G.
2013-01-01
Successful integer carrier-phase ambiguity resolution is crucial for high precision GNSS applications. It includes both integer estimation and evaluation. For integer estimation, the LAMBDA method has been applied in a wide variety of GNSS applications. The method’s popularity stems from its numeric
A Secret Image Sharing Method Using Integer Wavelet Transform
Directory of Open Access Journals (Sweden)
Li Ching-Chung
2007-01-01
Full Text Available A new image sharing method, based on the reversible integer-to-integer (ITI wavelet transform and Shamir's threshold scheme is presented, that provides highly compact shadows for real-time progressive transmission. This method, working in the wavelet domain, processes the transform coefficients in each subband, divides each of the resulting combination coefficients into shadows, and allows recovery of the complete secret image by using any or more shadows . We take advantages of properties of the wavelet transform multiresolution representation, such as coefficient magnitude decay and excellent energy compaction, to design combination procedures for the transform coefficients and processing sequences in wavelet subbands such that small shadows for real-time progressive transmission are obtained. Experimental results demonstrate that the proposed method yields small shadow images and has the capabilities of real-time progressive transmission and perfect reconstruction of secret images.
Two dimensional convolute integers for machine vision and image recognition
Edwards, Thomas R.
1988-01-01
Machine vision and image recognition require sophisticated image processing prior to the application of Artificial Intelligence. Two Dimensional Convolute Integer Technology is an innovative mathematical approach for addressing machine vision and image recognition. This new technology generates a family of digital operators for addressing optical images and related two dimensional data sets. The operators are regression generated, integer valued, zero phase shifting, convoluting, frequency sensitive, two dimensional low pass, high pass and band pass filters that are mathematically equivalent to surface fitted partial derivatives. These operators are applied non-recursively either as classical convolutions (replacement point values), interstitial point generators (bandwidth broadening or resolution enhancement), or as missing value calculators (compensation for dead array element values). These operators show frequency sensitive feature selection scale invariant properties. Such tasks as boundary/edge enhancement and noise or small size pixel disturbance removal can readily be accomplished. For feature selection tight band pass operators are essential. Results from test cases are given.
Integer-ambiguity resolution in astronomy and geodesy
Lannes, André
2013-01-01
Recent theoretical developments in astronomical aperture synthesis have revealed the existence of integer-ambiguity problems. Those problems, which appear in the self-calibration procedures of radio imaging, have been shown to be similar to the nearest-lattice point (NLP) problems encountered in high-precision geodetic positioning, and in global navigation satellite systems. In this paper, we analyse the theoretical aspects of the matter and propose new methods for solving those NLP problems. The related optimization aspects concern both the preconditioning stage, and the discrete-search stage in which the integer ambiguities are finally fixed. Our algorithms, which are described in an explicit manner, can easily be implemented. They lead to substantial gains in the processing time of both stages. Their efficiency was shown via intensive numerical tests.
Optimization of integer wavelet transforms based on difference correlation structures.
Li, Hongliang; Liu, Guizhong; Zhang, Zhongwei
2005-11-01
In this paper, a novel lifting integer wavelet transform based on difference correlation structure (DCCS-LIWT) is proposed. First, we establish a relationship between the performance of a linear predictor and the difference correlations of an image. The obtained results provide a theoretical foundation for the following construction of the optimal lifting filters. Then, the optimal prediction lifting coefficients in the sense of least-square prediction error are derived. DCCS-LIWT puts heavy emphasis on image inherent dependence. A distinct feature of this method is the use of the variance-normalized autocorrelation function of the difference image to construct a linear predictor and adapt the predictor to varying image sources. The proposed scheme also allows respective calculations of the lifting filters for the horizontal and vertical orientations. Experimental evaluation shows that the proposed method produces better results than the other well-known integer transforms for the lossless image compression.