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...
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…
A property of assignment type mixed integer linear programming problems
Benders, J.F.; van Nunen, J.A.E.E.
1982-01-01
In this paper we will proof that rather tight upper bounds can be given for the number of non-unique assignments that are achieved after solving the linear programming relaxation of some types of mixed integer linear assignment problems. Since in these cases the number of splitted assignments is
A mixed integer linear program for an integrated fishery | Hasan ...
African Journals Online (AJOL)
... and labour allocation of quota based integrated fisheries. We demonstrate the workability of our model with a numerical example and sensitivity analysis based on data obtained from one of the major fisheries in New Zealand. Keywords: mixed integer linear program, fishing, trawler scheduling, processing, quotas ORiON: ...
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.
Mixed-Integer Conic Linear Programming: Challenges and Perspectives
2013-10-01
The novel DCCs for MISOCO may be used in branch- and-cut algorithms when solving MISOCO problems. The experimental software CICLO was developed to...perform limited, but rigorous computational experiments. The CICLO solver utilizes continuous SOCO solvers, MOSEK, CPLES or SeDuMi, builds on the open...submitted Fall 2013. Software: 1. CICLO : Integer conic linear optimization package. Authors: J.C. Góez, T.K. Ralphs, Y. Fu, and T. Terlaky
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...
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.
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. © 2012 Wiley Periodicals, Inc.
Discovery of Boolean metabolic networks: integer linear programming based approach.
Qiu, Yushan; Jiang, Hao; Ching, Wai-Ki; Cheng, Xiaoqing
2018-04-11
Traditional drug discovery methods focused on the efficacy of drugs rather than their toxicity. However, toxicity and/or lack of efficacy are produced when unintended targets are affected in metabolic networks. Thus, identification of biological targets which can be manipulated to produce the desired effect with minimum side-effects has become an important and challenging topic. Efficient computational methods are required to identify the drug targets while incurring minimal side-effects. In this paper, we propose a graph-based computational damage model that summarizes the impact of enzymes on compounds in metabolic networks. An efficient method based on Integer Linear Programming formalism is then developed to identify the optimal enzyme-combination so as to minimize the side-effects. The identified target enzymes for known successful drugs are then verified by comparing the results with those in the existing literature. Side-effects reduction plays a crucial role in the study of drug development. A graph-based computational damage model is proposed and the theoretical analysis states the captured problem is NP-completeness. The proposed approaches can therefore contribute to the discovery of drug targets. Our developed software is available at " http://hkumath.hku.hk/~wkc/APBC2018-metabolic-network.zip ".
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.
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.
International Nuclear Information System (INIS)
Sergienko, I.V.; Golodnikov, A.N.
1984-01-01
This article applies the methods of decompositions, which are used to solve continuous linear problems, to integer and partially integer problems. The fall-vector method is used to solve the obtained coordinate problems. An algorithm of the fall-vector is described. The Kornai-Liptak decomposition principle is used to reduce the integer linear programming problem to integer linear programming problems of a smaller dimension and to a discrete coordinate problem with simple constraints
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.
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
In the paper, three frequently used operation optimisation methods are examined with respect to their impact on operation management of the combined utility technologies for electric power and DH (district heating) of eastern Denmark. The investigation focusses on individual plant operation...... differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... as a benchmark, as this type is frequently used, and has the lowest amount of constraints of the three. A comparison of the optimised operation of a number of units shows significant differences between the three methods. Compared to the reference, the use of binary integer variables, increases operation...
An Improved Search Approach for Solving Non-Convex Mixed-Integer Non Linear Programming Problems
Sitopu, Joni Wilson; Mawengkang, Herman; Syafitri Lubis, Riri
2018-01-01
The nonlinear mathematical programming problem addressed in this paper has a structure characterized by a subset of variables restricted to assume discrete values, which are linear and separable from the continuous variables. The strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method, has been developed. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points. Successful implementation of these algorithms was achieved on various test problems.
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.
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...
Directory of Open Access Journals (Sweden)
Animesh Biswas
2016-04-01
Full Text Available This paper deals with fuzzy goal programming approach to solve fuzzy linear bilevel integer programming problems with fuzzy probabilistic constraints following Pareto distribution and Frechet distribution. In the proposed approach a new chance constrained programming methodology is developed from the view point of managing those probabilistic constraints in a hybrid fuzzy environment. A method of defuzzification of fuzzy numbers using ?-cut has been adopted to reduce the problem into a linear bilevel integer programming problem. The individual optimal value of the objective of each DM is found in isolation to construct the fuzzy membership goals. Finally, fuzzy goal programming approach is used to achieve maximum degree of each of the membership goals by minimizing under deviational variables in the decision making environment. To demonstrate the efficiency of the proposed approach, a numerical example is provided.
Mixed integer linear programming model for dynamic supplier selection problem considering discounts
Directory of Open Access Journals (Sweden)
Adi Wicaksono Purnawan
2018-01-01
Full Text Available Supplier selection is one of the most important elements in supply chain management. This function involves evaluation of many factors such as, material costs, transportation costs, quality, delays, supplier capacity, storage capacity and others. Each of these factors varies with time, therefore, supplier identified for one period is not necessarily be same for the next period to supply the same product. So, mixed integer linear programming (MILP was developed to overcome the dynamic supplier selection problem (DSSP. In this paper, a mixed integer linear programming model is built to solve the lot-sizing problem with multiple suppliers, multiple periods, multiple products and quantity discounts. The buyer has to make a decision for some products which will be supplied by some suppliers for some periods cosidering by discount. To validate the MILP model with randomly generated data. The model is solved by Lingo 16.
A Mixed Integer Linear Programming Model for the North Atlantic Aircraft Trajectory Planning
Sbihi , Mohammed; Rodionova , Olga; Delahaye , Daniel; Mongeau , Marcel
2015-01-01
International audience; This paper discusses the trajectory planning problem for ights in the North Atlantic oceanic airspace (NAT). We develop a mathematical optimization framework in view of better utilizing available capacity by re-routing aircraft. The model is constructed by discretizing the problem parameters. A Mixed integer linear program (MILP) is proposed. Based on the MILP a heuristic to solve real-size instances is also introduced
Learning Bayesian network structure: towards the essential graph by integer linear programming tools
Czech Academy of Sciences Publication Activity Database
Studený, Milan; Haws, D.
2014-01-01
Roč. 55, č. 4 (2014), s. 1043-1071 ISSN 0888-613X R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : learning Bayesian network structure * integer linear programming * characteristic imset * essential graph Subject RIV: BA - General Mathematics Impact factor: 2.451, year: 2014 http://library.utia.cas.cz/separaty/2014/MTR/studeny-0427002.pdf
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.
Mixed Integer Linear Programming model for Crude Palm Oil Supply Chain Planning
Sembiring, Pasukat; Mawengkang, Herman; Sadyadharma, Hendaru; Bu'ulolo, F.; Fajriana
2018-01-01
The production process of crude palm oil (CPO) can be defined as the milling process of raw materials, called fresh fruit bunch (FFB) into end products palm oil. The process usually through a series of steps producing and consuming intermediate products. The CPO milling industry considered in this paper does not have oil palm plantation, therefore the FFB are supplied by several public oil palm plantations. Due to the limited availability of FFB, then it is necessary to choose from which plantations would be appropriate. This paper proposes a mixed integer linear programming model the supply chain integrated problem, which include waste processing. The mathematical programming model is solved using neighborhood search approach.
An Improved Method for Solving Multiobjective Integer Linear Fractional Programming Problem
Directory of Open Access Journals (Sweden)
Meriem Ait Mehdi
2014-01-01
Full Text Available We describe an improvement of Chergui and Moulaï’s method (2008 that generates the whole efficient set of a multiobjective integer linear fractional program based on the branch and cut concept. The general step of this method consists in optimizing (maximizing without loss of generality one of the fractional objective functions over a subset of the original continuous feasible set; then if necessary, a branching process is carried out until obtaining an integer feasible solution. At this stage, an efficient cut is built from the criteria’s growth directions in order to discard a part of the feasible domain containing only nonefficient solutions. Our contribution concerns firstly the optimization process where a linear program that we define later will be solved at each step rather than a fractional linear program. Secondly, local ideal and nadir points will be used as bounds to prune some branches leading to nonefficient solutions. The computational experiments show that the new method outperforms the old one in all the treated instances.
Optimal placement of capacitors in a radial network using conic and mixed integer linear programming
Energy Technology Data Exchange (ETDEWEB)
Jabr, R.A. [Electrical, Computer and Communication Engineering Department, Notre Dame University, P.O. Box: 72, Zouk Mikhael, Zouk Mosbeh (Lebanon)
2008-06-15
This paper considers the problem of optimally placing fixed and switched type capacitors in a radial distribution network. The aim of this problem is to minimize the costs associated with capacitor banks, peak power, and energy losses whilst satisfying a pre-specified set of physical and technical constraints. The proposed solution is obtained using a two-phase approach. In phase-I, the problem is formulated as a conic program in which all nodes are candidates for placement of capacitor banks whose sizes are considered as continuous variables. A global solution of the phase-I problem is obtained using an interior-point based conic programming solver. Phase-II seeks a practical optimal solution by considering capacitor sizes as discrete variables. The problem in this phase is formulated as a mixed integer linear program based on minimizing the L1-norm of deviations from the phase-I state variable values. The solution to the phase-II problem is obtained using a mixed integer linear programming solver. The proposed method is validated via extensive comparisons with previously published results. (author)
An improved exploratory search technique for pure integer linear programming problems
Fogle, F. R.
1990-01-01
The development is documented of a heuristic method for the solution of pure integer linear programming problems. The procedure draws its methodology from the ideas of Hooke and Jeeves type 1 and 2 exploratory searches, greedy procedures, and neighborhood searches. It uses an efficient rounding method to obtain its first feasible integer point from the optimal continuous solution obtained via the simplex method. Since this method is based entirely on simple addition or subtraction of one to each variable of a point in n-space and the subsequent comparison of candidate solutions to a given set of constraints, it facilitates significant complexity improvements over existing techniques. It also obtains the same optimal solution found by the branch-and-bound technique in 44 of 45 small to moderate size test problems. Two example problems are worked in detail to show the inner workings of the method. Furthermore, using an established weighted scheme for comparing computational effort involved in an algorithm, a comparison of this algorithm is made to the more established and rigorous branch-and-bound method. A computer implementation of the procedure, in PC compatible Pascal, is also presented and discussed.
A Mixed Integer Linear Programming Approach to Electrical Stimulation Optimization Problems.
Abouelseoud, Gehan; Abouelseoud, Yasmine; Shoukry, Amin; Ismail, Nour; Mekky, Jaidaa
2018-02-01
Electrical stimulation optimization is a challenging problem. Even when a single region is targeted for excitation, the problem remains a constrained multi-objective optimization problem. The constrained nature of the problem results from safety concerns while its multi-objectives originate from the requirement that non-targeted regions should remain unaffected. In this paper, we propose a mixed integer linear programming formulation that can successfully address the challenges facing this problem. Moreover, the proposed framework can conclusively check the feasibility of the stimulation goals. This helps researchers to avoid wasting time trying to achieve goals that are impossible under a chosen stimulation setup. The superiority of the proposed framework over alternative methods is demonstrated through simulation examples.
Lemmen-Gerdessen, van J.C.; Souverein, O.W.; Veer, van 't P.; Vries, de J.H.M.
2015-01-01
Objective To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Design Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear
Neutrosophic Integer Programming Problem
Directory of Open Access Journals (Sweden)
Mai Mohamed
2017-02-01
Full Text Available In this paper, we introduce the integer programming in neutrosophic environment, by considering coffecients of problem as a triangulare neutrosophic numbers. The degrees of acceptance, indeterminacy and rejection of objectives are simultaneously considered.
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.
Directory of Open Access Journals (Sweden)
Maoyuan Feng
2014-01-01
Full Text Available This study proposes a mixed integer linear programming (MILP model to optimize the spillways scheduling for reservoir flood control. Unlike the conventional reservoir operation model, the proposed MILP model specifies the spillways status (including the number of spillways to be open and the degree of the spillway opened instead of reservoir release, since the release is actually controlled by using the spillway. The piecewise linear approximation is used to formulate the relationship between the reservoir storage and water release for a spillway, which should be open/closed with a status depicted by a binary variable. The control order and symmetry rules of spillways are described and incorporated into the constraints for meeting the practical demand. Thus, a MILP model is set up to minimize the maximum reservoir storage. The General Algebraic Modeling System (GAMS and IBM ILOG CPLEX Optimization Studio (CPLEX software are used to find the optimal solution for the proposed MILP model. The China’s Three Gorges Reservoir, whose spillways are of five types with the total number of 80, is selected as the case study. It is shown that the proposed model decreases the flood risk compared with the conventional operation and makes the operation more practical by specifying the spillways status directly.
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.
Application of mixed-integer linear programming in a car seats assembling process
Directory of Open Access Journals (Sweden)
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.
Stochastic programming with integer recourse
van der Vlerk, Maarten Hendrikus
1995-01-01
In this thesis we consider two-stage stochastic linear programming models with integer recourse. Such models are at the intersection of two different branches of mathematical programming. On the one hand some of the model parameters are random, which places the problem in the field of stochastic
Optimal Airport Surface Traffic Planning Using Mixed-Integer Linear Programming
Directory of Open Access Journals (Sweden)
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.
Optimising the selection of food items for FFQs using Mixed Integer Linear Programming.
Gerdessen, Johanna C; Souverein, Olga W; van 't Veer, Pieter; de Vries, Jeanne Hm
2015-01-01
To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium. The food lists generated by the MILP model have good performance in terms of length, coverage and R 2 (explained variance) of all nutrients. MILP-generated food lists were 32-40 % shorter than a benchmark food list, whereas their quality in terms of R 2 was similar to that of the benchmark. The results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.
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.
Integer Linear Programming for Constrained Multi-Aspect Committee Review Assignment
Karimzadehgan, Maryam; Zhai, ChengXiang
2011-01-01
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. PMID:22711970
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. © The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.
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. PMID:22536398
Improving an Integer Linear Programming Model of an Ecovat Buffer by Adding Long-Term Planning
Directory of Open Access Journals (Sweden)
Gijs J. H. de Goeijen
2017-12-01
Full Text Available The Ecovat is a seasonal thermal storage solution consisting of a large underground water tank divided into a number of virtual segments that can be individually charged and discharged. The goal of the Ecovat is to supply heat demand to a neighborhood throughout the entire year. In this work, we extend an integer linear programming model to describe the charging and discharging of such an Ecovat buffer by adding a long-term (yearly planning step to the model. We compare the results from the model using this extension to previously obtained results and show significant improvements when looking at the combination of costs and the energy content of the buffer at the end of the optimization. Furthermore, we show that the model is very robust against prediction errors. For this, we compare two different cases: one case in which we assume perfect predictions are available and one case in which we assume no predictions are available. The largest observed difference in costs between these two cases is less than 2%.
A multiple objective mixed integer linear programming model for power generation expansion planning
Energy Technology Data Exchange (ETDEWEB)
Antunes, C. Henggeler; Martins, A. Gomes [INESC-Coimbra, Coimbra (Portugal); Universidade de Coimbra, Dept. de Engenharia Electrotecnica, Coimbra (Portugal); Brito, Isabel Sofia [Instituto Politecnico de Beja, Escola Superior de Tecnologia e Gestao, Beja (Portugal)
2004-03-01
Power generation expansion planning inherently involves multiple, conflicting and incommensurate objectives. Therefore, mathematical models become more realistic if distinct evaluation aspects, such as cost and environmental concerns, are explicitly considered as objective functions rather than being encompassed by a single economic indicator. With the aid of multiple objective models, decision makers may grasp the conflicting nature and the trade-offs among the different objectives in order to select satisfactory compromise solutions. This paper presents a multiple objective mixed integer linear programming model for power generation expansion planning that allows the consideration of modular expansion capacity values of supply-side options. This characteristic of the model avoids the well-known problem associated with continuous capacity values that usually have to be discretized in a post-processing phase without feedback on the nature and importance of the changes in the attributes of the obtained solutions. Demand-side management (DSM) is also considered an option in the planning process, assuming there is a sufficiently large portion of the market under franchise conditions. As DSM full costs are accounted in the model, including lost revenues, it is possible to perform an evaluation of the rate impact in order to further inform the decision process (Author)
Lyubetsky, Vassily; Gershgorin, Roman; Gorbunov, Konstantin
2017-12-06
Chromosome structure is a very limited model of the genome including the information about its chromosomes such as their linear or circular organization, the order of genes on them, and the DNA strand encoding a gene. Gene lengths, nucleotide composition, and intergenic regions are ignored. Although highly incomplete, such structure can be used in many cases, e.g., to reconstruct phylogeny and evolutionary events, to identify gene synteny, regulatory elements and promoters (considering highly conserved elements), etc. Three problems are considered; all assume unequal gene content and the presence of gene paralogs. The distance problem is to determine the minimum number of operations required to transform one chromosome structure into another and the corresponding transformation itself including the identification of paralogs in two structures. We use the DCJ model which is one of the most studied combinatorial rearrangement models. Double-, sesqui-, and single-operations as well as deletion and insertion of a chromosome region are considered in the model; the single ones comprise cut and join. In the reconstruction problem, a phylogenetic tree with chromosome structures in the leaves is given. It is necessary to assign the structures to inner nodes of the tree to minimize the sum of distances between terminal structures of each edge and to identify the mutual paralogs in a fairly large set of structures. A linear algorithm is known for the distance problem without paralogs, while the presence of paralogs makes it NP-hard. If paralogs are allowed but the insertion and deletion operations are missing (and special constraints are imposed), the reduction of the distance problem to integer linear programming is known. Apparently, the reconstruction problem is NP-hard even in the absence of paralogs. The problem of contigs is to find the optimal arrangements for each given set of contigs, which also includes the mutual identification of paralogs. We proved that these
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.
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.
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.
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.
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. Published by Oxford University Press 2017. This work is written by US Government employees and are in the public domain in the US.
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. © 2013.
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.
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.
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.
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.
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.
Li, Yanning; Canepa, Edward S.; Claudel, Christian G.
2013-01-01
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.
A fixed recourse integer programming approach towards a ...
African Journals Online (AJOL)
Regardless of the success that linear programming and integer linear programming has had in applications in engineering, business and economics, one has to challenge the assumed reality that these optimization models represent. In this paper the certainty assumptions of an integer linear program application is ...
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.
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 .
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.
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.
Directory of Open Access Journals (Sweden)
Akyene Tetteh
2017-04-01
Full Text Available Background: Although the Internet boosts business profitability, without certain activities like efficient transportation, scheduling, products ordered via the Internet may reach their destination very late. The environmental problems (vehicle part disposal, carbon monoxide [CO], nitrogen oxide [NOx] and hydrocarbons [HC] associated with transportation are mostly not accounted for by industries. Objectives: The main objective of this article is to minimising negative externalities cost in e-commerce environments. Method: The 0-1 mixed integer linear programming (0-1 MILP model was used to model the problem statement. The result was further analysed using the externality percentage impact factor (EPIF. Results: The simulation results suggest that (1 The mode of ordering refined petroleum products does not impact on the cost of distribution, (2 an increase in private cost is directly proportional to the externality cost, (3 externality cost is largely controlled by the government and number of vehicles used in the distribution and this is in no way influenced by the mode of request (i.e. Internet or otherwise and (4 externality cost may be reduce by using more ecofriendly fuel system.
Directory of Open Access Journals (Sweden)
Denny Nurkertamanda
2012-02-01
Full Text Available In paper cutting industry, cutting stock problem (CSP is a problem about how to cutting paper depends on quantity and specify of the demand. CSP related with dimension of pieces and rectangle which is use. In this research, we use one type dimension of rectangle and six type dimension of pieces and cutting all paper by two stage guillotine pattern. The major focus of this research is to formulate the paper cutting problem using integer linear programming. Cutting large objects into small pieces can be found in many industries. Inevitably, the cutting processes produce trim loss. On the rectangle we can put some different dimension of pieces then we can make certain pattern. The modification pattern have to produce minimum trim loss. Thus to develop optimal cutting pattern to reduce trim loss is the main purpose of this research. To reach that, we use branch and bound algorithm then continued with sensitivity analysis. From the research, we get optimum patten of paper cutting and quantity production for that pattern. Decision for quantity production depends on average demand every day. Beside that, we also give some alternative rules of production system which can take by the company. Keywords : Cutting stock problem, two stage guillotine pattern, branch and bound algorithm
International Nuclear Information System (INIS)
Mashayekh, Salman; Stadler, Michael; Cardoso, Gonçalo; Heleno, Miguel
2017-01-01
Highlights: • This paper presents a MILP model for optimal design of multi-energy microgrids. • Our microgrid design includes optimal technology portfolio, placement, and operation. • Our model includes microgrid electrical power flow and heat transfer equations. • The case study shows advantages of our model over aggregate single-node approaches. • The case study shows the accuracy of the integrated linearized power flow model. - Abstract: Optimal microgrid design is a challenging problem, especially for multi-energy microgrids with electricity, heating, and cooling loads as well as sources, and multiple energy carriers. To address this problem, this paper presents an optimization model formulated as a mixed-integer linear program, which determines the optimal technology portfolio, the optimal technology placement, and the associated optimal dispatch, in a microgrid with multiple energy types. The developed model uses a multi-node modeling approach (as opposed to an aggregate single-node approach) that includes electrical power flow and heat flow equations, and hence, offers the ability to perform optimal siting considering physical and operational constraints of electrical and heating/cooling networks. The new model is founded on the existing optimization model DER-CAM, a state-of-the-art decision support tool for microgrid planning and design. The results of a case study that compares single-node vs. multi-node optimal design for an example microgrid show the importance of multi-node modeling. It has been shown that single-node approaches are not only incapable of optimal DER placement, but may also result in sub-optimal DER portfolio, as well as underestimation of investment costs.
Optimization of Product Instantiation using Integer Programming
van den Broek, P.M.; Botterweck, Goetz; Jarzabek, Stan; Kishi, Tomoji
2010-01-01
We show that Integer Programming (IP) can be used as an optimization technique for the instantiation of products of feature models. This is done by showing that the constraints of feature models can be written in linear form. As particular IP technique, we use Gomory cutting planes. We have applied
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...... formulation provided four new best known lower bounds and, used in a matheuristic framework, improved eleven best known solutions. The computational experiments also show that the resulting integer programming models from the proposed formulation are more effectively solved for most of the instances....
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/. © 2016 Wiley Periodicals, Inc.
Jonrinaldi, Hadiguna, Rika Ampuh; Salastino, Rades
2017-11-01
Environmental consciousness has paid many attention nowadays. It is not only about how to recycle, remanufacture or reuse used end products but it is also how to optimize the operations of the reverse system. A previous research has proposed a design of reverse supply chain of biodiesel network from used cooking oil. However, the research focused on the design of the supply chain strategy not the operations of the supply chain. It only decided how to design the structure of the supply chain in the next few years, and the process of each stage will be conducted in the supply chain system in general. The supply chain system has not considered operational policies to be conducted by the companies in the supply chain. Companies need a policy for each stage of the supply chain operations to be conducted so as to produce the optimal supply chain system, including how to use all the resources that have been designed in order to achieve the objectives of the supply chain system. Therefore, this paper proposes a model to optimize the operational planning of a biodiesel supply chain network from used cooking oil. A mixed integer linear programming is developed to model the operational planning of biodiesel supply chain in order to minimize the total operational cost of the supply chain. Based on the implementation of the model developed, the total operational cost of the biodiesel supply chain incurred by the system is less than the total operational cost of supply chain based on the previous research during seven days of operational planning about amount of 2,743,470.00 or 0.186%. Production costs contributed to 74.6 % of total operational cost and the cost of purchasing the used cooking oil contributed to 24.1 % of total operational cost. So, the system should pay more attention to these two aspects as changes in the value of these aspects will cause significant effects to the change in the total operational cost of the supply chain.
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
Stochastic integer programming by dynamic programming
Lageweg, B.J.; Lenstra, J.K.; Rinnooy Kan, A.H.G.; Stougie, L.; Ermoliev, Yu.; Wets, R.J.B.
1988-01-01
Stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to
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
Domí nguez, Luis F.; Pistikopoulos, Efstratios N.
2010-01-01
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
Energy Technology Data Exchange (ETDEWEB)
Waddell, Lucas [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Muldoon, Frank [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Henry, Stephen Michael [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Hoffman, Matthew John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Zwerneman, April Marie [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Backlund, Peter [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Melander, Darryl J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lawton, Craig R. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Rice, Roy Eugene [Teledyne Brown Engineering, Huntsville, AL (United States)
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.
Directory of Open Access Journals (Sweden)
Baofeng Cai
2017-08-01
Full Text Available The Interconnected River System Network Project (IRSNP is a significant water supply engineering project, which is capable of effectively utilizing flood resources to generate ecological value, by connecting 198 lakes and ponds in western Jilin, northeast China. In this article, an optimization research approach has been proposed to maximize the incremental value of IRSNP ecosystem services. A double-sided chance-constrained integer linear program (DCCILP method has been proposed to support the optimization, which can deal with uncertainties presented as integers or random parameters that appear on both sides of the decision variable at the same time. The optimal scheme indicates that after rational optimization, the total incremental value of ecosystem services from the interconnected river system network project increased 22.25%, providing an increase in benefits of 3.26 × 109 ¥ compared to the original scheme. Most of the functional area is swamp wetland, which provides the greatest ecological benefits. Adjustment services increased obviously, implying that the optimization scheme prioritizes ecological benefits rather than supply and production services.
2013-01-01
that these constraints can often lead to significant reductions in the gap between the optimal solution and its non-integral linear programming bound relative to the prior art as well as often substantially faster processing of moderately hard problem instances. Conclusion We provide an indication of the conditions under which such an optimal enumeration approach is likely to be feasible, suggesting that these strategies are usable for relatively large numbers of taxa, although with stricter limits on numbers of variable sites. The work thus provides methodology suitable for provably optimal solution of some harder instances that resist all prior approaches. PMID:23343437
International Nuclear Information System (INIS)
Wouters, Carmen; Fraga, Eric S.; James, Adrian M.
2015-01-01
The integration of distributed generation units and microgrids in the current grid infrastructure requires an efficient and cost effective local energy system design. A mixed-integer linear programming model is presented to identify such optimal design. The electricity as well as the space heating and cooling demands of a small residential neighbourhood are satisfied through the consideration and combined use of distributed generation technologies, thermal units and energy storage with an optional interconnection with the central grid. Moreover, energy integration is allowed in the form of both optimised pipeline networks and microgrid operation. The objective is to minimise the total annualised cost of the system to meet its yearly energy demand. The model integrates the operational characteristics and constraints of the different technologies for several scenarios in a South Australian setting and is implemented in GAMS. The impact of energy integration is analysed, leading to the identification of key components for residential energy systems. Additionally, a multi-microgrid concept is introduced to allow for local clustering of households within neighbourhoods. The robustness of the model is shown through sensitivity analysis, up-scaling and an effort to address the variability of solar irradiation. - Highlights: • Distributed energy system planning is employed on a small residential scale. • Full energy integration is employed based on microgrid operation and tri-generation. • An MILP for local clustering of households in multi-microgrids is developed. • Micro combined heat and power units are key components for residential microgrids
Integer programming for the generalized high school timetabling problem
DEFF Research Database (Denmark)
Kristiansen, Simon; Sørensen, Matias; Stidsen, Thomas Riis
2015-01-01
, 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...
Bivium as a Mixed Integer Programming Problem
DEFF Research Database (Denmark)
Borghoff, Julia; Knudsen, Lars Ramkilde; Stolpe, Mathias
2009-01-01
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...
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.
Integer programming of cement distribution by train
Indarsih
2018-01-01
Cement industry in Central Java distributes cement by train to meet daily demand in Yogyakarta and Central Java area. There are five destination stations. For each destination station, there is a warehouse to load cements. Decision maker of cement industry have a plan to redesign the infrastructure and transportation system. The aim is to determine how many locomotives, train wagons, and containers and how to arrange train schedules with subject to the delivery time. For this purposes, we consider an integer programming to minimize the total of operational cost. Further, we will discuss a case study and the solution the problem can be calculated by LINGO software.
Linear Independence of -Logarithms over the Eisenstein Integers
Directory of Open Access Journals (Sweden)
Peter Bundschuh
2010-01-01
Full Text Available For fixed complex with ||>1, the -logarithm is the meromorphic continuation of the series ∑>0/(−1,||1,≠,2,3,…. In 2004, Tachiya showed that this is true in the Subcase =ℚ, ∈ℤ, =−1, and the present authors extended this result to arbitrary integer from an imaginary quadratic number field , and provided a quantitative version. In this paper, the earlier method, in particular its arithmetical part, is further developed to answer the above question in the affirmative if is the Eisenstein number field √ℚ(−3, an integer from , and a primitive third root of unity. Under these conditions, the linear independence holds also for 1,(,(−1, and both results are quantitative.
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....
Ferencz, Donald C.; Viterna, Larry A.
1991-01-01
ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.
S-parts of terms of integer linear recurrence sequences
Bugeaud, Y.; Evertse, J.H.
2017-01-01
Let S = {q1 , . . . , qs } be a finite, non-empty set of distinct prime numbers. For a non-zero integer m, write m = q1^ r1 . . . qs^rs M, where r1 , . . . , rs are non-negative integers and M is an integer relatively prime to q1 . . . qs. We define the S-part [m]_S of m by [m]_S := q1^r1 . . .
Solow, Daniel
2014-01-01
This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Menu-Driven Solver Of Linear-Programming Problems
Viterna, L. A.; Ferencz, D.
1992-01-01
Program assists inexperienced user in formulating linear-programming problems. A Linear Program Solver (ALPS) computer program is full-featured LP analysis program. Solves plain linear-programming problems as well as more-complicated mixed-integer and pure-integer programs. Also contains efficient technique for solution of purely binary linear-programming problems. Written entirely in IBM's APL2/PC software, Version 1.01. Packed program contains licensed material, property of IBM (copyright 1988, all rights reserved).
Optimal Diet Planning for Eczema Patient Using Integer Programming
Zhen Sheng, Low; Sufahani, Suliadi
2018-04-01
Human diet planning is conducted by choosing appropriate food items that fulfill the nutritional requirements into the diet formulation. This paper discusses the application of integer programming to build the mathematical model of diet planning for eczema patients. The model developed is used to solve the diet problem of eczema patients from young age group. The integer programming is a scientific approach to select suitable food items, which seeks to minimize the costs, under conditions of meeting desired nutrient quantities, avoiding food allergens and getting certain foods into the diet that brings relief to the eczema conditions. This paper illustrates that the integer programming approach able to produce the optimal and feasible solution to deal with the diet problem of eczema patient.
New Approaches for Very Large-Scale Integer Programming
2016-06-24
DISTRIBUTION/ AVAILABILITY STATEMENT Approved for Public Release 13. SUPPLEMENTARY NOTES 14. ABSTRACT The focus of this project is new computational... heuristics for integer programs in order to rapidly improve dual bounds. 2. Choosing good branching variables in branch-and-bound algorithms for MIP. 3...programming, algorithms, parallel processing, machine learning, heuristics 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT UU 18. NUMBER OF
Karloff, Howard
1991-01-01
To this reviewer’s knowledge, this is the first book accessible to the upper division undergraduate or beginning graduate student that surveys linear programming from the Simplex Method…via the Ellipsoid algorithm to Karmarkar’s algorithm. Moreover, its point of view is algorithmic and thus it provides both a history and a case history of work in complexity theory. The presentation is admirable; Karloff's style is informal (even humorous at times) without sacrificing anything necessary for understanding. Diagrams (including horizontal brackets that group terms) aid in providing clarity. The end-of-chapter notes are helpful...Recommended highly for acquisition, since it is not only a textbook, but can also be used for independent reading and study. —Choice Reviews The reader will be well served by reading the monograph from cover to cover. The author succeeds in providing a concise, readable, understandable introduction to modern linear programming. —Mathematics of Computing This is a textbook intend...
International Nuclear Information System (INIS)
Esmaeily, Ali; Ahmadi, Abdollah; Raeisi, Fatima; Ahmadi, Mohammad Reza; Esmaeel Nezhad, Ali; Janghorbani, Mohammadreza
2017-01-01
A new optimization framework based on MILP model is introduced in the paper for the problem of stochastic self-scheduling of hydrothermal units known as HTSS Problem implemented in a joint energy and reserve electricity market with day-ahead mechanism. The proposed MILP framework includes some practical constraints such as the cost due to valve-loading effect, the limit due to DRR and also multi-POZs, which have been less investigated in electricity market models. For the sake of more accuracy, for hydro generating units’ model, multi performance curves are also used. The problem proposed in this paper is formulated using a model on the basis of a stochastic optimization technique while the objective function is maximizing the expected profit utilizing MILP technique. The suggested stochastic self-scheduling model employs the price forecast error in order to take into account the uncertainty due to price. Besides, LMCS is combined with roulette wheel mechanism so that the scenarios corresponding to the non-spinning reserve price and spinning reserve price as well as the energy price at each hour of the scheduling are generated. Finally, the IEEE 118-bus power system is used to indicate the performance and the efficiency of the suggested technique. - Highlights: • Characterizing the uncertainties of price and FOR of units. • Replacing the fixed ramping rate constraints with the dynamic ones. • Proposing linearized model for the valve-point effects of thermal units. • Taking into consideration the multi-POZs relating to the thermal units. • Taking into consideration the multi-performance curves of hydroelectric units.
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...
Heuristic Methods of Integer Programming and Its Applications in Economics
Directory of Open Access Journals (Sweden)
Dominika Crnjac Milić
2010-12-01
Full Text Available A short overview of the results related to integer programming is described in the introductory part of this paper. Furthermore, there is a list of literature related to this field. The main part of the paper analyses the Heuristic method which yields a very fast result without the use of significant mathematical tools.
Discovering workflow nets using integer linear programming
van Zelst, S.J.; van Dongen, B.F.; van der Aalst, W.M.P.; Verbeek, H.M.W.
Process mining is concerned with the analysis, understanding and improvement of business processes. Process discovery, i.e. discovering a process model based on an event log, is considered the most challenging process mining task. State-of-the-art process discovery algorithms only discover local
A program package for solving linear optimization problems
International Nuclear Information System (INIS)
Horikami, Kunihiko; Fujimura, Toichiro; Nakahara, Yasuaki
1980-09-01
Seven computer programs for the solution of linear, integer and quadratic programming (four programs for linear programming, one for integer programming and two for quadratic programming) have been prepared and tested on FACOM M200 computer, and auxiliary programs have been written to make it easy to use the optimization program package. The characteristics of each program are explained and the detailed input/output descriptions are given in order to let users know how to use them. (author)
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.
A Mixed Integer Programming for Port Anzali Development Plan
Mahdieh Allahviranloo
2009-01-01
This paper introduces a mixed integer programming model to find the optimum development plan for port Anzali. The model minimizes total system costs taking into account both port infrastructure costs and shipping costs. Due to the multipurpose function of the port, the model consists of 1020 decision variables and 2490 constraints. Results of the model determine the optimum number of berths that should be constructed in each period and for each type of cargo. In addition to, the results of se...
Penempatan Optimal Phasor Measurement Unit (PMU) Dengan Integer Programming
Amrulloh, Yunan Helmy
2013-01-01
Phasor Measurement Unit (PMU) merupakan peralatan yang mampu memberikan pengukuran fasor tegangan dan arus secara real-time. PMU dapat digunakan untuk monitoring, proteksi dan kontrol pada sistem tenaga listrik. Tugas akhir ini membahas penempatan PMU secara optimal berdasarkan topologi jaringan sehingga sistem tenaga listrik dapat diobservasi. Penempatan optimal PMU dirumuskan sebagai masalah Binary Integer Programming (BIP) yang akan memberikan variabel dengan pilihan nilai (0,1) yang menu...
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.
Directory of Open Access Journals (Sweden)
Reyes Zotelo, Yunuem
2017-12-01
Full Text Available En este trabajo se propone un modelo de programación lineal entera para planificar la producción de un conjunto de artículos finales con demanda independiente. El modelo para la planificación maestra de producción (PMP está diseñado considerando los costes de producción e inventario, así como las restricciones definidas por el mismo proceso productivo en cuanto a instalaciones y tiempos de producción. El objetivo del modelo propuesto es la minimización de los costes implicados; concretamente, el tiempo ocioso y extra de los recursos, así como la consideración de un nivel mínimo de servicio ligado a la demanda diferida. La validación del modelo considera datos pertenecientes a la demanda de cada producto en un horizonte de 12 semanas y compara cinco escenarios en los que se modifican algunos aspectos del sistema y diferentes niveles de servicio. Por último, los resultados obtenidos para cada uno de los escenarios exponen la mejora obtenida por el modelo propuesto respecto al procedimiento actual en la empresa objeto de estudio. || In this work, we propose an integer linear programming model for production scheduling of a group of finished products with independent demand. The model for the master production scheduling (MPS is designed by considering production and inventory costs, as well as the productive process constraints regarding installations and production times. The aim of the proposed model is the minimization of the costs involved; specifically, undertime and overtime costs of resources, as well as the consideration of a minimum service level related to the deferred demand. The validation of the model considers data belonging to the demand of each product in a 12-week planning horizon and compares five scenarios in which some characteristics of the system and different service levels are modified. Finally, the results obtained for each one of the scenarios expose the improvement obtained by the proposed model with
Equitably Distributing Quality of Marine Security Guards Using Integer Programming
2013-03-01
ARB BALMOD COM DoD DoS E HAF HQ 10 IP IQ LP MOS MCESG MSG MSGAT NLP NMC OSAB PCS PP&O Q RSO SAl SD SE SNCO T-ODP LIST OF...and Eurasia 2 Abu Dhabi, United Arab Emirates India and the Middle East 3 Bangkok, Thailand East Asia and Pacific 4 Fort Lauderdale, Florida South...integer, goal, and quadratic programming. LP models and nonlinear programming ( NLP ) models are very similar in model development for both maximizing
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
Linear programming foundations and extensions
Vanderbei, Robert J
2001-01-01
Linear Programming: Foundations and Extensions is an introduction to the field of optimization. The book emphasizes constrained optimization, beginning with a substantial treatment of linear programming, and proceeding to convex analysis, network flows, integer programming, quadratic programming, and convex optimization. The book is carefully written. Specific examples and concrete algorithms precede more abstract topics. Topics are clearly developed with a large number of numerical examples worked out in detail. Moreover, Linear Programming: Foundations and Extensions underscores the purpose of optimization: to solve practical problems on a computer. Accordingly, the book is coordinated with free efficient C programs that implement the major algorithms studied: -The two-phase simplex method; -The primal-dual simplex method; -The path-following interior-point method; -The homogeneous self-dual methods. In addition, there are online JAVA applets that illustrate various pivot rules and variants of the simplex m...
Binary integer programming solution for troubleshooting with dependent actions
Czech Academy of Sciences Publication Activity Database
Lín, Václav
2017-01-01
Roč. 53, č. 3 (2017), s. 493-512 ISSN 0023-5954 R&D Projects: GA ČR GA13-20012S Institutional support: RVO:67985556 Keywords : binary integer programming * decision-theoretic troubleshooting Subject RIV: JD - Computer Applications, Robotics OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.379, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/lin-0476547.pdf
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…
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.
Towards Merging Binary Integer Programming Techniques with Genetic Algorithms
Directory of Open Access Journals (Sweden)
Reza Zamani
2017-01-01
Full Text Available This paper presents a framework based on merging a binary integer programming technique with a genetic algorithm. The framework uses both lower and upper bounds to make the employed mathematical formulation of a problem as tight as possible. For problems whose optimal solutions cannot be obtained, precision is traded with speed through substituting the integrality constrains in a binary integer program with a penalty. In this way, instead of constraining a variable u with binary restriction, u is considered as real number between 0 and 1, with the penalty of Mu(1-u, in which M is a large number. Values not near to the boundary extremes of 0 and 1 make the component of Mu(1-u large and are expected to be avoided implicitly. The nonbinary values are then converted to priorities, and a genetic algorithm can use these priorities to fill its initial pool for producing feasible solutions. The presented framework can be applied to many combinatorial optimization problems. Here, a procedure based on this framework has been applied to a scheduling problem, and the results of computational experiments have been discussed, emphasizing the knowledge generated and inefficiencies to be circumvented with this framework in future.
Determining on-fault earthquake magnitude distributions from integer programming
Geist, Eric L.; Parsons, Thomas E.
2018-01-01
Earthquake magnitude distributions among faults within a fault system are determined from regional seismicity and fault slip rates using binary integer programming. A synthetic earthquake catalog (i.e., list of randomly sampled magnitudes) that spans millennia is first formed, assuming that regional seismicity follows a Gutenberg-Richter relation. Each earthquake in the synthetic catalog can occur on any fault and at any location. The objective is to minimize misfits in the target slip rate for each fault, where slip for each earthquake is scaled from its magnitude. The decision vector consists of binary variables indicating which locations are optimal among all possibilities. Uncertainty estimates in fault slip rates provide explicit upper and lower bounding constraints to the problem. An implicit constraint is that an earthquake can only be located on a fault if it is long enough to contain that earthquake. A general mixed-integer programming solver, consisting of a number of different algorithms, is used to determine the optimal decision vector. A case study is presented for the State of California, where a 4 kyr synthetic earthquake catalog is created and faults with slip ≥3 mm/yr are considered, resulting in >106 variables. The optimal magnitude distributions for each of the faults in the system span a rich diversity of shapes, ranging from characteristic to power-law distributions.
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.
Screening synteny blocks in pairwise genome comparisons through integer programming.
Tang, Haibao; Lyons, Eric; Pedersen, Brent; Schnable, James C; Paterson, Andrew H; Freeling, Michael
2011-04-18
It is difficult to accurately interpret chromosomal correspondences such as true orthology and paralogy due to significant divergence of genomes from a common ancestor. Analyses are particularly problematic among lineages that have repeatedly experienced whole genome duplication (WGD) events. To compare multiple "subgenomes" derived from genome duplications, we need to relax the traditional requirements of "one-to-one" syntenic matchings of genomic regions in order to reflect "one-to-many" or more generally "many-to-many" matchings. However this relaxation may result in the identification of synteny blocks that are derived from ancient shared WGDs that are not of interest. For many downstream analyses, we need to eliminate weak, low scoring alignments from pairwise genome comparisons. Our goal is to objectively select subset of synteny blocks whose total scores are maximized while respecting the duplication history of the genomes in comparison. We call this "quota-based" screening of synteny blocks in order to appropriately fill a quota of syntenic relationships within one genome or between two genomes having WGD events. We have formulated the synteny block screening as an optimization problem known as "Binary Integer Programming" (BIP), which is solved using existing linear programming solvers. The computer program QUOTA-ALIGN performs this task by creating a clear objective function that maximizes the compatible set of synteny blocks under given constraints on overlaps and depths (corresponding to the duplication history in respective genomes). Such a procedure is useful for any pairwise synteny alignments, but is most useful in lineages affected by multiple WGDs, like plants or fish lineages. For example, there should be a 1:2 ploidy relationship between genome A and B if genome B had an independent WGD subsequent to the divergence of the two genomes. We show through simulations and real examples using plant genomes in the rosid superorder that the quota
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 Allocation of Static Var Compensator via Mixed Integer Conic Programming
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xiaohu [ORNL; Shi, Di [Global Energy Interconnection Research Institute North America (GEIRI North America), California; Wang, Zhiwei [Global Energy Interconnection Research Institute North America (GEIRI North America), California; Huang, Junhui [Global Energy Interconnection Research Institute North America (GEIRI North America), California; Wang, Xu [Global Energy Interconnection Research Institute North America (GEIRI North America), California; Liu, Guodong [ORNL; Tomsovic, Kevin [University of Tennessee, Knoxville (UTK)
2017-01-01
Shunt FACTS devices, such as, a Static Var Compensator (SVC), are capable of providing local reactive power compensation. They are widely used in the network to reduce the real power loss and improve the voltage profile. This paper proposes a planning model based on mixed integer conic programming (MICP) to optimally allocate SVCs in the transmission network considering load uncertainty. The load uncertainties are represented by a number of scenarios. Reformulation and linearization techniques are utilized to transform the original non-convex model into a convex second order cone programming (SOCP) model. Numerical case studies based on the IEEE 30-bus system demonstrate the effectiveness of the proposed planning model.
Penempatan Optimal Phasor Measurement Unit (PMU dengan Integer Programming
Directory of Open Access Journals (Sweden)
Yunan Helmy Amrulloh
2013-09-01
Full Text Available Phasor Measurement Unit (PMU merupakan peralatan yang mampu memberikan pengukuran fasor tegangan dan arus secara real-time. PMU dapat digunakan untuk monitoring, proteksi dan kontrol pada sistem tenaga listrik. Tugas akhir ini membahas penempatan PMU secara optimal berdasarkan topologi jaringan sehingga sistem tenaga listrik dapat diobservasi. Penempatan optimal PMU dirumuskan sebagai masalah Binary Integer Programming (BIP yang akan memberikan variabel dengan pilihan nilai (0,1 yang menunjukkan tempat yang harus dipasang PMU. Dalam tugas akhir ini, BIP diterapkan untuk menyelesaikan masalah penempatan PMU secara optimal pada sistem tenaga listrik Jawa-Bali 500 KV yang selanjutnya diterapkan dengan penambahan konsep incomplete observability. Hasil simulasi menunjukkan bahwa penerapan BIP pada sistem dengan incomplete observability memberikan jumlah PMU yang lebih sedikit dibandingkan dengan sistem tanpa konsep incomplete observability.
Applications and algorithms for mixed integer nonlinear programming
International Nuclear Information System (INIS)
Leyffer, Sven; Munson, Todd; Linderoth, Jeff; Luedtke, James; Miller, Andrew
2009-01-01
The mathematical modeling of systems often requires the use of both nonlinear and discrete components. Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Nonlinear functions are required to accurately represent physical properties such as pressure, stress, temperature, and equilibrium. Problems involving both discrete variables and nonlinear constraint functions are known as mixed-integer nonlinear programs (MINLPs) and are among the most challenging computational optimization problems faced by researchers and practitioners. In this paper, we describe relevant scientific applications that are naturally modeled as MINLPs, we provide an overview of available algorithms and software, and we describe ongoing methodological advances for solving MINLPs. These algorithmic advances are making increasingly larger instances of this important family of problems tractable.
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.
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.
An Integer Programming Formulation of the Minimum Common String Partition Problem.
Directory of Open Access Journals (Sweden)
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.
ALPS - A LINEAR PROGRAM SOLVER
Viterna, L. A.
1994-01-01
Linear programming is a widely-used engineering and management tool. Scheduling, resource allocation, and production planning are all well-known applications of linear programs (LP's). Most LP's are too large to be solved by hand, so over the decades many computer codes for solving LP's have been developed. ALPS, A Linear Program Solver, is a full-featured LP analysis program. ALPS can solve plain linear programs as well as more complicated mixed integer and pure integer programs. ALPS also contains an efficient solution technique for pure binary (0-1 integer) programs. One of the many weaknesses of LP solvers is the lack of interaction with the user. ALPS is a menu-driven program with no special commands or keywords to learn. In addition, ALPS contains a full-screen editor to enter and maintain the LP formulation. These formulations can be written to and read from plain ASCII files for portability. For those less experienced in LP formulation, ALPS contains a problem "parser" which checks the formulation for errors. ALPS creates fully formatted, readable reports that can be sent to a printer or output file. ALPS is written entirely in IBM's APL2/PC product, Version 1.01. The APL2 workspace containing all the ALPS code can be run on any APL2/PC system (AT or 386). On a 32-bit system, this configuration can take advantage of all extended memory. The user can also examine and modify the ALPS code. The APL2 workspace has also been "packed" to be run on any DOS system (without APL2) as a stand-alone "EXE" file, but has limited memory capacity on a 640K system. A numeric coprocessor (80X87) is optional but recommended. The standard distribution medium for ALPS is a 5.25 inch 360K MS-DOS format diskette. IBM, IBM PC and IBM APL2 are registered trademarks of International Business Machines Corporation. MS-DOS is a registered trademark of Microsoft Corporation.
Canepa, Edward S.; Claudel, Christian G.
2012-01-01
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.
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.
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
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.
Reduction of Linear Programming to Linear Approximation
Vaserstein, Leonid N.
2006-01-01
It is well known that every Chebyshev linear approximation problem can be reduced to a linear program. In this paper we show that conversely every linear program can be reduced to a Chebyshev linear approximation problem.
Li, Zukui; Ding, Ran; Floudas, Christodoulos A.
2011-01-01
Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented. PMID:21935263
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
FATCOP: A Fault Tolerant Condor-PVM Mixed Integer Program Solver
National Research Council Canada - National Science Library
Chen, Qun
1999-01-01
We describe FATCOP, a new parallel mixed integer program solver written in PVM. The implementation uses the Condor resource management system to provide a virtual machine composed of otherwise idle computers...
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 ...
Joint shape segmentation with linear programming
Huang, Qixing
2011-01-01
We present an approach to segmenting shapes in a heterogenous shape database. Our approach segments the shapes jointly, utilizing features from multiple shapes to improve the segmentation of each. The approach is entirely unsupervised and is based on an integer quadratic programming formulation of the joint segmentation problem. The program optimizes over possible segmentations of individual shapes as well as over possible correspondences between segments from multiple shapes. The integer quadratic program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape segmentation significantly outperforms single-shape segmentation techniques. © 2011 ACM.
Tuey, R. C.
1972-01-01
Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.
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 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.
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.
Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.
1982-01-01
The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.
International Nuclear Information System (INIS)
Rogner, H.H.
1989-01-01
The submitted sections on linear programming are extracted from 'Theorie und Technik der Planung' (1978) by W. Blaas and P. Henseler and reformulated for presentation at the Workshop. They consider a brief introduction to the theory of linear programming and to some essential aspects of the SIMPLEX solution algorithm for the purposes of economic planning processes. 1 fig
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
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.
50 Years of Integer Programming 1958-2008 From the Early Years to the State-of-the-Art
Jünger, Michael; Naddef, Denis
2010-01-01
In 1958, Ralph E. Gomory transformed the field of integer programming when he published a paper that described a cutting-plane algorithm for pure integer programs and announced that the method could be refined to give a finite algorithm for integer programming. In 2008, to commemorate the anniversary of this seminal paper, a special workshop celebrating fifty years of integer programming was held in Aussois, France, as part of the 12th Combinatorial Optimization Workshop. It contains reprints of key historical articles and written versions of survey lectures on six of the hottest topics in the
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...
Brameier, Markus
2007-01-01
Presents a variant of Genetic Programming that evolves imperative computer programs as linear sequences of instructions, in contrast to the more traditional functional expressions or syntax trees. This book serves as a reference for researchers, but also contains sufficient introduction for students and those who are new to the field
An Integer Programming Model for Multi-Echelon Supply Chain Decision Problem Considering Inventories
Harahap, Amin; Mawengkang, Herman; Siswadi; Effendi, Syahril
2018-01-01
In this paper we address a problem that is of significance to the industry, namely the optimal decision of a multi-echelon supply chain and the associated inventory systems. By using the guaranteed service approach to model the multi-echelon inventory system, we develop a mixed integer; programming model to simultaneously optimize the transportation, inventory and network structure of a multi-echelon supply chain. To solve the model we develop a direct search approach using a strategy of releasing nonbasic variables from their bounds, combined with the “active constraint” method. This strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points.
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
there is the complicating factor that some of the variables are required to be integral. The resulting class of problems is named multiobjective mixed integer programming (MOMIP) problems. Solving these kinds of optimization problems exactly requires a method that can generate the whole set of nondominated points (the...... 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......, and one of the two objectives has only integer variables. The proposed method is able to find the full set of nondominated points. It is tested on a large number of problem instances, from six different classes of MOMIP problems. The results reveal that the developed biobjective branch and bound method...
DEFF Research Database (Denmark)
Liu, Zhaoxi; Wu, Qiuwei; Oren, Shmuel S.
2017-01-01
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...
Schultz, R.; Stougie, L.; Vlerk, van der M.H.
1998-01-01
In this paper we present a framework for solving stochastic programs with complete integer recourse and discretely distributed right-hand side vector, using Gröbner basis methods from computational algebra to solve the numerous second-stage integer programs. Using structural properties of the
Optimization Research of Generation Investment Based on Linear Programming Model
Wu, Juan; Ge, Xueqian
Linear programming is an important branch of operational research and it is a mathematical method to assist the people to carry out scientific management. GAMS is an advanced simulation and optimization modeling language and it will combine a large number of complex mathematical programming, such as linear programming LP, nonlinear programming NLP, MIP and other mixed-integer programming with the system simulation. In this paper, based on the linear programming model, the optimized investment decision-making of generation is simulated and analyzed. At last, the optimal installed capacity of power plants and the final total cost are got, which provides the rational decision-making basis for optimized investments.
Linear programming using Matlab
Ploskas, Nikolaos
2017-01-01
This book offers a theoretical and computational presentation of a variety of linear programming algorithms and methods with an emphasis on the revised simplex method and its components. A theoretical background and mathematical formulation is included for each algorithm as well as comprehensive numerical examples and corresponding MATLAB® code. The MATLAB® implementations presented in this book are sophisticated and allow users to find solutions to large-scale benchmark linear programs. Each algorithm is followed by a computational study on benchmark problems that analyze the computational behavior of the presented algorithms. As a solid companion to existing algorithmic-specific literature, this book will be useful to researchers, scientists, mathematical programmers, and students with a basic knowledge of linear algebra and calculus. The clear presentation enables the reader to understand and utilize all components of simplex-type methods, such as presolve techniques, scaling techniques, pivoting ru...
Combinatorial therapy discovery using mixed integer linear programming.
Pang, Kaifang; Wan, Ying-Wooi; Choi, William T; Donehower, Lawrence A; Sun, Jingchun; Pant, Dhruv; Liu, Zhandong
2014-05-15
Combinatorial therapies play increasingly important roles in combating complex diseases. Owing to the huge cost associated with experimental methods in identifying optimal drug combinations, computational approaches can provide a guide to limit the search space and reduce cost. However, few computational approaches have been developed for this purpose, and thus there is a great need of new algorithms for drug combination prediction. Here we proposed to formulate the optimal combinatorial therapy problem into two complementary mathematical algorithms, Balanced Target Set Cover (BTSC) and Minimum Off-Target Set Cover (MOTSC). Given a disease gene set, BTSC seeks a balanced solution that maximizes the coverage on the disease genes and minimizes the off-target hits at the same time. MOTSC seeks a full coverage on the disease gene set while minimizing the off-target set. Through simulation, both BTSC and MOTSC demonstrated a much faster running time over exhaustive search with the same accuracy. When applied to real disease gene sets, our algorithms not only identified known drug combinations, but also predicted novel drug combinations that are worth further testing. In addition, we developed a web-based tool to allow users to iteratively search for optimal drug combinations given a user-defined gene set. Our tool is freely available for noncommercial use at http://www.drug.liuzlab.org/. zhandong.liu@bcm.edu Supplementary data are available at Bioinformatics online.
Fitting boxes to Manhattan scenes using linear integer programming
Li, Minglei; Nan, Liangliang; Liu, Shaochuang
2016-01-01
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
Directory of Open Access Journals (Sweden)
Nelson Maculan
2003-01-01
Full Text Available We present integer linear models with a polynomial number of variables and constraints for combinatorial optimization problems in graphs: optimum elementary cycles, optimum elementary paths and optimum tree problems.Apresentamos modelos lineares inteiros com um número polinomial de variáveis e restrições para problemas de otimização combinatória em grafos: ciclos elementares ótimos, caminhos elementares ótimos e problemas em árvores ótimas.
Approximation in two-stage stochastic integer programming
W. Romeijnders; L. Stougie (Leen); M. van der Vlerk
2014-01-01
htmlabstractApproximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value.
Approximation in two-stage stochastic integer programming
Romeijnders, W.; Stougie, L.; van der Vlerk, M.H.
2014-01-01
Approximation algorithms are the prevalent solution methods in the field of stochastic programming. Problems in this field are very hard to solve. Indeed, most of the research in this field has concentrated on designing solution methods that approximate the optimal solution value. However,
Integer goal programming approach for finding a compromise ...
African Journals Online (AJOL)
In second model the cost and time spent on repairing the components are considered as two different objectives. Selective maintenance operation is used to select the repairable components and a multi-objective goal programming algorithm is proposed to obtain compromise selection of repairable components for the two ...
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 algorithm. The drastic reduction of space needed allows us to solve much larger instances than was possible before using this technique....
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.
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...... applied to the TPC-C benchmark and the heuristic is shown to obtain solutions with costs close to the ones found using the quadratic program....
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.......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...
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.
Chenlu Miao; Gang Du; Yi Xia; Danping Wang
2016-01-01
Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP) to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP), which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard pr...
Urselmann, Maren; Emmerich, Michael T. M.; Till, Jochen; Sand, Guido; Engell, Sebastian
2007-07-01
Engineering optimization often deals with large, mixed-integer search spaces with a rigid structure due to the presence of a large number of constraints. Metaheuristics, such as evolutionary algorithms (EAs), are frequently suggested as solution algorithms in such cases. In order to exploit the full potential of these algorithms, it is important to choose an adequate representation of the search space and to integrate expert-knowledge into the stochastic search operators, without adding unnecessary bias to the search. Moreover, hybridisation with mathematical programming techniques such as mixed-integer programming (MIP) based on a problem decomposition can be considered for improving algorithmic performance. In order to design problem-specific EAs it is desirable to have a set of design guidelines that specify properties of search operators and representations. Recently, a set of guidelines has been proposed that gives rise to so-called Metric-based EAs (MBEAs). Extended by the minimal moves mutation they allow for a generalization of EA with self-adaptive mutation strength in discrete search spaces. In this article, a problem-specific EA for process engineering task is designed, following the MBEA guidelines and minimal moves mutation. On the background of the application, the usefulness of the design framework is discussed, and further extensions and corrections proposed. As a case-study, a two-stage stochastic programming problem in chemical batch process scheduling is considered. The algorithm design problem can be viewed as the choice of a hierarchical decision structure, where on different layers of the decision process symmetries and similarities can be exploited for the design of minimal moves. After a discussion of the design approach and its instantiation for the case-study, the resulting problem-specific EA/MIP is compared to a straightforward application of a canonical EA/MIP and to a monolithic mathematical programming algorithm. In view of the
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
DEFF Research Database (Denmark)
Pour, Shahrzad M.; Drake, John H.; Ejlertsen, Lena Secher
2017-01-01
A railway signaling system is a complex and interdependent system which should ensure the safe operation of trains. We introduce and address a mixed integer optimisation model for the preventive signal maintenance crew scheduling problem in the Danish railway system. The problem contains many...... to feed as ‘warm start’ solutions to a Mixed Integer Programming (MIP) solver for further optimisation. We apply the CP/MIP framework to a section of the Danish rail network and benchmark our results against both direct application of a MIP solver and modelling the problem as a Constraint Optimisation...
Domí nguez, Luis F.; Pistikopoulos, Efstratios N.
2012-01-01
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
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.
A MICROCOMPUTER LINEAR PROGRAMMING PACKAGE: AN ALTERNATIVE TO MAINFRAMES
Laughlin, David H.
1984-01-01
This paper presents the capabilities and limitations of a microcomputer linear programming package. The solution algorithm is a version of the revised simplex. Rapid problem entry, user ease of operation, sensitivity analyses on objective function and right hand sides are advantages. A problem size of 150 activities and 64 constraints can be solved in present form. Due to problem size, limitations and lack of parametric and integer programming routines, this package is thought to have the mos...
Wihartiko, F. D.; Wijayanti, H.; Virgantari, F.
2018-03-01
Genetic Algorithm (GA) is a common algorithm used to solve optimization problems with artificial intelligence approach. Similarly, the Particle Swarm Optimization (PSO) algorithm. Both algorithms have different advantages and disadvantages when applied to the case of optimization of the Model Integer Programming for Bus Timetabling Problem (MIPBTP), where in the case of MIPBTP will be found the optimal number of trips confronted with various constraints. The comparison results show that the PSO algorithm is superior in terms of complexity, accuracy, iteration and program simplicity in finding the optimal solution.
Linear programming computation
PAN, Ping-Qi
2014-01-01
With emphasis on computation, this book is a real breakthrough in the field of LP. In addition to conventional topics, such as the simplex method, duality, and interior-point methods, all deduced in a fresh and clear manner, it introduces the state of the art by highlighting brand-new and advanced results, including efficient pivot rules, Phase-I approaches, reduced simplex methods, deficient-basis methods, face methods, and pivotal interior-point methods. In particular, it covers the determination of the optimal solution set, feasible-point simplex method, decomposition principle for solving large-scale problems, controlled-branch method based on generalized reduced simplex framework for solving integer LP problems.
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).
Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach
International Nuclear Information System (INIS)
Catalao, J.P.S.; Pousinho, H.M.I.; Mendes, V.M.F.
2010-01-01
This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach.
Scheduling of head-dependent cascaded hydro systems: Mixed-integer quadratic programming approach
Energy Technology Data Exchange (ETDEWEB)
Catalao, J.P.S.; Pousinho, H.M.I. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)
2010-03-15
This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent cascaded hydro systems. We propose a novel mixed-integer quadratic programming approach, considering not only head-dependency, but also discontinuous operating regions and discharge ramping constraints. Thus, an enhanced short-term hydro scheduling is provided due to the more realistic modeling presented in this paper. Numerical results from two case studies, based on Portuguese cascaded hydro systems, illustrate the proficiency of the proposed approach. (author)
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.
Klumpp, A. R.; Lawson, C. L.
1988-01-01
Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.
An integer programming model for a forest harvest problem in Pinus pinaster stands
Energy Technology Data Exchange (ETDEWEB)
Fonseca, T. F.; Cerveira, A.; Mota, A.
2012-11-01
The study addresses the special case of a management plan for maritime pine (Pinus pinaster Ait.) in common lands. The study area refers to 4,432 ha of maritime pine stands in North Portugal (Perimetro Florestal do Barroso in the county of Ribeira de Pena), distributed among five common lands called baldio areas. Those lands are co-managed by the Official Forest Services and the local communities, essentially for timber production, using empirical guidance. As the current procedure does not guarantee the best thinning and clear-cutting scheduling, it was considered important to develop easy-to-use models, supported by optimization techniques, to be employed by the forest managers in the harvest planning of these communitarian forests. Planning of the thinning and clear-cutting operations involved certain conditions, such as: (1) the optimal age for harvesting; (2) the maximum stand density permitted; (3) the minimum volume to be cut; (4) the guarantee of incomes for each of the five baldios in at least a two year period; (5) balanced incomes during the length of the projection period. In order to evaluate the sustainability of the wood resources, a set of constraints lower bounding the average ending age was additionally tested. The problem was formulated as an integer linear programming model where the incomes from thinning and clear-cutting are maximized while considering the constraints mentioned above. Five major scenarios were simulated. The simplest one allows for silvicultural constraints only, whereas the other four consider these constraints besides different management options. Two of them introduce joint management of all common areas with or without constraints addressing balanced distribution of incomes during the plan horizon, whilst the other two consider the same options but for individual management of the baldios. The proposed model is easy to apply, providing immediate advantages for short and mid-term planning periods compared to the empirical
Directory of Open Access Journals (Sweden)
Phil Diamond
2003-01-01
Full Text Available Sensitivity of output of a linear operator to its input can be quantified in various ways. In Control Theory, the input is usually interpreted as disturbance and the output is to be minimized in some sense. In stochastic worst-case design settings, the disturbance is considered random with imprecisely known probability distribution. The prior set of probability measures can be chosen so as to quantify how far the disturbance deviates from the white-noise hypothesis of Linear Quadratic Gaussian control. Such deviation can be measured by the minimal Kullback-Leibler informational divergence from the Gaussian distributions with zero mean and scalar covariance matrices. The resulting anisotropy functional is defined for finite power random vectors. Originally, anisotropy was introduced for directionally generic random vectors as the relative entropy of the normalized vector with respect to the uniform distribution on the unit sphere. The associated a-anisotropic norm of a matrix is then its maximum root mean square or average energy gain with respect to finite power or directionally generic inputs whose anisotropy is bounded above by a≥0. We give a systematic comparison of the anisotropy functionals and the associated norms. These are considered for unboundedly growing fragments of homogeneous Gaussian random fields on multidimensional integer lattice to yield mean anisotropy. Correspondingly, the anisotropic norms of finite matrices are extended to bounded linear translation invariant operators over such fields.
Linear Programming and Network Flows
Bazaraa, Mokhtar S; Sherali, Hanif D
2011-01-01
The authoritative guide to modeling and solving complex problems with linear programming-extensively revised, expanded, and updated The only book to treat both linear programming techniques and network flows under one cover, Linear Programming and Network Flows, Fourth Edition has been completely updated with the latest developments on the topic. This new edition continues to successfully emphasize modeling concepts, the design and analysis of algorithms, and implementation strategies for problems in a variety of fields, including industrial engineering, management science, operations research
Elementary linear programming with applications
Kolman, Bernard
1995-01-01
Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations. The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear program
Linear Programming across the Curriculum
Yoder, S. Elizabeth; Kurz, M. Elizabeth
2015-01-01
Linear programming (LP) is taught in different departments across college campuses with engineering and management curricula. Modeling an LP problem is taught in every linear programming class. As faculty teaching in Engineering and Management departments, the depth to which teachers should expect students to master this particular type of…
A Mixed Integer Programming Poultry Feed Ration Optimisation Problem Using the Bat Algorithm
Directory of Open Access Journals (Sweden)
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.
Planning of fuel coal imports using a mixed integer programming method
International Nuclear Information System (INIS)
Shih, L.H.
1997-01-01
In the public utility and commercial fuel industries, commodities from multiple supply sources are sometimes blended before use to reduce costs and assure quality. A typical example of these commodities is the fuel coal used in coal fired power plants. The diversity of the supply sources for these plants makes the planning and scheduling of fuel coal logistics difficult, especially for a power company that has more than one power plant. This study proposes a mixed integer programming model that provides planning and scheduling of coal imports from multiple suppliers for the Taiwan Power Company. The objective is to minimize total inventory cost by minimizing procurement cost, transportation cost and holding cost. Constraints on the system include company procurement policy, power plant demand, harbor unloading capacity, inventory balance equations, blending requirements, and safety stock. An example problem is presented using the central coal logistics system of the Taiwan Power Company to demonstrate the validity of the proposed model
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
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......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...... 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...
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
. The potential for making cost-effective and energy-efficient liner-shipping networks using operations research (OR) is huge and neglected. The implementation of logistic planning tools based upon OR has enhanced performance of airlines, railways, and general transportation companies, but within the field......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...... 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...
Planning of fuel coal imports using a mixed integer programming method
Energy Technology Data Exchange (ETDEWEB)
Shih, L.H. [National Cheng Kung University, Tainan (Taiwan). Dept. of Mineral and Petroleum Engineering
1997-12-31
In the public utility and commercial fuel industries, commodities from multiple supply sources are sometimes blended before use to reduce costs and assure quality. A typical example of these commodities is the fuel coal used in coal fired power plants. The diversity of the supply sources for these plants makes the planning and scheduling of fuel coal logistics difficult, especially for a power company that has more than one power plant. This study proposes a mixed integer programming model that provides planning and scheduling of coal imports from multiple suppliers for the Taiwan Power Company. The objective is to minimize total inventory cost by minimizing procurement cost, transportation cost and holding cost. Constraints on the system include company procurement policy, power plant demand, harbor unloading capacity, inventory balance equations, blending requirements, and safety stock. An example problem is presented using the central coal logistics system of the Taiwan Power Company to demonstrate the validity of the proposed model.
Integrative improvement method and mixed-integer programming in system planning
International Nuclear Information System (INIS)
Sadegheih, A.
2002-01-01
In this paper, system planning network is formulated for mixed-integer programming and a Ga. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The Dc load flow equations for the network are embedded in the constraints of the mathematical model to avoid sub-optimal solutions that can arise if the enforcement of such constraints is done in an indirect way. The solution of the model gives the best line additions. and also provides information regarding the optimal generation at each generation point. This method of solutions is demonstrated on the expansion of a 5 bus -bar system to 6 bus-bars
Personnel scheduling using an integer programming model- an application at Avanti Blue-Nile Hotels.
Kassa, Biniyam Asmare; Tizazu, Anteneh Eshetu
2013-01-01
In this paper, we report perhaps a first of its kind application of management science in the Ethiopian hotel industry. Avanti Blue Nile Hotels, a newly established five star hotel in Bahir Dar, is the company for which we developed an integer programming model that determines an optimal weekly shift schedule for the Hotel's engineering department personnel while satisfying several constraints including weekly rest requirements per employee, rest requirements between working shifts per employee, required number of personnel per shift, and other constraints. The model is implemented on an excel solver routine. The model enables the company's personnel department management to develop a fair personnel schedule as needed and to effectively utilize personnel resources while satisfying several technical, legal and economic requirements. These encouraging achievements make us optimistic about the gains other Ethiopian organizations can amass by introducing management science approaches in their management planning and decision making systems.
Advances in mixed-integer programming methods for chemical production scheduling.
Velez, Sara; Maravelias, Christos T
2014-01-01
The goal of this paper is to critically review advances in the area of chemical production scheduling over the past three decades and then present two recently proposed solution methods that have led to dramatic computational enhancements. First, we present a general framework and problem classification and discuss modeling and solution methods with an emphasis on mixed-integer programming (MIP) techniques. Second, we present two solution methods: (a) a constraint propagation algorithm that allows us to compute parameters that are then used to tighten MIP scheduling models and (b) a reformulation that introduces new variables, thus leading to effective branching. We also present computational results and an example illustrating how these methods are implemented, as well as the resulting enhancements. We close with a discussion of open research challenges and future research directions.
Bi-objective integer programming for RNA secondary structure prediction with pseudoknots.
Legendre, Audrey; Angel, Eric; Tahi, Fariza
2018-01-15
RNA structure prediction is an important field in bioinformatics, and numerous methods and tools have been proposed. Pseudoknots are specific motifs of RNA secondary structures that are difficult to predict. Almost all existing methods are based on a single model and return one solution, often missing the real structure. An alternative approach would be to combine different models and return a (small) set of solutions, maximizing its quality and diversity in order to increase the probability that it contains the real structure. We propose here an original method for predicting RNA secondary structures with pseudoknots, based on integer programming. We developed a generic bi-objective integer programming algorithm allowing to return optimal and sub-optimal solutions optimizing simultaneously two models. This algorithm was then applied to the combination of two known models of RNA secondary structure prediction, namely MEA and MFE. The resulting tool, called BiokoP, is compared with the other methods in the literature. The results show that the best solution (structure with the highest F 1 -score) is, in most cases, given by BiokoP. Moreover, the results of BiokoP are homogeneous, regardless of the pseudoknot type or the presence or not of pseudoknots. Indeed, the F 1 -scores are always higher than 70% for any number of solutions returned. The results obtained by BiokoP show that combining the MEA and the MFE models, as well as returning several optimal and several sub-optimal solutions, allow to improve the prediction of secondary structures. One perspective of our work is to combine better mono-criterion models, in particular to combine a model based on the comparative approach with the MEA and the MFE models. This leads to develop in the future a new multi-objective algorithm to combine more than two models. BiokoP is available on the EvryRNA platform: https://EvryRNA.ibisc.univ-evry.fr .
International Nuclear Information System (INIS)
Khrennikov, Andrei; Klein, Moshe; Mor, Tal
2010-01-01
In number theory, a partition of a positive integer n is a way of writing n as a sum of positive integers. The number of partitions of n is given by the partition function p(n). Inspired by quantum information processing, we extend the concept of partitions in number theory as follows: for an integer n, we treat each partition as a basis state of a quantum system representing that number n, so that the Hilbert-space that corresponds to that integer n is of dimension p(n); the 'classical integer' n can thus be generalized into a (pure) quantum state ||ψ(n) > which is a superposition of the partitions of n, in the same way that a quantum bit (qubit) is a generalization of a classical bit. More generally, ρ(n) is a density matrix in that same Hilbert-space (a probability distribution over pure states). Inspired by the notion of quantum numbers in quantum theory (such as in Bohr's model of the atom), we then try to go beyond the partitions, by defining (via recursion) the notion of 'sub-partitions' in number theory. Combining the two notions mentioned above, sub-partitions and quantum integers, we finally provide an alternative definition of the quantum integers [the pure-state |ψ'(n)> and the mixed-state ρ'(n),] this time using the sub-partitions as the basis states instead of the partitions, for describing the quantum number that corresponds to the integer n.
A Two-Stage Stochastic Mixed-Integer Programming Approach to the Smart House Scheduling Problem
Ozoe, Shunsuke; Tanaka, Yoichi; Fukushima, Masao
A “Smart House” is a highly energy-optimized house equipped with photovoltaic systems (PV systems), electric battery systems, fuel cell cogeneration systems (FC systems), electric vehicles (EVs) and so on. Smart houses are attracting much attention recently thanks to their enhanced ability to save energy by making full use of renewable energy and by achieving power grid stability despite an increased power draw for installed PV systems. Yet running a smart house's power system, with its multiple power sources and power storages, is no simple task. In this paper, we consider the problem of power scheduling for a smart house with a PV system, an FC system and an EV. We formulate the problem as a mixed integer programming problem, and then extend it to a stochastic programming problem involving recourse costs to cope with uncertain electricity demand, heat demand and PV power generation. Using our method, we seek to achieve the optimal power schedule running at the minimum expected operation cost. We present some results of numerical experiments with data on real-life demands and PV power generation to show the effectiveness of our method.
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.
International Nuclear Information System (INIS)
Santos Coelho, Leandro dos
2009-01-01
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
An integer programming formulation of the parsimonious loss of heterozygosity problem.
Catanzaro, Daniele; Labbé, Martine; Halldórsson, Bjarni V
2013-01-01
A loss of heterozygosity (LOH) event occurs when, by the laws of Mendelian inheritance, an individual should be heterozygote at a given site but, due to a deletion polymorphism, is not. Deletions play an important role in human disease and their detection could provide fundamental insights for the development of new diagnostics and treatments. In this paper, we investigate the parsimonious loss of heterozygosity problem (PLOHP), i.e., the problem of partitioning suspected polymorphisms from a set of individuals into a minimum number of deletion areas. Specifically, we generalize Halldórsson et al.'s work by providing a more general formulation of the PLOHP and by showing how one can incorporate different recombination rates and prior knowledge about the locations of deletions. Moreover, we show that the PLOHP can be formulated as a specific version of the clique partition problem in a particular class of graphs called undirected catch-point interval graphs and we prove its general $({\\cal NP})$-hardness. Finally, we provide a state-of-the-art integer programming (IP) formulation and strengthening valid inequalities to exactly solve real instances of the PLOHP containing up to 9,000 individuals and 3,000 SNPs. Our results give perspectives on the mathematics of the PLOHP and suggest new directions on the development of future efficient exact solution approaches.
Construction of Fixed Rate Non-Binary WOM Codes Based on Integer Programming
Fujino, Yoju; Wadayama, Tadashi
In this paper, we propose a construction of non-binary WOM (Write-Once-Memory) codes for WOM storages such as flash memories. The WOM codes discussed in this paper are fixed rate WOM codes where messages in a fixed alphabet of size $M$ can be sequentially written in the WOM storage at least $t^*$-times. In this paper, a WOM storage is modeled by a state transition graph. The proposed construction has the following two features. First, it includes a systematic method to determine the encoding regions in the state transition graph. Second, the proposed construction includes a labeling method for states by using integer programming. Several novel WOM codes for $q$ level flash memories with 2 cells are constructed by the proposed construction. They achieve the worst numbers of writes $t^*$ that meet the known upper bound in many cases. In addition, we constructed fixed rate non-binary WOM codes with the capability to reduce ICI (inter cell interference) of flash cells. One of the advantages of the proposed construction is its flexibility. It can be applied to various storage devices, to various dimensions (i.e, number of cells), and various kind of additional constraints.
WORKFORCE SIZING AND SCHEDULING FOR A SERVICE CONTRACTOR USING INTEGER PROGRAMMING
Directory of Open Access Journals (Sweden)
D.G. Conradie
2012-01-01
Full Text Available
ENGLISH ABSTRACT: Operations Research is perceived to be on the verge of demise as a decision support tool in industry. However, this is not true, since the relevancy and interdisciplinary nature of Operations Research makes it an indispensable part of operations management. What should rather be asked is how Operations Research is introduced to undergraduate industrial engineering students. This paper reports on one of the optimisation initiatives undertaken for a service contractor using integer programming as part of a semester project. Although the model addresses specific business issues related to the contractor, it can easily be generalised for other applications.
AFRIKAANSE OPSOMMING: Operasionele Navorsing word geag as ’n kwynende besluitnemingsinstrument in die nywerheid. Dit is egter onwaar, aangesien die toepaslikheid en interdissiplinêre karakter van Operasionele Navorsing dit ‘n onmisbare rol laat speel in operasionele bestuur. Die vraag wat eerder gevra moet word is hoe Operasionele Navorsing aan voorgraadse bedryfsingenieurswesestudente aangebied word. Hierdie artikel doen verslag oor een van die optimerings-inisiatiewe wat as deel van ‘n semesterprojek vir ‘n diensverskaffer uitgevoer is, en maak van heeltal-programmering gebruik. Alhoewel die model kontrakteur-spesifieke besigheidsreëls aanspreek, kan dit maklik veralgemeen word vir wyer toepassing.
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.
Integer 1/0 Knapsack Problem Dynamic Programming Approach in Building Maintenance Optimization
Directory of Open Access Journals (Sweden)
Viska Dewi Fawzy
2017-12-01
Full Text Available The most common problem in urban areas is the high public demand and the limited provision of housing. In meeting the needs of affordable housing for low income communities, the Government of Indonesia implements Rusunawa Project. Object of this research is Pandanarang Rusunawa. Rusunawa Pandanarang is one of the vertical housing in Cilacap that is facing deterioration issue and needs good maintenance management. This study aims at insetting priority and optimizing maintenance plan due to limited funds (limited budget and the amount of damage that must be repaired.This study uses one of the optimization methods of Dynamic Programing on the application of Integer 1/0 Knapsack Problem, to determine an schedule the maintenance activities. The Criteria that are used such as: the level of building components damage and the level of occupants participation. In the first criterion, the benefit (p is the percentage of damage that is fixed with the cost (w. While on the second criterion, the benefit (p is the percentage of occupant participation rate on the maintenance activities with the cost (w. For the budget of Rp 125.000.000, 00, it was obtained from the simulation that the value of the optimum solution on the first criterion at the 7th stage of 71.88% with total cost Rp 106.000.000, 00. At the second criterion, the value of the optimum solution at the 7th stage of 89.29% with total cost Rp 124.000.000, 00.
Directory of Open Access Journals (Sweden)
Chenlu Miao
2016-01-01
Full Text Available Many leader-follower relationships exist in product family design engineering problems. We use bilevel programming (BLP to reflect the leader-follower relationship and describe such problems. Product family design problems have unique characteristics; thus, mixed integer nonlinear BLP (MINLBLP, which has both continuous and discrete variables and multiple independent lower-level problems, is widely used in product family optimization. However, BLP is difficult in theory and is an NP-hard problem. Consequently, using traditional methods to solve such problems is difficult. Genetic algorithms (GAs have great value in solving BLP problems, and many studies have designed GAs to solve BLP problems; however, such GAs are typically designed for special cases that do not involve MINLBLP with one or multiple followers. Therefore, we propose a bilevel GA to solve these particular MINLBLP problems, which are widely used in product family problems. We give numerical examples to demonstrate the effectiveness of the proposed algorithm. In addition, a reducer family case study is examined to demonstrate practical applications of the proposed BLGA.
Alvarado, Michelle; Ntaimo, Lewis
2018-03-01
Oncology clinics are often burdened with scheduling large volumes of cancer patients for chemotherapy treatments under limited resources such as the number of nurses and chairs. These cancer patients require a series of appointments over several weeks or months and the timing of these appointments is critical to the treatment's effectiveness. Additionally, the appointment duration, the acuity levels of each appointment, and the availability of clinic nurses are uncertain. The timing constraints, stochastic parameters, rising treatment costs, and increased demand of outpatient oncology clinic services motivate the need for efficient appointment schedules and clinic operations. In this paper, we develop three mean-risk stochastic integer programming (SIP) models, referred to as SIP-CHEMO, for the problem of scheduling individual chemotherapy patient appointments and resources. These mean-risk models are presented and an algorithm is devised to improve computational speed. Computational results were conducted using a simulation model and results indicate that the risk-averse SIP-CHEMO model with the expected excess mean-risk measure can decrease patient waiting times and nurse overtime when compared to deterministic scheduling algorithms by 42 % and 27 %, respectively.
A bi-objective integer programming model for partly-restricted flight departure scheduling.
Zhong, Han; Guan, Wei; Zhang, Wenyi; Jiang, Shixiong; Fan, Lingling
2018-01-01
The normal studies on air traffic departure scheduling problem (DSP) mainly deal with an independent airport in which the departure traffic is not affected by surrounded airports, which, however, is not a consistent case. In reality, there still exist cases where several commercial airports are closely located and one of them possesses a higher priority. During the peak hours, the departure activities of the lower-priority airports are usually required to give way to those of higher-priority airport. These giving-way requirements can inflict a set of changes on the modeling of departure scheduling problem with respect to the lower-priority airports. To the best of our knowledge, studies on DSP under this condition are scarce. Accordingly, this paper develops a bi-objective integer programming model to address the flight departure scheduling of the partly-restricted (e.g., lower-priority) one among several adjacent airports. An adapted tabu search algorithm is designed to solve the current problem. It is demonstrated from the case study of Tianjin Binhai International Airport in China that the proposed method can obviously improve the operation efficiency, while still realizing superior equity and regularity among restricted flows.
175 Years of Linear Programming
Indian Academy of Sciences (India)
polynomial-time solvability of linear programming, that is, testing if a polyhedron Q E ~ ... Q is rational, i.e. all extreme points and rays of Q are ra- tional vectors or ..... rithrll terminates with an interior solution, a post-processing step is usually ...
175 Years of Linear Programming
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 10. 175 Years of Linear Programming - Max Flow = Min Cut. Vijay Chandru M R Rao. Series Article Volume 4 Issue 10 October 1999 pp 22-39. Fulltext. Click here to view fulltext PDF. Permanent link:
175 Years of Linear Programming
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 5. 175 Years of Linear Programming - Pune's Gift. Vijay Chandru M R Rao. Series Article Volume 4 Issue 5 May ... Computer Science and Automation, IISc Bangalore 560012, India. Director, Indian Institute of Management, Bannerghatta Road, ...
Tang, Jiafu; Liu, Yang; Fung, Richard; Luo, Xinggang
2008-12-01
Manufacturers have a legal accountability to deal with industrial waste generated from their production processes in order to avoid pollution. Along with advances in waste recovery techniques, manufacturers may adopt various recycling strategies in dealing with industrial waste. With reuse strategies and technologies, byproducts or wastes will be returned to production processes in the iron and steel industry, and some waste can be recycled back to base material for reuse in other industries. This article focuses on a recovery strategies optimization problem for a typical class of industrial waste recycling process in order to maximize profit. There are multiple strategies for waste recycling available to generate multiple byproducts; these byproducts are then further transformed into several types of chemical products via different production patterns. A mixed integer programming model is developed to determine which recycling strategy and which production pattern should be selected with what quantity of chemical products corresponding to this strategy and pattern in order to yield maximum marginal profits. The sales profits of chemical products and the set-up costs of these strategies, patterns and operation costs of production are considered. A simulated annealing (SA) based heuristic algorithm is developed to solve the problem. Finally, an experiment is designed to verify the effectiveness and feasibility of the proposed method. By comparing a single strategy to multiple strategies in an example, it is shown that the total sales profit of chemical products can be increased by around 25% through the simultaneous use of multiple strategies. This illustrates the superiority of combinatorial multiple strategies. Furthermore, the effects of the model parameters on profit are discussed to help manufacturers organize their waste recycling network.
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.
Searching for optimal integer solutions to set partitioning problems using column generation
Bredström, David; Jörnsten, Kurt; Rönnqvist, Mikael
2007-01-01
We describe a new approach to produce integer feasible columns to a set partitioning problem directly in solving the linear programming (LP) relaxation using column generation. Traditionally, column generation is aimed to solve the LP relaxation as quick as possible without any concern of the integer properties of the columns formed. In our approach we aim to generate the columns forming the optimal integer solution while simultaneously solving the LP relaxation. By this we can re...
Directory of Open Access Journals (Sweden)
Ricardo França Santos
2012-01-01
Full Text Available This work tries to solve a typical logistics problem of Navy of Brazil regards the allocation, transportation and distribution of genera refrigerated for Military Organizations within Grande Rio (RJ. After a brief review of literature on Linear/Integer Programming and some of their applications, we proposed the use of Integer Programming, using the Excel’s Solver as a tool for obtaining the optimal load configuration for the fleet, obtaining the lower distribution costs in order to meet the demand schedule. The assumptions were met in a first attempt with a single spreadsheet, but it could not find a convergent solution, without degeneration problems and with a reasonable solution time. A second solution was proposed separating the problem into three phases, which allowed us to highlight the potential and limitations of the Solver tool. This study showed the importance of formulating a realistic model and of a detailed critical analysis, which could be seen through the lack of convergence of the first solution and the success achieved by the second one.
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...
Irmeilyana, Puspita, Fitri Maya; Indrawati
2016-02-01
The pricing for wireless networks is developed by considering linearity factors, elasticity price and price factors. Mixed Integer Nonlinear Programming of wireless pricing model is proposed as the nonlinear programming problem that can be solved optimally using LINGO 13.0. The solutions are expected to give some information about the connections between the acceptance factor and the price. Previous model worked on the model that focuses on bandwidth as the QoS attribute. The models attempt to maximize the total price for a connection based on QoS parameter. The QoS attributes used will be the bandwidth and the end to end delay that affect the traffic. The maximum goal to maximum price is achieved when the provider determine the requirement for the increment or decrement of price change due to QoS change and amount of QoS value.
DEFF Research Database (Denmark)
Escudero, Laureano F.; Monge, Juan Francisco; Morales, Dolores Romero
2015-01-01
In this paper we consider multiperiod mixed 0–1 linear programming models under uncertainty. We propose a risk averse strategy using stochastic dominance constraints (SDC) induced by mixed-integer linear recourse as the risk measure. The SDC strategy extends the existing literature to the multist...
Mixed integer programming model for optimizing the layout of an ICU vehicle
Directory of Open Access Journals (Sweden)
García-Sánchez Álvaro
2009-12-01
Full Text Available Abstract Background This paper presents a Mixed Integer Programming (MIP model for designing the layout of the Intensive Care Units' (ICUs patient care space. In particular, this MIP model was developed for optimizing the layout for materials to be used in interventions. This work was developed within the framework of a joint project between the Madrid Technical Unverstity and the Medical Emergency Services of the Madrid Regional Government (SUMMA 112. Methods The first task was to identify the relevant information to define the characteristics of the new vehicles and, in particular, to obtain a satisfactory interior layout to locate all the necessary materials. This information was gathered from health workers related to ICUs. With that information an optimization model was developed in order to obtain a solution. From the MIP model, a first solution was obtained, consisting of a grid to locate the different materials needed for the ICUs. The outcome from the MIP model was discussed with health workers to tune the solution, and after slightly altering that solution to meet some requirements that had not been included in the mathematical model, the eventual solution was approved by the persons responsible for specifying the characteristics of the new vehicles. According to the opinion stated by the SUMMA 112's medical group responsible for improving the ambulances (the so-called "coaching group", the outcome was highly satisfactory. Indeed, the final design served as a basis to draw up the requirements of a public tender. Results As a result from solving the Optimization model, a grid was obtained to locate the different necessary materials for the ICUs. This grid had to be slightly altered to meet some requirements that had not been included in the mathematical model. The results were discussed with the persons responsible for specifying the characteristics of the new vehicles. Conclusion The outcome was highly satisfactory. Indeed, the final
On the linear programming bound for linear Lee codes.
Astola, Helena; Tabus, Ioan
2016-01-01
Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.
Directory of Open Access Journals (Sweden)
I Gede Agus Widyadana
2001-01-01
Full Text Available The decisions to choose appropriate tools for solving industrial problems are not just tools that achieve optimal solution only but it should consider computation time too. One of industrial problems that still difficult to achieve both criteria is scheduling problem. This paper discuss comparison between mixed integer programming which result optimal solution and heuristic method to solve job shop scheduling problem with separable sequence-dependent setup. The problems are generated and the result shows that the heuristic methods still cannot satisfy optimal solution.
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.
Ranking Forestry Investments With Parametric Linear Programming
Paul A. Murphy
1976-01-01
Parametric linear programming is introduced as a technique for ranking forestry investments under multiple constraints; it combines the advantages of simple tanking and linear programming as capital budgeting tools.
Multi-task feature selection in microarray data by binary integer programming.
Lan, Liang; Vucetic, Slobodan
2013-12-20
A major challenge in microarray classification is that the number of features is typically orders of magnitude larger than the number of examples. In this paper, we propose a novel feature filter algorithm to select the feature subset with maximal discriminative power and minimal redundancy by solving a quadratic objective function with binary integer constraints. To improve the computational efficiency, the binary integer constraints are relaxed and a low-rank approximation to the quadratic term is applied. The proposed feature selection algorithm was extended to solve multi-task microarray classification problems. We compared the single-task version of the proposed feature selection algorithm with 9 existing feature selection methods on 4 benchmark microarray data sets. The empirical results show that the proposed method achieved the most accurate predictions overall. We also evaluated the multi-task version of the proposed algorithm on 8 multi-task microarray datasets. The multi-task feature selection algorithm resulted in significantly higher accuracy than when using the single-task feature selection methods.
The use of mixed-integer programming for inverse treatment planning with pre-defined field segments
International Nuclear Information System (INIS)
Bednarz, Greg; Michalski, Darek; Houser, Chris; Huq, M. Saiful; Xiao Ying; Rani, Pramila Anne; Galvin, James M.
2002-01-01
Complex intensity patterns generated by traditional beamlet-based inverse treatment plans are often very difficult to deliver. In the approach presented in this work the intensity maps are controlled by pre-defining field segments to be used for dose optimization. A set of simple rules was used to define a pool of allowable delivery segments and the mixed-integer programming (MIP) method was used to optimize segment weights. The optimization problem was formulated by combining real variables describing segment weights with a set of binary variables, used to enumerate voxels in targets and critical structures. The MIP method was compared to the previously used Cimmino projection algorithm. The field segmentation approach was compared to an inverse planning system with a traditional beamlet-based beam intensity optimization. In four complex cases of oropharyngeal cancer the segmental inverse planning produced treatment plans, which competed with traditional beamlet-based IMRT plans. The mixed-integer programming provided mechanism for imposition of dose-volume constraints and allowed for identification of the optimal solution for feasible problems. Additional advantages of the segmental technique presented here are: simplified dosimetry, quality assurance and treatment delivery. (author)
International Nuclear Information System (INIS)
Zhang, Jianyun; Liu, Pei; Zhou, Zhe; Ma, Linwei; Li, Zheng; Ni, Weidou
2014-01-01
Highlights: • Integration of heat streams with HRSG in a polygeneration system is studied. • A mixed-integer nonlinear programming model is proposed to optimize heat network. • Operating parameters and heat network configuration are optimized simultaneously. • The optimized heat network highly depends on the HRSG type and model specification. - Abstract: A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant; however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification
Computer Program For Linear Algebra
Krogh, F. T.; Hanson, R. J.
1987-01-01
Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.
The linear programming bound for binary linear codes
Brouwer, A.E.
1993-01-01
Combining Delsarte's (1973) linear programming bound with the information that certain weights cannot occur, new upper bounds for dmin (n,k), the maximum possible minimum distance of a binary linear code with given word length n and dimension k, are derived.
Linear programming algorithms and applications
Vajda, S
1981-01-01
This text is based on a course of about 16 hours lectures to students of mathematics, statistics, and/or operational research. It is intended to introduce readers to the very wide range of applicability of linear programming, covering problems of manage ment, administration, transportation and a number of other uses which are mentioned in their context. The emphasis is on numerical algorithms, which are illustrated by examples of such modest size that the solutions can be obtained using pen and paper. It is clear that these methods, if applied to larger problems, can also be carried out on automatic (electronic) computers. Commercially available computer packages are, in fact, mainly based on algorithms explained in this book. The author is convinced that the user of these algorithms ought to be knowledgeable about the underlying theory. Therefore this volume is not merely addressed to the practitioner, but also to the mathematician who is interested in relatively new developments in algebraic theory and in...
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.
Joint shape segmentation with linear programming
Huang, Qixing; Koltun, Vladlen; Guibas, Leonidas
2011-01-01
program is solved via a linear programming relaxation, using a block coordinate descent procedure that makes the optimization feasible for large databases. We evaluate the presented approach on the Princeton segmentation benchmark and show that joint shape
Timetabling an Academic Department with Linear Programming.
Bezeau, Lawrence M.
This paper describes an approach to faculty timetabling and course scheduling that uses computerized linear programming. After reviewing the literature on linear programming, the paper discusses the process whereby a timetable was created for a department at the University of New Brunswick. Faculty were surveyed with respect to course offerings…
Günlük, O.; Woeginger, G.J.
2011-01-01
This volume contains the 33 papers presented at IPCO 2011, the 15th Conference on Integer Programming and Combinatorial Optimization, held during June 15–17, 2011 at the IBM T.J. Watson Research Center in New York, USA. IPCO conferences are sponsored by the Mathematical Optimization Society. The
M. ZANGIABADI; H. R. MALEKI
2007-01-01
In the real-world optimization problems, coefficients of the objective function are not known precisely and can be interpreted as fuzzy numbers. In this paper we define the concepts of optimality for linear programming problems with fuzzy parameters based on those for multiobjective linear programming problems. Then by using the concept of comparison of fuzzy numbers, we transform a linear programming problem with fuzzy parameters to a multiobjective linear programming problem. To this end, w...
Gorissen, B.L.; den Hertog, D.; Hoffmann, A.L.
2013-01-01
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
Enhancement of Linear Circuit Program
DEFF Research Database (Denmark)
Gaunholt, Hans; Dabu, Mihaela; Beldiman, Octavian
1996-01-01
In this report a preliminary user friendly interface has been added to the LCP2 program making it possible to describe an electronic circuit by actually drawing the circuit on the screen. Component values and other options and parameters can easily be set by the aid of the interface. The interface...
The Use of Linear Programming for Prediction.
Schnittjer, Carl J.
The purpose of the study was to develop a linear programming model to be used for prediction, test the accuracy of the predictions, and compare the accuracy with that produced by curvilinear multiple regression analysis. (Author)
Sparsity Prevention Pivoting Method for Linear Programming
DEFF Research Database (Denmark)
Li, Peiqiang; Li, Qiyuan; Li, Canbing
2018-01-01
When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper....... The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...
Sparsity Prevention Pivoting Method for Linear Programming
DEFF Research Database (Denmark)
Li, Peiqiang; Li, Qiyuan; Li, Canbing
2018-01-01
. The principle of this method is avoided choosing the row which the value of the element in the b vector is zero as the row of the pivot element to make the matrix in linear programming density and ensure that most subsequent steps will improve the value of the objective function. One step following......When the simplex algorithm is used to calculate a linear programming problem, if the matrix is a sparse matrix, it will be possible to lead to many zero-length calculation steps, and even iterative cycle will appear. To deal with the problem, a new pivoting method is proposed in this paper...... this principle is inserted to reselect the pivot element in the existing linear programming algorithm. Both the conditions for inserting this step and the maximum number of allowed insertion steps are determined. In the case study, taking several numbers of linear programming problems as examples, the results...
A Direct Heuristic Algorithm for Linear Programming
Indian Academy of Sciences (India)
Abstract. An (3) mathematically non-iterative heuristic procedure that needs no artificial variable is presented for solving linear programming problems. An optimality test is included. Numerical experiments depict the utility/scope of such a procedure.
Using linear integer programming for multi-site land-use allocation
Aerts, J.C.J.H.; Eisinger, E.; Heuvelink, G.B.M.; Stewart, Th.J.
2003-01-01
Research in the area of spatial decision support (SDS) and resource allocation has recently generated increased attention for integrating optimization techniques with GIS. In this paper we address the use of spatial optimization techniques for solving multi-site land-use allocation (MLUA) problems,
Optimal Airport Surface Traffic Planning Using Mixed-Integer Linear Programming
Roling, P.C.; Visser, H.G.
2008-01-01
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
Mixed-integer linear program for an optimal hybrid energy network topology
Mazairac, L.A.J.; Salenbien, R.; de Vries, B.
2015-01-01
Existing networks do not have the quantitative and qualitative capacity to facilitate the transition towards distributed renewable energy sources. Irregular production of energy over time at different locations will alter the current patters of energy flow, necessitating the implementation of short-
A Mixed-Integer Linear Programming Problem which is Efficiently Solvable.
1987-10-01
ger prongramn rg versions or the problem is not ac’hievable in genieral for sparse inistancves of’ P rolem(r Mi. Th le remrai nder or thris paper is...rClazes c:oIh edge (i,I*) by comlpli urg +- rnirr(z 3, ,x + a,j). A sirnI) le analysis (11 vto Nei [131 indicates why whe Iellinan-Ford algorithm works...ari cl(cck to iceat reguilar rnct’vtuls. For c’xamiic, oi1cc Wwitiil pcroccc’ssicg svlstcici1 rccjcilrcc thicit I iisc wires ice repeated verr 200W
Optimized Waterspace Management and Scheduling Using Mixed-Integer Linear Programming
2016-01-01
PANAMA CITY DIVISION PANAMA CITY, FLORIDA 32407-7001 5(3257...task. This paper is outlined as follows: in Section 2, we discuss the general setup of the the MCM scheduling problem, including the definition of the...Suite 1425 Arlington, VA 22203-1995 Naval Surface Warfare Center, Panama City Division 1 ATTN: Technical Library 110 Vernon Avenue Panama City, FL 32407 27
Canepa, Edward S.; Bayen, Alexandre M.; Claudel, Christian G.
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
Canepa, Edward S.; Claudel, Christian G.
2013-01-01
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
Mixed Integer Linear Programming for new trends in wind farm cable routing
DEFF Research Database (Denmark)
Fischetti, Martina; Pisinger, David
2018-01-01
The efficient production of green energy plays an import role in modern economies. In this paper we address the optimization of cable connections between turbines in an offshore wind park. Different versions of this problem have been studied recently. In a previous joint project with Vattenfall BA...
Evaluation of film dosemeters by linear programming
International Nuclear Information System (INIS)
Kragh, P.; Nitschke, J.
1992-01-01
An evaluation method for multi-component dosemeters is described which uses linear programming in order to decrease the dependence on energy and direction. The results of this method are more accurate than those obtained with the evaluation methods so far applied in film dosimetry. In addition, systematic errors can be given when evaluating individual measurements. Combined linear programming, as a special case of the presented method, is described taking a film dosemeter of particular type as an example. (orig.) [de
Linear programming mathematics, theory and algorithms
1996-01-01
Linear Programming provides an in-depth look at simplex based as well as the more recent interior point techniques for solving linear programming problems. Starting with a review of the mathematical underpinnings of these approaches, the text provides details of the primal and dual simplex methods with the primal-dual, composite, and steepest edge simplex algorithms. This then is followed by a discussion of interior point techniques, including projective and affine potential reduction, primal and dual affine scaling, and path following algorithms. Also covered is the theory and solution of the linear complementarity problem using both the complementary pivot algorithm and interior point routines. A feature of the book is its early and extensive development and use of duality theory. Audience: The book is written for students in the areas of mathematics, economics, engineering and management science, and professionals who need a sound foundation in the important and dynamic discipline of linear programming.
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
Fuzzy Multi-objective Linear Programming Approach
Directory of Open Access Journals (Sweden)
Amna Rehmat
2007-07-01
Full Text Available Traveling salesman problem (TSP is one of the challenging real-life problems, attracting researchers of many fields including Artificial Intelligence, Operations Research, and Algorithm Design and Analysis. The problem has been well studied till now under different headings and has been solved with different approaches including genetic algorithms and linear programming. Conventional linear programming is designed to deal with crisp parameters, but information about real life systems is often available in the form of vague descriptions. Fuzzy methods are designed to handle vague terms, and are most suited to finding optimal solutions to problems with vague parameters. Fuzzy multi-objective linear programming, an amalgamation of fuzzy logic and multi-objective linear programming, deals with flexible aspiration levels or goals and fuzzy constraints with acceptable deviations. In this paper, a methodology, for solving a TSP with imprecise parameters, is deployed using fuzzy multi-objective linear programming. An example of TSP with multiple objectives and vague parameters is discussed.
Cheng, Guanhui; Huang, Guohe; Dong, Cong; Xu, Ye; Chen, Jiapei; Chen, Xiujuan; Li, Kailong
2017-03-01
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
Portfolio optimization using fuzzy linear programming
Pandit, Purnima K.
2013-09-01
Portfolio Optimization (PO) is a problem in Finance, in which investor tries to maximize return and minimize risk by carefully choosing different assets. Expected return and risk are the most important parameters with regard to optimal portfolios. In the simple form PO can be modeled as quadratic programming problem which can be put into equivalent linear form. PO problems with the fuzzy parameters can be solved as multi-objective fuzzy linear programming problem. In this paper we give the solution to such problems with an illustrative example.
Some Properties of Multiple Parameters Linear Programming
Directory of Open Access Journals (Sweden)
Maoqin Li
2010-01-01
Full Text Available We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function f can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of f at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.
Some Properties of Multiple Parameters Linear Programming
Directory of Open Access Journals (Sweden)
Yan Hong
2010-01-01
Full Text Available Abstract We consider a linear programming problem in which the right-hand side vector depends on multiple parameters. We study the characters of the optimal value function and the critical regions based on the concept of the optimal partition. We show that the domain of the optimal value function can be decomposed into finitely many subsets with disjoint relative interiors, which is different from the result based on the concept of the optimal basis. And any directional derivative of at any point can be computed by solving a linear programming problem when only an optimal solution is available at the point.
PCX, Interior-Point Linear Programming Solver
International Nuclear Information System (INIS)
Czyzyk, J.
2004-01-01
1 - Description of program or function: PCX solves linear programming problems using the Mehrota predictor-corrector interior-point algorithm. PCX can be called as a subroutine or used in stand-alone mode, with data supplied from an MPS file. The software incorporates modules that can be used separately from the linear programming solver, including a pre-solve routine and data structure definitions. 2 - Methods: The Mehrota predictor-corrector method is a primal-dual interior-point method for linear programming. The starting point is determined from a modified least squares heuristic. Linear systems of equations are solved at each interior-point iteration via a sparse Cholesky algorithm native to the code. A pre-solver is incorporated in the code to eliminate inefficiencies in the user's formulation of the problem. 3 - Restriction on the complexity of the problem: There are no size limitations built into the program. The size of problem solved is limited by RAM and swap space on the user's computer
Spline smoothing of histograms by linear programming
Bennett, J. O.
1972-01-01
An algorithm for an approximating function to the frequency distribution is obtained from a sample of size n. To obtain the approximating function a histogram is made from the data. Next, Euclidean space approximations to the graph of the histogram using central B-splines as basis elements are obtained by linear programming. The approximating function has area one and is nonnegative.
Generalised Assignment Matrix Methodology in Linear Programming
Jerome, Lawrence
2012-01-01
Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…
Fuzzy linear programming approach for solving transportation
Indian Academy of Sciences (India)
Transportation problem (TP) is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature. The central concept in this problem is to find the least total transportation cost of a commodity in order to satisfy demands at ...
The simplex method of linear programming
Ficken, Frederick A
1961-01-01
This concise but detailed and thorough treatment discusses the rudiments of the well-known simplex method for solving optimization problems in linear programming. Geared toward undergraduate students, the approach offers sufficient material for readers without a strong background in linear algebra. Many different kinds of problems further enrich the presentation. The text begins with examinations of the allocation problem, matrix notation for dual problems, feasibility, and theorems on duality and existence. Subsequent chapters address convex sets and boundedness, the prepared problem and boun
Updating Linear Schedules with Lowest Cost: a Linear Programming Model
Biruk, Sławomir; Jaśkowski, Piotr; Czarnigowska, Agata
2017-10-01
Many civil engineering projects involve sets of tasks repeated in a predefined sequence in a number of work areas along a particular route. A useful graphical representation of schedules of such projects is time-distance diagrams that clearly show what process is conducted at a particular point of time and in particular location. With repetitive tasks, the quality of project performance is conditioned by the ability of the planner to optimize workflow by synchronizing the works and resources, which usually means that resources are planned to be continuously utilized. However, construction processes are prone to risks, and a fully synchronized schedule may expire if a disturbance (bad weather, machine failure etc.) affects even one task. In such cases, works need to be rescheduled, and another optimal schedule should be built for the changed circumstances. This typically means that, to meet the fixed completion date, durations of operations have to be reduced. A number of measures are possible to achieve such reduction: working overtime, employing more resources or relocating resources from less to more critical tasks, but they all come at a considerable cost and affect the whole project. The paper investigates the problem of selecting the measures that reduce durations of tasks of a linear project so that the cost of these measures is kept to the minimum and proposes an algorithm that could be applied to find optimal solutions as the need to reschedule arises. Considering that civil engineering projects, such as road building, usually involve less process types than construction projects, the complexity of scheduling problems is lower, and precise optimization algorithms can be applied. Therefore, the authors put forward a linear programming model of the problem and illustrate its principle of operation with an example.
Directory of Open Access Journals (Sweden)
Yılmaz GÖKŞEN
2016-11-01
Full Text Available Production factors include labour, capital, nature and technology in traditional organization management. Nowadays, creativity, innovation and ability can be added to these. Competition is intense both in private and public sectors. Workforce can be said to be the main source enriching the organization and making it complex. What makes the organizational powerful is that talented personnel can make new ideas to be productive by using their creativity. From this point of view workforce productivity is important parameter in organizational efficiency. Workforce productivity in organizations where there are too many employees is primarily related to employ the personnel in a right position. The appointment of employees to work in accordance with their capabilities increase efficiency. This situation makes the structure of the workforce and make the organization be capable of competing with the rivals. The Assignment model of the type of linear programming models is a mathematical method used to match the right person for the right job. The coefficients of the variables in the objective function of the assignment model constitute potential contributions of employees. Factors that make contributions in different types of jobs are different and expert opinion is needed for the evaluation of these factors. In this study, more than 1000 people who work for Dokuz Eylul University as drivers, food handlers, technicians, office workers, securities and servants are taken into consideration. Gender, level of education, the distance from working place, marital status, number of children and tenure of these employees have been included in the analysis. Analytical hierarchy process which is a method of multi-criteria decision-making model has been preferred as a method. Specific criteria have been determined for each occupational group depending on this method. Later, weighted average for these criteria in question have been found. With these values belonging
International program on linear electric motors
Energy Technology Data Exchange (ETDEWEB)
Dawson, G.E.; Eastham, A.R.; Parker, J.H.
1992-05-01
The International Program on Linear Electric Motors (LEM) was initiated for the purposes of commumication and coordination between various centers of expertise in LEM technology in Germany, Japan and Canada. Furthermore, it was intended to provide assessment and support of the planning of technological developments and for dissemination of information to researchers, service operators and policy makers, and to ensure that full advantage can be taken if opportunities for technology transfer occur. In the process, the program was able to provide closer contacts between researchers, to enhance and encourage collaborative research and development, and to facilitate joint ventures in advanced transportation technologies. Work done under the program is documented, and seminar materials presented by Canadian researchers in Italy, and by Italian researchers at Queen's University in Canada are presented. Five separate abstracts have been prepared for the main body of the report and the seminar materials.
Controller design approach based on linear programming.
Tanaka, Ryo; Shibasaki, Hiroki; Ogawa, Hiromitsu; Murakami, Takahiro; Ishida, Yoshihisa
2013-11-01
This study explains and demonstrates the design method for a control system with a load disturbance observer. Observer gains are determined by linear programming (LP) in terms of the Routh-Hurwitz stability criterion and the final-value theorem. In addition, the control model has a feedback structure, and feedback gains are determined to be the linear quadratic regulator. The simulation results confirmed that compared with the conventional method, the output estimated by our proposed method converges to a reference input faster when a load disturbance is added to a control system. In addition, we also confirmed the effectiveness of the proposed method by performing an experiment with a DC motor. © 2013 ISA. Published by ISA. All rights reserved.
International Nuclear Information System (INIS)
Wang, Xingwei; Cai, Yanpeng; Chen, Jiajun; Dai, Chao
2013-01-01
In this study, a GFIPMIP (grey-forecasting interval-parameter mixed-integer programming) approach was developed for supporting IEEM (integrated electric-environmental management) in Beijing. It was an attempt to incorporate an energy-forecasting model within a general modeling framework at the municipal level. The developed GFIPMIP model can not only forecast electric demands, but also reflect dynamic, interactive, and uncertain characteristics of the IEEM system in Beijing. Moreover, it can address issues regarding power supply, and emission reduction of atmospheric pollutants and GHG (greenhouse gas). Optimal solutions were obtained related to power generation patterns and facility capacity expansion schemes under a series of system constraints. Two scenarios were analyzed based on multiple environmental policies. The results were useful for helping decision makers identify desired management strategies to guarantee the city's power supply and mitigate emissions of GHG and atmospheric pollutants. The results also suggested that the developed GFIPMIP model be applicable to similar engineering problems. - Highlights: • A grey-forecasting interval-parameter mixed integer programming (GFIPMIP) approach was developed. • It could reflect dynamic, interactive, and uncertain characteristics of an IEEM system. • The developed GFIPMIP approach was used for supporting IEEM system planning in Beijing. • Two scenarios were established based on different environmental policies and management targets. • Optimal schemes for power generation, energy supply, and environmental protection were identified
Game Theory and its Relationship with Linear Programming Models ...
African Journals Online (AJOL)
Game Theory and its Relationship with Linear Programming Models. ... This paper shows that game theory and linear programming problem are closely related subjects since any computing method devised for ... AJOL African Journals Online.
Introduction to linear programming: Coalitional game experiments
Energy Technology Data Exchange (ETDEWEB)
Lucas, W.
1994-12-31
Many solution notions in the multiperson cooperative games (in characteristic function form) make use of linear programming (LP). The popular concept of the {open_quotes}core{close_quotes} of a coalitional game is a special type of LP. It can be introduced in a very simple and quite exciting manner by means of a group experiment. A total of fifty dollars will be given to three randomly selected attendees who will take part in an experiment during this talk, presuming they behave in a Pareto optimal manner. Furthermore, the dual of the particular LP for the core gives rise to the idea of {open_quotes}balanced sets{close_quotes} which is an interesting combinatorial structure in its own right.
Robust Control Design via Linear Programming
Keel, L. H.; Bhattacharyya, S. P.
1998-01-01
This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order. The closed loop specifications considered here are given in terms of a target performance vector representing a desired set of closed loop transfer functions connecting various signals. In general these point targets are unattainable with a fixed order controller. By enlarging the target from a fixed point set to an interval set the solvability conditions with a fixed order controller are relaxed and a solution is more easily enabled. Results from the parametric robust control literature can be used to design the interval target family so that the performance deterioration is acceptable, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications.
Stochastic linear programming models, theory, and computation
Kall, Peter
2011-01-01
This new edition of Stochastic Linear Programming: Models, Theory and Computation has been brought completely up to date, either dealing with or at least referring to new material on models and methods, including DEA with stochastic outputs modeled via constraints on special risk functions (generalizing chance constraints, ICC’s and CVaR constraints), material on Sharpe-ratio, and Asset Liability Management models involving CVaR in a multi-stage setup. To facilitate use as a text, exercises are included throughout the book, and web access is provided to a student version of the authors’ SLP-IOR software. Additionally, the authors have updated the Guide to Available Software, and they have included newer algorithms and modeling systems for SLP. The book is thus suitable as a text for advanced courses in stochastic optimization, and as a reference to the field. From Reviews of the First Edition: "The book presents a comprehensive study of stochastic linear optimization problems and their applications. … T...
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.
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.
Optimized remedial groundwater extraction using linear programming
International Nuclear Information System (INIS)
Quinn, J.J.
1995-01-01
Groundwater extraction systems are typically installed to remediate contaminant plumes or prevent further spread of contamination. These systems are expensive to install and maintain. A traditional approach to designing such a wellfield uses a series of trial-and-error simulations to test the effects of various well locations and pump rates. However, the optimal locations and pump rates of extraction wells are difficult to determine when objectives related to the site hydrogeology and potential pumping scheme are considered. This paper describes a case study of an application of linear programming theory to determine optimal well placement and pump rates. The objectives of the pumping scheme were to contain contaminant migration and reduce contaminant concentrations while minimizing the total amount of water pumped and treated. Past site activities at the area under study included disposal of contaminants in pits. Several groundwater plumes have been identified, and others may be present. The area of concern is bordered on three sides by a wetland, which receives a portion of its input budget as groundwater discharge from the pits. Optimization of the containment pumping scheme was intended to meet three goals: (1) prevent discharge of contaminated groundwater to the wetland, (2) minimize the total water pumped and treated (cost benefit), and (3) avoid dewatering of the wetland (cost and ecological benefits). Possible well locations were placed at known source areas. To constrain the problem, the optimization program was instructed to prevent any flow toward the wetland along a user-specified border. In this manner, the optimization routine selects well locations and pump rates so that a groundwater divide is produced along this boundary
An Approach for Solving Linear Fractional Programming Problems
Andrew Oyakhobo Odior
2012-01-01
Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebr...
A Fuzzy Linear Programming Approach for Aggregate Production Planning
DEFF Research Database (Denmark)
Iris, Cagatay; Cevikcan, Emre
2014-01-01
a mathematical programming framework for aggregate production planning problem under imprecise data environment. After providing background information about APP problem, together with fuzzy linear programming, the fuzzy linear programming model of APP is solved on an illustrative example for different a...
A New Finite Continuation Algorithm for Linear Programming
DEFF Research Database (Denmark)
Madsen, Kaj; Nielsen, Hans Bruun; Pinar, Mustafa
1996-01-01
We describe a new finite continuation algorithm for linear programming. The dual of the linear programming problem with unit lower and upper bounds is formulated as an $\\ell_1$ minimization problem augmented with the addition of a linear term. This nondifferentiable problem is approximated...... by a smooth problem. It is shown that the minimizers of the smooth problem define a family of piecewise-linear paths as a function of a smoothing parameter. Based on this property, a finite algorithm that traces these paths to arrive at an optimal solution of the linear program is developed. The smooth...
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...
RSM 1.0 - A RESUPPLY SCHEDULER USING INTEGER OPTIMIZATION
Viterna, L. A.
1994-01-01
RSM, Resupply Scheduling Modeler, is a fully menu-driven program that uses integer programming techniques to determine an optimum schedule for replacing components on or before the end of a fixed replacement period. Although written to analyze the electrical power system on the Space Station Freedom, RSM is quite general and can be used to model the resupply of almost any system subject to user-defined resource constraints. RSM 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 computationally intensive, integer programming was required for accuracy when modeling systems with small quantities of components. Input values for component life cane be real numbers, RSM converts them to integers by dividing the lifetime by the period duration, then reducing the result to the next lowest integer. For each component, there is a set of constraints that insure that it is replaced before its lifetime expires. RSM includes user-defined constraints such as transportation mass and volume limits, as well as component life, available repair crew time and assembly sequences. A weighting factor allows the program to minimize factors such as cost. The program then performs an iterative analysis, which is displayed during the processing. A message gives the first period in which resources are being exceeded on each iteration. If the scheduling problem is unfeasible, the final message will also indicate the first period in which resources were exceeded. RSM is written in APL2 for IBM PC series computers and compatibles. A stand-alone executable version of RSM is provided; however, this is a "packed" version of RSM which can only utilize the memory within the 640K DOS limit. This executable requires at least 640K of memory and DOS 3.1 or higher. Source code for an APL2/PC workspace version is also provided. This version of RSM can make full use of any
International Nuclear Information System (INIS)
Piacentino, A.; Cardona, F.
2008-01-01
The optimization of synthesis, design and operation in trigeneration systems for building applications is a quite complex task, due to the high number of decision variables, the presence of irregular heat, cooling and electric load profiles and the variable electricity price. Consequently, computer-aided techniques are usually adopted to achieve the optimal solution, based either on iterative techniques, linear or non-linear programming or evolutionary search. Large efforts have been made in improving algorithm efficiency, which have resulted in an increasingly rapid convergence to the optimal solution and in reduced calculation time; robust algorithm have also been formulated, assuming stochastic behaviour for energy loads and prices. This paper is based on the assumption that margins for improvements in the optimization of trigeneration systems still exist, which require an in-depth understanding of plant's energetic behaviour. Robustness in the optimization of trigeneration systems has more to do with a 'correct and comprehensive' than with an 'efficient' modelling, being larger efforts required to energy specialists rather than to experts in efficient algorithms. With reference to a mixed integer linear programming model implemented in MatLab for a trigeneration system including a pressurized (medium temperature) heat storage, the relevant contribute of thermoeconomics and energo-environmental analysis in the phase of mathematical modelling and code testing are shown
An approach for solving linear fractional programming problems ...
African Journals Online (AJOL)
The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality ...
Directory of Open Access Journals (Sweden)
Tunjo Perić
2017-01-01
Full Text Available This paper presents and analyzes the applicability of three linearization techniques used for solving multi-objective linear fractional programming problems using the goal programming method. The three linearization techniques are: (1 Taylor’s polynomial linearization approximation, (2 the method of variable change, and (3 a modification of the method of variable change proposed in [20]. All three linearization techniques are presented and analyzed in two variants: (a using the optimal value of the objective functions as the decision makers’ aspirations, and (b the decision makers’ aspirations are given by the decision makers. As the criteria for the analysis we use the efficiency of the obtained solutions and the difficulties the analyst comes upon in preparing the linearization models. To analyze the applicability of the linearization techniques incorporated in the linear goal programming method we use an example of a financial structure optimization problem.
Hard equality constrained integer knapsacks
Aardal, K.I.; Lenstra, A.K.; Cook, W.J.; Schulz, A.S.
2002-01-01
We consider the following integer feasibility problem: "Given positive integer numbers a 0, a 1,..., a n, with gcd(a 1,..., a n) = 1 and a = (a 1,..., a n), does there exist a nonnegative integer vector x satisfying ax = a 0?" Some instances of this type have been found to be extremely hard to solve
A Sawmill Manager Adapts To Change With Linear Programming
George F. Dutrow; James E. Granskog
1973-01-01
Linear programming provides guidelines for increasing sawmill capacity and flexibility and for determining stumpagepurchasing strategy. The operator of a medium-sized sawmill implemented improvements suggested by linear programming analysis; results indicate a 45 percent increase in revenue and a 36 percent hike in volume processed.
Analytic central path, sensitivity analysis and parametric linear programming
A.G. Holder; J.F. Sturm; S. Zhang (Shuzhong)
1998-01-01
textabstractIn this paper we consider properties of the central path and the analytic center of the optimal face in the context of parametric linear programming. We first show that if the right-hand side vector of a standard linear program is perturbed, then the analytic center of the optimal face
Application of the simplex method of linear programming model to ...
African Journals Online (AJOL)
This work discussed how the simplex method of linear programming could be used to maximize the profit of any business firm using Saclux Paint Company as a case study. It equally elucidated the effect variation in the optimal result obtained from linear programming model, will have on any given firm. It was demonstrated ...
Comparison of open-source linear programming solvers.
Energy Technology Data Exchange (ETDEWEB)
Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.; Jones, Katherine A.; Martin, Nathaniel; Detry, Richard Joseph
2013-10-01
When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.
Integrating Linear Programming and Analytical Hierarchical ...
African Journals Online (AJOL)
Study area is about 28000 ha of Keleibar- Chai Watershed, located in eastern Azerbaijan, Iran. Socio-economic information collected through a two-stage survey of 19 villages, including 300 samples. Thematic maps also have summarized Ecological factors, including physical and economic data. A comprehensive Linear ...
Introductory Linear Regression Programs in Undergraduate Chemistry.
Gale, Robert J.
1982-01-01
Presented are simple programs in BASIC and FORTRAN to apply the method of least squares. They calculate gradients and intercepts and express errors as standard deviations. An introduction of undergraduate students to such programs in a chemistry class is reviewed, and issues instructors should be aware of are noted. (MP)
Bilevel programming problems theory, algorithms and applications to energy networks
Dempe, Stephan; Pérez-Valdés, Gerardo A; Kalashnykova, Nataliya; Kalashnikova, Nataliya
2015-01-01
This book describes recent theoretical findings relevant to bilevel programming in general, and in mixed-integer bilevel programming in particular. It describes recent applications in energy problems, such as the stochastic bilevel optimization approaches used in the natural gas industry. New algorithms for solving linear and mixed-integer bilevel programming problems are presented and explained.
International Nuclear Information System (INIS)
Oluleye, Gbemi; Smith, Robin
2016-01-01
Highlights: • MILP model developed for integration of waste heat recovery technologies in process sites. • Five thermodynamic cycles considered for exploitation of industrial waste heat. • Temperature and quantity of multiple waste heat sources considered. • Interactions with the site utility system considered. • Industrial case study presented to illustrate application of the proposed methodology. - Abstract: Thermodynamic cycles such as organic Rankine cycles, absorption chillers, absorption heat pumps, absorption heat transformers, and mechanical heat pumps are able to utilize wasted thermal energy in process sites for the generation of electrical power, chilling and heat at a higher temperature. In this work, a novel systematic framework is presented for optimal integration of these technologies in process sites. The framework is also used to assess the best design approach for integrating waste heat recovery technologies in process sites, i.e. stand-alone integration or a systems-oriented integration. The developed framework allows for: (1) selection of one or more waste heat sources (taking into account the temperatures and thermal energy content), (2) selection of one or more technology options and working fluids, (3) selection of end-uses of recovered energy, (4) exploitation of interactions with the existing site utility system and (5) the potential for heat recovery via heat exchange is also explored. The methodology is applied to an industrial case study. Results indicate a systems-oriented design approach reduces waste heat by 24%; fuel consumption by 54% and CO_2 emissions by 53% with a 2 year payback, and stand-alone design approach reduces waste heat by 12%; fuel consumption by 29% and CO_2 emissions by 20.5% with a 4 year payback. Therefore, benefits from waste heat utilization increase when interactions between the existing site utility system and the waste heat recovery technologies are explored simultaneously. The case study also shows that the novel methodology can select and design optimal solutions for waste heat exploitation which are technically, economically and environmentally feasible from a range of technology options, heat sources and end-uses of recovered energy.
Moreno-Camacho, Carlos A.; Montoya-Torres, Jairo R.; Vélez-Gallego, Mario C.
2018-06-01
Only a few studies in the available scientific literature address the problem of having a group of workers that do not share identical levels of productivity during the planning horizon. This study considers a workforce scheduling problem in which the actual processing time is a function of the scheduling sequence to represent the decline in workers' performance, evaluating two classical performance measures separately: makespan and maximum tardiness. Several mathematical models are compared with each other to highlight the advantages of each approach. The mathematical models are tested with randomly generated instances available from a public e-library.
International Nuclear Information System (INIS)
Canizes, Bruno; Soares, João; Faria, Pedro; Vale, Zita
2013-01-01
Highlights: • Ancillary services market management. • Ancillary services requirements forecast based on Artificial Neural Network. • Ancillary services clearing mechanisms without complex bids and with complex bids. - Abstract: Ancillary services represent a good business opportunity that must be considered by market players. This paper presents a new methodology for ancillary services market dispatch. The method considers the bids submitted to the market and includes a market clearing mechanism based on deterministic optimization. An Artificial Neural Network is used for day-ahead prediction of Regulation Down, regulation-up, Spin Reserve and Non-Spin Reserve requirements. Two test cases based on California Independent System Operator data concerning dispatch of Regulation Down, Regulation Up, Spin Reserve and Non-Spin Reserve services are included in this paper to illustrate the application of the proposed method: (1) dispatch considering simple bids; (2) dispatch considering complex bids
Lütke Entrup, M.; Günther, H.O.; Beek, van P.; Grunow, M.; Seiler, T.
2005-01-01
In the production of perishable products such as dairy, meat or bakery goods, the consideration of shelf life in production planning is of particular importance. Retail customers with relatively low inventory turns can benefit significantly from longer product shelf life as wastage and out-of-stock
Chen, Pei-Hua
2017-05-01
This rejoinder responds to the commentary by van der Linden and Li entiled "Comment on Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" on the article "Three-Element Item Selection Procedures for Multiple Forms Assembly: An Item Matching Approach" by Chen. Van der Linden and Li made a strong statement calling for the cessation of test assembly heuristics development, and instead encouraged embracing mixed integer programming (MIP). This article points out the nondeterministic polynomial (NP)-hard nature of MIP problems and how solutions found using heuristics could be useful in an MIP context. Although van der Linden and Li provided several practical examples of test assembly supporting their view, the examples ignore the cases in which a slight change of constraints or item pool data might mean it would not be possible to obtain solutions as quickly as before. The article illustrates the use of heuristic solutions to improve both the performance of MIP solvers and the quality of solutions. Additional responses to the commentary by van der Linden and Li are included.
Non-linear programming method in optimization of fast reactors
International Nuclear Information System (INIS)
Pavelesku, M.; Dumitresku, Kh.; Adam, S.
1975-01-01
Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)
Pop, P.C.; Still, Georg J.
1999-01-01
In linear programming it is known that an appropriate non-homogeneous Farkas Lemma leads to a short proof of the strong duality results for a pair of primal and dual programs. By using a corresponding generalized Farkas lemma we give a similar proof of the strong duality results for semidefinite
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
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
Duality in non-linear programming
Jeyalakshmi, K.
2018-04-01
In this paper we consider duality and converse duality for a programming problem involving convex objective and constraint functions with finite dimensional range. We do not assume any constraint qualification. The dual is presented by reducing the problem to a standard Lagrange multiplier problem.
Directory of Open Access Journals (Sweden)
Yi-hua Zhong
2013-01-01
Full Text Available Recently, various methods have been developed for solving linear programming problems with fuzzy number, such as simplex method and dual simplex method. But their computational complexities are exponential, which is not satisfactory for solving large-scale fuzzy linear programming problems, especially in the engineering field. A new method which can solve large-scale fuzzy number linear programming problems is presented in this paper, which is named a revised interior point method. Its idea is similar to that of interior point method used for solving linear programming problems in crisp environment before, but its feasible direction and step size are chosen by using trapezoidal fuzzy numbers, linear ranking function, fuzzy vector, and their operations, and its end condition is involved in linear ranking function. Their correctness and rationality are proved. Moreover, choice of the initial interior point and some factors influencing the results of this method are also discussed and analyzed. The result of algorithm analysis and example study that shows proper safety factor parameter, accuracy parameter, and initial interior point of this method may reduce iterations and they can be selected easily according to the actual needs. Finally, the method proposed in this paper is an alternative method for solving fuzzy number linear programming problems.
Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs
Zuidwijk, Rob
2005-01-01
textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an optimal solution are investigated, and the optimal solution is studied on a so-called critical range of the initial data, in which certain properties such as the optimal basis in linear programming are ...
General guidelines solution for linear programming with fuzzy coefficients
Directory of Open Access Journals (Sweden)
Sergio Gerardo de los Cobos Silva
2013-08-01
Full Text Available This work introduce to the Possibilistic Programming and the Fuzzy Programming as paradigms that allow to resolve problems of linear programming when the coefficients of the model or the restrictions on the same are presented as fuzzy numbers, rather than exact numbers (crisp. This work presents some examples based on [1].
Energy Technology Data Exchange (ETDEWEB)
Koa, A.S.; Chang, N.B. [University of Central Florida, Orlando, FL (United States). Dept. for Civil & Environmental Engineering
2008-07-15
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{sub 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 case 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.
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.
Nazri, Engku Muhammad; Yusof, Nur Ai'Syah; Ahmad, Norazura; Shariffuddin, Mohd Dino Khairri; Khan, Shazida Jan Mohd
2017-11-01
Prioritizing and making decisions on what student activities to be selected and conducted to fulfill the aspiration of a university as translated in its strategic plan must be executed with transparency and accountability. It is becoming even more crucial, particularly for universities in Malaysia with the recent budget cut imposed by the Malaysian government. In this paper, we illustrated how 0-1 integer programming (0-1 IP) model was implemented to select which activities among the forty activities proposed by the student body of Universiti Utara Malaysia (UUM) to be implemented for the 2017/2018 academic year. Two different models were constructed. The first model was developed to determine the minimum total budget that should be given to the student body by the UUM management to conduct all the activities that can fulfill the minimum targeted number of activities as stated in its strategic plan. On the other hand, the second model was developed to determine which activities to be selected based on the total budget already allocated beforehand by the UUM management towards fulfilling the requirements as set in its strategic plan. The selection of activities for the second model, was also based on the preference of the members of the student body whereby the preference value for each activity was determined using Compromised-Analytical Hierarchy Process. The outputs from both models were compared and discussed. The technique used in this study will be useful and suitable to be implemented by organizations with key performance indicator-oriented programs and having limited budget allocation issues.
Large-scale linear programs in planning and prediction.
2017-06-01
Large-scale linear programs are at the core of many traffic-related optimization problems in both planning and prediction. Moreover, many of these involve significant uncertainty, and hence are modeled using either chance constraints, or robust optim...
Evaluating forest management policies by parametric linear programing
Daniel I. Navon; Richard J. McConnen
1967-01-01
An analytical and simulation technique, parametric linear programing explores alternative conditions and devises an optimal management plan for each condition. Its application in solving policy-decision problems in the management of forest lands is illustrated in an example.
Formulated linear programming problems from game theory and its ...
African Journals Online (AJOL)
Formulated linear programming problems from game theory and its computer implementation using Tora package. ... Game theory, a branch of operations research examines the various concepts of decision ... AJOL African Journals Online.
Near-Regular Structure Discovery Using Linear Programming
Huang, Qixing; Guibas, Leonidas J.; Mitra, Niloy J.
2014-01-01
as an optimization and efficiently solve it using linear programming techniques. Our optimization has a discrete aspect, that is, the connectivity relationships among the elements, as well as a continuous aspect, namely the locations of the elements of interest. Both
Linear Programming and Its Application to Pattern Recognition Problems
Omalley, M. J.
1973-01-01
Linear programming and linear programming like techniques as applied to pattern recognition problems are discussed. Three relatively recent research articles on such applications are summarized. The main results of each paper are described, indicating the theoretical tools needed to obtain them. A synopsis of the author's comments is presented with regard to the applicability or non-applicability of his methods to particular problems, including computational results wherever given.
EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.
Jarvis, John J.; And Others
Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…
The RANDOM computer program: A linear congruential random number generator
Miles, R. F., Jr.
1986-01-01
The RANDOM Computer Program is a FORTRAN program for generating random number sequences and testing linear congruential random number generators (LCGs). The linear congruential form of random number generator is discussed, and the selection of parameters of an LCG for a microcomputer described. This document describes the following: (1) The RANDOM Computer Program; (2) RANDOM.MOD, the computer code needed to implement an LCG in a FORTRAN program; and (3) The RANCYCLE and the ARITH Computer Programs that provide computational assistance in the selection of parameters for an LCG. The RANDOM, RANCYCLE, and ARITH Computer Programs are written in Microsoft FORTRAN for the IBM PC microcomputer and its compatibles. With only minor modifications, the RANDOM Computer Program and its LCG can be run on most micromputers or mainframe computers.
Wei, Peng; Sridhar, Banavar; Chen, Neil Yi-Nan; Sun, Dengfent
2012-01-01
A class of strategies has been proposed to reduce contrail formation in the United States airspace. A 3D grid based on weather data and the cruising altitude level of aircraft is adjusted to avoid the persistent contrail potential area with the consideration to fuel-efficiency. In this paper, the authors introduce a contrail avoidance strategy on 3D grid by considering additional operationally feasible constraints from an air traffic controller's aspect. First, shifting too many aircraft to the same cruising level will make the miles-in-trail at this level smaller than the safety separation threshold. Furthermore, the high density of aircraft at one cruising level may exceed the workload for the traffic controller. Therefore, in our new model we restrict the number of total aircraft at each level. Second, the aircraft count variation for successive intervals cannot be too drastic since the workload to manage climbing/descending aircraft is much larger than managing cruising aircraft. The contrail reduction is formulated as an integer-programming problem and the problem is shown to have the property of total unimodularity. Solving the corresponding relaxed linear programming with the simplex method provides an optimal and integral solution to the problem. Simulation results are provided to illustrate the methodology.
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α-uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α=2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c=e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c=1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α≥3, minimum vertex covers on α-uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c=e/(α-1) where the replica symmetry is broken.
Takabe, Satoshi; Hukushima, Koji
2016-05-01
Typical behavior of the linear programming (LP) problem is studied as a relaxation of the minimum vertex cover (min-VC), a type of integer programming (IP) problem. A lattice-gas model on the Erdös-Rényi random graphs of α -uniform hyperedges is proposed to express both the LP and IP problems of the min-VC in the common statistical mechanical model with a one-parameter family. Statistical mechanical analyses reveal for α =2 that the LP optimal solution is typically equal to that given by the IP below the critical average degree c =e in the thermodynamic limit. The critical threshold for good accuracy of the relaxation extends the mathematical result c =1 and coincides with the replica symmetry-breaking threshold of the IP. The LP relaxation for the minimum hitting sets with α ≥3 , minimum vertex covers on α -uniform random graphs, is also studied. Analytic and numerical results strongly suggest that the LP relaxation fails to estimate optimal values above the critical average degree c =e /(α -1 ) where the replica symmetry is broken.
Planning Student Flow with Linear Programming: A Tunisian Case Study.
Bezeau, Lawrence
A student flow model in linear programming format, designed to plan the movement of students into secondary and university programs in Tunisia, is described. The purpose of the plan is to determine a sufficient number of graduating students that would flow back into the system as teachers or move into the labor market to meet fixed manpower…
Linear Programming for Vocational Education Planning. Interim Report.
Young, Robert C.; And Others
The purpose of the paper is to define for potential users of vocational education management information systems a quantitative analysis technique and its utilization to facilitate more effective planning of vocational education programs. Defining linear programming (LP) as a management technique used to solve complex resource allocation problems…
Garbageless reversible implementation of integer linear transformations
DEFF Research Database (Denmark)
Burignat, Stéphane; Vermeirsch, Kenneth; De Vos, Alexis
2013-01-01
inputs. The resulting reversible circuit is able to perform both the forward transform and the inverse transform. Which of the two computations that actually is performed, simply depends on the orientation of the circuit when it is inserted in a computer board (if one takes care to provide...
Using linear programming to analyze and optimize stochastic flow lines
DEFF Research Database (Denmark)
Helber, Stefan; Schimmelpfeng, Katja; Stolletz, Raik
2011-01-01
This paper presents a linear programming approach to analyze and optimize flow lines with limited buffer capacities and stochastic processing times. The basic idea is to solve a huge but simple linear program that models an entire simulation run of a multi-stage production process in discrete time...... programming and hence allows us to solve buffer allocation problems. We show under which conditions our method works well by comparing its results to exact values for two-machine models and approximate simulation results for longer lines....
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
Computer Corner: Spreadsheets, Power Series, Generating Functions, and Integers.
Snow, Donald R.
1989-01-01
Implements a table algorithm on a spreadsheet program and obtains functions for several number sequences such as the Fibonacci and Catalan numbers. Considers other applications of the table algorithm to integers represented in various number bases. (YP)
Linear program differentiation for single-channel speech separation
DEFF Research Database (Denmark)
Pearlmutter, Barak A.; Olsson, Rasmus Kongsgaard
2006-01-01
Many apparently difficult problems can be solved by reduction to linear programming. Such problems are often subproblems within larger systems. When gradient optimisation of the entire larger system is desired, it is necessary to propagate gradients through the internally-invoked LP solver....... For instance, when an intermediate quantity z is the solution to a linear program involving constraint matrix A, a vector of sensitivities dE/dz will induce sensitivities dE/dA. Here we show how these can be efficiently calculated, when they exist. This allows algorithmic differentiation to be applied...... to algorithms that invoke linear programming solvers as subroutines, as is common when using sparse representations in signal processing. Here we apply it to gradient optimisation of over complete dictionaries for maximally sparse representations of a speech corpus. The dictionaries are employed in a single...
International Nuclear Information System (INIS)
Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen
2012-01-01
Highlights: ► Inexact piecewise-linearization-based fuzzy flexible programming is proposed. ► It’s the first application to waste management under multiple complexities. ► It tackles nonlinear economies-of-scale effects in interval-parameter constraints. ► It estimates costs more accurately than the linear-regression-based model. ► Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP’s advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP’s solutions demonstrate
Linear Parametric Sensitivity Analysis of the Constraint Coefficient Matrix in Linear Programs
R.A. Zuidwijk (Rob)
2005-01-01
textabstractSensitivity analysis is used to quantify the impact of changes in the initial data of linear programs on the optimal value. In particular, parametric sensitivity analysis involves a perturbation analysis in which the effects of small changes of some or all of the initial data on an
Synthesizing Dynamic Programming Algorithms from Linear Temporal Logic Formulae
Rosu, Grigore; Havelund, Klaus
2001-01-01
The problem of testing a linear temporal logic (LTL) formula on a finite execution trace of events, generated by an executing program, occurs naturally in runtime analysis of software. We present an algorithm which takes an LTL formula and generates an efficient dynamic programming algorithm. The generated algorithm tests whether the LTL formula is satisfied by a finite trace of events given as input. The generated algorithm runs in linear time, its constant depending on the size of the LTL formula. The memory needed is constant, also depending on the size of the formula.
International Nuclear Information System (INIS)
Shaban Boloukat, Mohammad Hadi; Akbari Foroud, Asghar
2016-01-01
This paper represents a stochastic approach for long-term optimal resource expansion planning of a grid-connected microgrid (MG) containing different technologies as intermittent renewable energy resources, energy storage systems and thermal resources. Maximizing profit and reliability, along with minimizing investment and operation costs, are major objectives which have been considered in this model. Also, the impacts of intermittency and uncertainty in renewable energy resources were investigated. The interval linear programming (ILP) was applied for modelling inherent stochastic nature of the renewable energy resources. ILP presents some superiority in modelling of uncertainties in MG planning. The problem was formulated as a mixed-integer linear programming. It has been demonstrated previously that the benders decomposition (BD) served as an effective tool for solving such problems. BD divides the original problem into a master (investment) problem and operation and reliability subproblems. In this paper a multiperiod MG planning is presented, considering life time, maximum penetration limit of each technology, interest rate, capital recovery factor and investment fund. Real-time energy exchange with the utility is covered, with a consideration of variable tariffs at different load blocks. The presented approach can help MG planners to adopt best decision under various uncertainty levels based on their budgetary policies. - Highlights: • Considering uncertain nature of the renewable resources with applying ILP. • Considering the effect of intermittency of renewable in MG planning. • Multiobjective MG planning problem which covers cost, profit and reliability. • Multiperiod approach for MG planning considering life time and MPL of technologies. • Presenting real-time energy exchange with the utility considering variable tariffs.
An Instructional Note on Linear Programming--A Pedagogically Sound Approach.
Mitchell, Richard
1998-01-01
Discusses the place of linear programming in college curricula and the advantages of using linear-programming software. Lists important characteristics of computer software used in linear programming for more effective teaching and learning. (ASK)
Applied Research of Enterprise Cost Control Based on Linear Programming
Directory of Open Access Journals (Sweden)
Yu Shuo
2015-01-01
This paper researches the enterprise cost control through the linear programming model, and analyzes the restriction factors of the labor of enterprise production, raw materials, processing equipment, sales price, and other factors affecting the enterprise income, so as to obtain an enterprise cost control model based on the linear programming. This model can calculate rational production mode in the case of limited resources, and acquire optimal enterprise income. The production guiding program and scheduling arrangement of the enterprise can be obtained through calculation results, so as to provide scientific and effective guidance for the enterprise production. This paper adds the sensitivity analysis in the linear programming model, so as to learn about the stability of the enterprise cost control model based on linear programming through the sensitivity analysis, and verify the rationality of the model, and indicate the direction for the enterprise cost control. The calculation results of the model can provide a certain reference for the enterprise planning in the market economy environment, which have strong reference and practical significance in terms of the enterprise cost control.
International Nuclear Information System (INIS)
Oh, S.-D.; Kwak, H.-Y.
2005-01-01
An optimal planning for gas turbine cogeneration system has been studied. The planning problem considered in this study is to determine the optimal configuration of the system equipments and optimal operational policy of the system when the annual energy demands of electric power, heat and cooling are given a priori. The main benefit of the optimal planning is to minimize operational costs and to save energy by efficient energy utilization. A mixed-integer linear programming and the branch and bound algorithm have been adopted to obtain the optimal solution. Both the optimal configuration of the system equipments and the optimal operation policy has been obtained based on annual cost method. The planning method employed here may be applied to the planning problem of the cogeneration plant to any specific building or hotel. (author)
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.
Non-linear nuclear engineering models as genetic programming application
International Nuclear Information System (INIS)
Domingos, Roberto P.; Schirru, Roberto; Martinez, Aquilino S.
1997-01-01
This work presents a Genetic Programming paradigm and a nuclear application. A field of Artificial Intelligence, based on the concepts of Species Evolution and Natural Selection, can be understood as a self-programming process where the computer is the main agent responsible for the discovery of a program able to solve a given problem. In the present case, the problem was to find a mathematical expression in symbolic form, able to express the existent relation between equivalent ratio of a fuel cell, the enrichment of fuel elements and the multiplication factor. Such expression would avoid repeatedly reactor physics codes execution for core optimization. The results were compared with those obtained by different techniques such as Neural Networks and Linear Multiple Regression. Genetic Programming has shown to present a performance as good as, and under some features superior to Neural Network and Linear Multiple Regression. (author). 10 refs., 8 figs., 1 tabs
Optimal traffic control in highway transportation networks using linear programming
Li, Yanning; Canepa, Edward S.; Claudel, Christian G.
2014-01-01
of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can
LCPT: a program for finding linear canonical transformations
International Nuclear Information System (INIS)
Char, B.W.; McNamara, B.
1979-01-01
This article describes a MACSYMA program to compute symbolically a canonical linear transformation between coordinate systems. The difficulties in implementation of this canonical small physics problem are also discussed, along with the implications that may be drawn from such difficulties about widespread MACSYMA usage by the community of computational/theoretical physicists
Fitting program for linear regressions according to Mahon (1996)
Energy Technology Data Exchange (ETDEWEB)
2018-01-09
This program takes the users' Input data and fits a linear regression to it using the prescription presented by Mahon (1996). Compared to the commonly used York fit, this method has the correct prescription for measurement error propagation. This software should facilitate the proper fitting of measurements with a simple Interface.
Linear Programming, the Simplex Algorithm and Simple Polytopes
Directory of Open Access Journals (Sweden)
Das Bhusan
2010-09-01
Full Text Available In the first part of the paper we survey some far reaching applications of the basis facts of linear programming to the combinatorial theory of simple polytopes. In the second part we discuss some recent developments concurring the simplex algorithm. We describe sub-exponential randomized pivot roles and upper bounds on the diameter of graphs of polytopes.
Interior-Point Methods for Linear Programming: A Review
Singh, J. N.; Singh, D.
2002-01-01
The paper reviews some recent advances in interior-point methods for linear programming and indicates directions in which future progress can be made. Most of the interior-point methods belong to any of three categories: affine-scaling methods, potential reduction methods and central path methods. These methods are discussed together with…
A Partitioning and Bounded Variable Algorithm for Linear Programming
Sheskin, Theodore J.
2006-01-01
An interesting new partitioning and bounded variable algorithm (PBVA) is proposed for solving linear programming problems. The PBVA is a variant of the simplex algorithm which uses a modified form of the simplex method followed by the dual simplex method for bounded variables. In contrast to the two-phase method and the big M method, the PBVA does…
A Spreadsheet-Based, Matrix Formulation Linear Programming Lesson
DEFF Research Database (Denmark)
Harrod, Steven
2009-01-01
The article focuses on the spreadsheet-based, matrix formulation linear programming lesson. According to the article, it makes a higher level of theoretical mathematics approachable by a wide spectrum of students wherein many may not be decision sciences or quantitative methods majors. Moreover...
175 Years of Linear Programming - Minimax and Cake Topography
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 4; Issue 7. 175 Years of Linear Programming - Minimax and Cake Topography. Vijay Chandru M R Rao. Series Article Volume 4 Issue 7 July 1999 pp 4-13. Fulltext. Click here to view fulltext PDF. Permanent link:
Analysis of Students' Errors on Linear Programming at Secondary ...
African Journals Online (AJOL)
The purpose of this study was to identify secondary school students' errors on linear programming at 'O' level. It is based on the fact that students' errors inform teaching hence an essential tool for any serious mathematics teacher who intends to improve mathematics teaching. The study was guided by a descriptive survey ...
Linear decomposition approach for a class of nonconvex programming problems.
Shen, Peiping; Wang, Chunfeng
2017-01-01
This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.
International Nuclear Information System (INIS)
Frahm, K M; Shepelyansky, D L; Chepelianskii, A D
2012-01-01
We 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 approximately 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 us to find this vector for matrices of billion size. This network provides a new PageRank order of integers. (paper)
Train Repathing in Emergencies Based on Fuzzy Linear Programming
Directory of Open Access Journals (Sweden)
Xuelei Meng
2014-01-01
Full Text Available Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.
Train repathing in emergencies based on fuzzy linear programming.
Meng, Xuelei; Cui, Bingmou
2014-01-01
Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.
Relaxation Methods for Strictly Convex Regularizations of Piecewise Linear Programs
International Nuclear Information System (INIS)
Kiwiel, K. C.
1998-01-01
We give an algorithm for minimizing the sum of a strictly convex function and a convex piecewise linear function. It extends several dual coordinate ascent methods for large-scale linearly constrained problems that occur in entropy maximization, quadratic programming, and network flows. In particular, it may solve exact penalty versions of such (possibly inconsistent) problems, and subproblems of bundle methods for nondifferentiable optimization. It is simple, can exploit sparsity, and in certain cases is highly parallelizable. Its global convergence is established in the recent framework of B -functions (generalized Bregman functions)
A LINEAR PROGRAMMING ALGORITHM FOR LEAST-COST SCHEDULING
Directory of Open Access Journals (Sweden)
AYMAN H AL-MOMANI
1999-12-01
Full Text Available In this research, some concepts of linear programming and critical path method are reviewed to describe recent modeling structures that have been of great value in analyzing extended planning horizon project time-cost trade-offs problems. A simplified representation of a small project and a linear programming model is formulated to represent this system. Procedures to solve these various problems formulations were cited and the final solution is obtained using LINDO program. The model developed represents many restrictions and management considerations of the project. It could be used by construction managers in a planning stage to explore numerous possible opportunities to the contractor and predict the effect of a decision on the construction to facilitate a preferred operating policy given different management objectives. An implementation using this method is shown to outperform several other techniques and a large class of test problems. Linear programming show that the algorithm is very promising in practice on a wide variety of time-cost trade-offs problems. This method is simple, applicable to a large network, and generates a shorter computational time at low cost, along with an increase in robustness.
A goal programming procedure for solving fuzzy multiobjective fractional linear programming problems
Directory of Open Access Journals (Sweden)
Tunjo Perić
2014-12-01
Full Text Available This paper presents a modification of Pal, Moitra and Maulik's goal programming procedure for fuzzy multiobjective linear fractional programming problem solving. The proposed modification of the method allows simpler solving of economic multiple objective fractional linear programming (MOFLP problems, enabling the obtained solutions to express the preferences of the decision maker defined by the objective function weights. The proposed method is tested on the production planning example.
No-signaling quantum key distribution: solution by linear programming
Hwang, Won-Young; Bae, Joonwoo; Killoran, Nathan
2015-02-01
We outline a straightforward approach for obtaining a secret key rate using only no-signaling constraints and linear programming. Assuming an individual attack, we consider all possible joint probabilities. Initially, we study only the case where Eve has binary outcomes, and we impose constraints due to the no-signaling principle and given measurement outcomes. Within the remaining space of joint probabilities, by using linear programming, we get bound on the probability of Eve correctly guessing Bob's bit. We then make use of an inequality that relates this guessing probability to the mutual information between Bob and a more general Eve, who is not binary-restricted. Putting our computed bound together with the Csiszár-Körner formula, we obtain a positive key generation rate. The optimal value of this rate agrees with known results, but was calculated in a more straightforward way, offering the potential of generalization to different scenarios.
Planning under uncertainty solving large-scale stochastic linear programs
Energy Technology Data Exchange (ETDEWEB)
Infanger, G. [Stanford Univ., CA (United States). Dept. of Operations Research]|[Technische Univ., Vienna (Austria). Inst. fuer Energiewirtschaft
1992-12-01
For many practical problems, solutions obtained from deterministic models are unsatisfactory because they fail to hedge against certain contingencies that may occur in the future. Stochastic models address this shortcoming, but up to recently seemed to be intractable due to their size. Recent advances both in solution algorithms and in computer technology now allow us to solve important and general classes of practical stochastic problems. We show how large-scale stochastic linear programs can be efficiently solved by combining classical decomposition and Monte Carlo (importance) sampling techniques. We discuss the methodology for solving two-stage stochastic linear programs with recourse, present numerical results of large problems with numerous stochastic parameters, show how to efficiently implement the methodology on a parallel multi-computer and derive the theory for solving a general class of multi-stage problems with dependency of the stochastic parameters within a stage and between different stages.
Optimal selection for shielding materials by fuzzy linear programming
International Nuclear Information System (INIS)
Kanai, Y.; Miura, N.; Sugasawa, S.
1996-01-01
An application of fuzzy linear programming methods to optimization of a radiation shield is presented. The main purpose of the present study is the choice of materials and the search of the ratio of mixture-component as the first stage of the methodology on optimum shielding design according to individual requirements of nuclear reactor, reprocessing facility, shipping cask installing spent fuel, ect. The characteristic values for the shield optimization may be considered their cost, spatial space, weight and some shielding qualities such as activation rate and total dose rate for neutron and gamma ray (includes secondary gamma ray). This new approach can reduce huge combination calculations for conventional two-valued logic approaches to representative single shielding calculation by group-wised optimization parameters determined in advance. Using the fuzzy linear programming method, possibilities for reducing radiation effects attainable in optimal compositions hydrated, lead- and boron-contained materials are investigated
Algorithmic Trading with Developmental and Linear Genetic Programming
Wilson, Garnett; Banzhaf, Wolfgang
A developmental co-evolutionary genetic programming approach (PAM DGP) and a standard linear genetic programming (LGP) stock trading systemare applied to a number of stocks across market sectors. Both GP techniques were found to be robust to market fluctuations and reactive to opportunities associated with stock price rise and fall, with PAMDGP generating notably greater profit in some stock trend scenarios. Both algorithms were very accurate at buying to achieve profit and selling to protect assets, while exhibiting bothmoderate trading activity and the ability to maximize or minimize investment as appropriate. The content of the trading rules produced by both algorithms are also examined in relation to stock price trend scenarios.
Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution
Energy Technology Data Exchange (ETDEWEB)
Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)
2014-06-19
This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.
MAGDM linear-programming models with distinct uncertain preference structures.
Xu, Zeshui S; Chen, Jian
2008-10-01
Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.
An algorithm for the solution of dynamic linear programs
Psiaki, Mark L.
1989-01-01
The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation
Matzke, Orville R.
The purpose of this study was to formulate a linear programming model to simulate a foundation type support program and to apply this model to a state support program for the public elementary and secondary school districts in the State of Iowa. The model was successful in producing optimal solutions to five objective functions proposed for…
Spreading Sequences Generated Using Asymmetrical Integer-Number Maps
Directory of Open Access Journals (Sweden)
V. Sebesta
2007-09-01
Full Text Available Chaotic sequences produced by piecewise linear maps can be transformed to binary sequences. The binary sequences are optimal for the asynchronous DS/CDMA systems in case of certain shapes of the maps. This paper is devoted to the one-to-one integer-number maps derived from the suitable asymmetrical piecewise linear maps. Such maps give periodic integer-number sequences, which can be transformed to the binary sequences. The binary sequences produced via proposed modified integer-number maps are perfectly balanced and embody good autocorrelation and crosscorrelation properties. The number of different binary sequences is sizable. The sequences are suitable as spreading sequences in DS/CDMA systems.
Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen
2018-01-01
With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP
Liang, Bin; Li, Yongbao; Wei, Ran; Guo, Bin; Xu, Xuang; Liu, Bo; Li, Jiafeng; Wu, Qiuwen; Zhou, Fugen
2018-01-05
With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l 1 norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP
Landman, Bruce M
2003-01-01
Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students something quite rare for a book at this level: a glimpse into the world of mathematical research and the opportunity to begin pondering unsolved problems themselves. In addition to being the first truly accessible book on Ramsey theory, this innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subarea of Ramsey theory. The result is a breakthrough book that will engage students, teachers, and researchers alike.
A Primal-Dual Interior Point-Linear Programming Algorithm for MPC
DEFF Research Database (Denmark)
Edlund, Kristian; Sokoler, Leo Emil; Jørgensen, John Bagterp
2009-01-01
Constrained optimal control problems for linear systems with linear constraints and an objective function consisting of linear and l1-norm terms can be expressed as linear programs. We develop an efficient primal-dual interior point algorithm for solution of such linear programs. The algorithm...
Ji, Zhiwei; Wang, Bing; Yan, Ke; Dong, Ligang; Meng, Guanmin; Shi, Lei
2017-12-21
In recent years, the integration of 'omics' technologies, high performance computation, and mathematical modeling of biological processes marks that the systems biology has started to fundamentally impact the way of approaching drug discovery. The LINCS public data warehouse provides detailed information about cell responses with various genetic and environmental stressors. It can be greatly helpful in developing new drugs and therapeutics, as well as improving the situations of lacking effective drugs, drug resistance and relapse in cancer therapies, etc. In this study, we developed a Ternary status based Integer Linear Programming (TILP) method to infer cell-specific signaling pathway network and predict compounds' treatment efficacy. The novelty of our study is that phosphor-proteomic data and prior knowledge are combined for modeling and optimizing the signaling network. To test the power of our approach, a generic pathway network was constructed for a human breast cancer cell line MCF7; and the TILP model was used to infer MCF7-specific pathways with a set of phosphor-proteomic data collected from ten representative small molecule chemical compounds (most of them were studied in breast cancer treatment). Cross-validation indicated that the MCF7-specific pathway network inferred by TILP were reliable predicting a compound's efficacy. Finally, we applied TILP to re-optimize the inferred cell-specific pathways and predict the outcomes of five small compounds (carmustine, doxorubicin, GW-8510, daunorubicin, and verapamil), which were rarely used in clinic for breast cancer. In the simulation, the proposed approach facilitates us to identify a compound's treatment efficacy qualitatively and quantitatively, and the cross validation analysis indicated good accuracy in predicting effects of five compounds. In summary, the TILP model is useful for discovering new drugs for clinic use, and also elucidating the potential mechanisms of a compound to targets.
Integer-valued trawl processes
DEFF Research Database (Denmark)
Barndorff-Nielsen, Ole E.; Lunde, Asger; Shephard, Neil
2014-01-01
the probabilistic properties of such processes in detail and, in addition, study volatility modulation and multivariate extensions within the new modelling framework. Moreover, we describe how the parameters of a trawl process can be estimated and obtain promising estimation results in our simulation study. Finally......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...
Optimal traffic control in highway transportation networks using linear programming
Li, Yanning
2014-06-01
This article presents a framework for the optimal control of boundary flows on transportation networks. The state of the system is modeled by a first order scalar conservation law (Lighthill-Whitham-Richards PDE). Based on an equivalent formulation of the Hamilton-Jacobi PDE, the problem of controlling the state of the system on a network link in a finite horizon can be posed as a Linear Program. Assuming all intersections in the network are controllable, we show that the optimization approach can be extended to an arbitrary transportation network, preserving linear constraints. Unlike previously investigated transportation network control schemes, this framework leverages the intrinsic properties of the Halmilton-Jacobi equation, and does not require any discretization or boolean variables on the link. Hence this framework is very computational efficient and provides the globally optimal solution. The feasibility of this framework is illustrated by an on-ramp metering control example.
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
A recurrent neural network for solving bilevel linear programming problem.
He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie; Huang, Junjian
2014-04-01
In this brief, based on the method of penalty functions, a recurrent neural network (NN) modeled by means of a differential inclusion is proposed for solving the bilevel linear programming problem (BLPP). Compared with the existing NNs for BLPP, the model has the least number of state variables and simple structure. Using nonsmooth analysis, the theory of differential inclusions, and Lyapunov-like method, the equilibrium point sequence of the proposed NNs can approximately converge to an optimal solution of BLPP under certain conditions. Finally, the numerical simulations of a supply chain distribution model have shown excellent performance of the proposed recurrent NNs.
A scalable parallel algorithm for multiple objective linear programs
Wiecek, Malgorzata M.; Zhang, Hong
1994-01-01
This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.
The MARX Modulator Development Program for the International Linear Collider
International Nuclear Information System (INIS)
Leyh, G.E.
2006-01-01
The International Linear Collider (ILC) Marx Modulator Development Program at SLAC is working towards developing a full-scale ILC Marx ''Reference Design'' modulator prototype, with the goal of significantly reducing the size and cost of the ILC modulator while improving overall modulator efficiency and availability. The ILC Reference Design prototype will provide a proof-of-concept model to industry in advance of Phase II SBIR funding, and also allow operation of the new 10MW L-Band Klystron prototypes immediately upon their arrival at SLAC
Marginal cost of electricity conservation: an application of linear program
International Nuclear Information System (INIS)
Silveira, A.M. da; Hollanda, J.B. de
1987-01-01
This paper is addressed ti the planning of electricity industry when the use of energetically efficient appliances (conservation) is financed by the utilities. It is based on the Linear Programming Model proposed by Masse and Boiteaux for planning of conventional energy sources, where one unity of electricity (Kw/Kw h) saved is treated as if it were a generator of equivalent size. In spite of the formal simplicity of the models it can support interesting concessions on the subject of a electrical energy conservation policy. (author)
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.
Polymorphic Uncertain Linear Programming for Generalized Production Planning Problems
Directory of Open Access Journals (Sweden)
Xinbo Zhang
2014-01-01
Full Text Available A polymorphic uncertain linear programming (PULP model is constructed to formulate a class of generalized production planning problems. In accordance with the practical environment, some factors such as the consumption of raw material, the limitation of resource and the demand of product are incorporated into the model as parameters of interval and fuzzy subsets, respectively. Based on the theory of fuzzy interval program and the modified possibility degree for the order of interval numbers, a deterministic equivalent formulation for this model is derived such that a robust solution for the uncertain optimization problem is obtained. Case study indicates that the constructed model and the proposed solution are useful to search for an optimal production plan for the polymorphic uncertain generalized production planning problems.
van den Akker, R.
2007-01-01
This thesis adresses statistical problems in econometrics. The first part contributes statistical methodology for nonnegative integer-valued time series. The second part of this thesis discusses semiparametric estimation in copula models and develops semiparametric lower bounds for a large class of
Rewrite systems for integer arithmetic
H.R. Walters (Pum); H. Zantema (Hans)
1995-01-01
textabstractWe present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground confluent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by
Rewrite systems for integer arithmetic
Walters, H.R.; Zantema, H.
1994-01-01
We present three term rewrite systems for integer arithmetic with addition, multiplication, and, in two cases, subtraction. All systems are ground con uent and terminating; termination is proved by semantic labelling and recursive path order. The first system represents numbers by successor and
A few Smarandache Integer Sequences
Ibstedt, Henry
2010-01-01
This paper deals with the analysis of a few Smarandache Integer Sequences which first appeared in Properties or the Numbers, F. Smarandache, University or Craiova Archives, 1975. The first four sequences are recurrence generated sequences while the last three are concatenation sequences.
AN APPLICATION FOR EFFICIENT TELECOMMUNICATION NETWORKS PROVISIONING USING LINEAR PROGRAMMING
Directory of Open Access Journals (Sweden)
Maria Augusta Soares Machado
2015-03-01
Full Text Available This paper presents a practical proposition for the application of the Linear Programming quantitative method in order to assist planning and control of customer circuit delivery activities in telecommunications companies working with the corporative market. Based upon data provided for by a telecom company operating in Brazil, the Linear Programming method was employed for one of the classical problems of determining the optimum mix of production quantities for a set of five products of that company: Private Telephone Network, Internet Network, Intranet Network, Low Speed Data Network, and High Speed Data Network, in face of several limitations of the productive resources, seeking to maximize the company’s monthly revenue. By fitting the production data available into a primary model, observation was made as to what number of monthly activations for each product would be mostly optimized in order to achieve maximum revenues in the company. The final delivery of a complete network was not observed but the delivery of the circuits that make it up, and this was a limiting factor for the study herein, which, however, brings an innovative proposition for the planning of private telecommunications network provisioning.
Assembling networks of microbial genomes using linear programming.
Holloway, Catherine; Beiko, Robert G
2010-11-20
Microbial genomes exhibit complex sets of genetic affinities due to lateral genetic transfer. Assessing the relative contributions of parent-to-offspring inheritance and gene sharing is a vital step in understanding the evolutionary origins and modern-day function of an organism, but recovering and showing these relationships is a challenging problem. We have developed a new approach that uses linear programming to find between-genome relationships, by treating tables of genetic affinities (here, represented by transformed BLAST e-values) as an optimization problem. Validation trials on simulated data demonstrate the effectiveness of the approach in recovering and representing vertical and lateral relationships among genomes. Application of the technique to a set comprising Aquifex aeolicus and 75 other thermophiles showed an important role for large genomes as 'hubs' in the gene sharing network, and suggested that genes are preferentially shared between organisms with similar optimal growth temperatures. We were also able to discover distinct and common genetic contributors to each sequenced representative of genus Pseudomonas. The linear programming approach we have developed can serve as an effective inference tool in its own right, and can be an efficient first step in a more-intensive phylogenomic analysis.
Linear programming based on neural networks for radiotherapy treatment planning
International Nuclear Information System (INIS)
Xingen Wu; Limin Luo
2000-01-01
In this paper, we propose a neural network model for linear programming that is designed to optimize radiotherapy treatment planning (RTP). This kind of neural network can be easily implemented by using a kind of 'neural' electronic system in order to obtain an optimization solution in real time. We first give an introduction to the RTP problem and construct a non-constraint objective function for the neural network model. We adopt a gradient algorithm to minimize the objective function and design the structure of the neural network for RTP. Compared to traditional linear programming methods, this neural network model can reduce the time needed for convergence, the size of problems (i.e., the number of variables to be searched) and the number of extra slack and surplus variables needed. We obtained a set of optimized beam weights that result in a better dose distribution as compared to that obtained using the simplex algorithm under the same initial condition. The example presented in this paper shows that this model is feasible in three-dimensional RTP. (author)
A Study of Joint Cost Inclusion in Linear Programming Optimization
Directory of Open Access Journals (Sweden)
P. Armaos
2013-08-01
Full Text Available The concept of Structural Optimization has been a topic or research over the past century. Linear Programming Optimization has proved being the most reliable method of structural optimization. Global advances in linear programming optimization have been recently powered by University of Sheffield researchers, to include joint cost, self-weight and buckling considerations. A joint cost inclusion scopes to reduce the number of joints existing in an optimized structural solution, transforming it to a practically viable solution. The topic of the current paper is to investigate the effects of joint cost inclusion, as this is currently implemented in the optimization code. An extended literature review on this subject was conducted prior to familiarization with small scale optimization software. Using IntelliFORM software, a structured series of problems were set and analyzed. The joint cost tests examined benchmark problems and their consequent changes in the member topology, as the design domain was expanding. The findings of the analyses were remarkable and are being commented further on. The distinct topologies of solutions created by optimization processes are also recognized. Finally an alternative strategy of penalizing joints is presented.
How to Use Linear Programming for Information System Performances Optimization
Directory of Open Access Journals (Sweden)
Hell Marko
2014-09-01
Full Text Available Background: Organisations nowadays operate in a very dynamic environment, and therefore, their ability of continuously adjusting the strategic plan to the new conditions is a must for achieving their strategic objectives. BSC is a well-known methodology for measuring performances enabling organizations to learn how well they are doing. In this paper, “BSC for IS” will be proposed in order to measure the IS impact on the achievement of organizations’ business goals. Objectives: The objective of this paper is to present the original procedure which is used to enhance the BSC methodology in planning the optimal targets of IS performances value in order to maximize the organization's effectiveness. Methods/Approach: The method used in this paper is the quantitative methodology - linear programming. In the case study, linear programming is used for optimizing organization’s strategic performance. Results: Results are shown on the example of a case study national park. An optimal performance value for the strategic objective has been calculated, as well as an optimal performance value for each DO (derived objective. Results are calculated in Excel, using Solver Add-in. Conclusions: The presentation of methodology through the case study of a national park shows that this methodology, though it requires a high level of formalisation, provides a very transparent performance calculation.
Applications exponential approximation by integer shifts of Gaussian functions
Directory of Open Access Journals (Sweden)
S. M. Sitnik
2013-01-01
Full Text Available In this paper we consider approximations of functions using integer shifts of Gaussians – quadratic exponentials. A method is proposed to find coefficients of node functions by solving linear systems of equations. The explicit formula for the determinant of the system is found, based on it solvability of linear system under consideration is proved and uniqueness of its solution. We compare results with known ones and briefly indicate applications to signal theory.
Aether: leveraging linear programming for optimal cloud computing in genomics.
Luber, Jacob M; Tierney, Braden T; Cofer, Evan M; Patel, Chirag J; Kostic, Aleksandar D
2018-05-01
Across biology, we are seeing rapid developments in scale of data production without a corresponding increase in data analysis capabilities. Here, we present Aether (http://aether.kosticlab.org), an intuitive, easy-to-use, cost-effective and scalable framework that uses linear programming to optimally bid on and deploy combinations of underutilized cloud computing resources. Our approach simultaneously minimizes the cost of data analysis and provides an easy transition from users' existing HPC pipelines. Data utilized are available at https://pubs.broadinstitute.org/diabimmune and with EBI SRA accession ERP005989. Source code is available at (https://github.com/kosticlab/aether). Examples, documentation and a tutorial are available at http://aether.kosticlab.org. chirag_patel@hms.harvard.edu or aleksandar.kostic@joslin.harvard.edu. Supplementary data are available at Bioinformatics online.
Linear programming phase unwrapping for dual-wavelength digital holography.
Wang, Zhaomin; Jiao, Jiannan; Qu, Weijuan; Yang, Fang; Li, Hongru; Tian, Ailing; Asundi, Anand
2017-01-20
A linear programming phase unwrapping method in dual-wavelength digital holography is proposed and verified experimentally. The proposed method uses the square of height difference as a convergence standard and theoretically gives the boundary condition in a searching process. A simulation was performed by unwrapping step structures at different levels of Gaussian noise. As a result, our method is capable of recovering the discontinuities accurately. It is robust and straightforward. In the experiment, a microelectromechanical systems sample and a cylindrical lens were measured separately. The testing results were in good agreement with true values. Moreover, the proposed method is applicable not only in digital holography but also in other dual-wavelength interferometric techniques.
Microgrid Reliability Modeling and Battery Scheduling Using Stochastic Linear Programming
Energy Technology Data Exchange (ETDEWEB)
Cardoso, Goncalo; Stadler, Michael; Siddiqui, Afzal; Marnay, Chris; DeForest, Nicholas; Barbosa-Povoa, Ana; Ferrao, Paulo
2013-05-23
This paper describes the introduction of stochastic linear programming into Operations DER-CAM, a tool used to obtain optimal operating schedules for a given microgrid under local economic and environmental conditions. This application follows previous work on optimal scheduling of a lithium-iron-phosphate battery given the output uncertainty of a 1 MW molten carbonate fuel cell. Both are in the Santa Rita Jail microgrid, located in Dublin, California. This fuel cell has proven unreliable, partially justifying the consideration of storage options. Several stochastic DER-CAM runs are executed to compare different scenarios to values obtained by a deterministic approach. Results indicate that using a stochastic approach provides a conservative yet more lucrative battery schedule. Lower expected energy bills result, given fuel cell outages, in potential savings exceeding 6percent.
CONTRIBUTION OF A LINEAR PROGRAMMING VBA MODULE TO STUDENTS PEFORMANCE
Directory of Open Access Journals (Sweden)
KUČÍRKOVÁ Lenka
2010-12-01
Full Text Available This paper deals with the application of freeware modules as a teaching support of Operations Research methods at the Department of Systems Engineering, Czech university of Life Sciences (CULS Prague. In particular, we concentrated on a linear programming module and measured the impact on student performance. The motivation for this evaluation is based on a current development of a new module that focuses on Traveling Salesman Problem. First, we explain the current situation both worldwide and in the Czech Republic and the CULS Prague. Subsequently, we describe the content of students’ exams and statistical methods applied to the evaluation. Finally, we analyze and generalize the obtained results. The students exams have show a positive impact of the modules. Further, our analysis has proven that this impact is statistically significant. The findings motivate us to made new modules for other methods.
Local beam angle optimization with linear programming and gradient search
International Nuclear Information System (INIS)
Craft, David
2007-01-01
The optimization of beam angles in IMRT planning is still an open problem, with literature focusing on heuristic strategies and exhaustive searches on discrete angle grids. We show how a beam angle set can be locally refined in a continuous manner using gradient-based optimization in the beam angle space. The gradient is derived using linear programming duality theory. Applying this local search to 100 random initial angle sets of a phantom pancreatic case demonstrates the method, and highlights the many-local-minima aspect of the BAO problem. Due to this function structure, we recommend a search strategy of a thorough global search followed by local refinement at promising beam angle sets. Extensions to nonlinear IMRT formulations are discussed. (note)
Optimization of refinery product blending by using linear programming
International Nuclear Information System (INIS)
Ristikj, Julija; Tripcheva-Trajkovska, Loreta; Rikaloski, Ice; Markovska, Liljana
1999-01-01
The product slate of a simple refinery consists mainly of liquefied petroleum gas, leaded and unleaded gasoline, jet fuel, diesel fuel, extra light heating oil and fuel oil. The quality of the oil products (fuels) for sale has to comply with the adopted standards for liquid fuels, and the produced quantities have to be comply with the market needs. The oil products are manufactured by blending two or more different fractions which quantities and physical-chemical properties depend on the crude oil type, the way and conditions of processing, and at the same time the fractions are used to blend one or more products. It is in producer's interest to do the blending in an optimal way, namely, to satisfy the requirements for the oil products quality and quantity with a maximal usage of the available fractions and, of course, with a maximal profit out of the sold products. This could be accomplished by applying linear programming, that is by using a linear model for oil products blending optimization. (Author)
Towards lexicographic multi-objective linear programming using grossone methodology
Cococcioni, Marco; Pappalardo, Massimo; Sergeyev, Yaroslav D.
2016-10-01
Lexicographic Multi-Objective Linear Programming (LMOLP) problems can be solved in two ways: preemptive and nonpreemptive. The preemptive approach requires the solution of a series of LP problems, with changing constraints (each time the next objective is added, a new constraint appears). The nonpreemptive approach is based on a scalarization of the multiple objectives into a single-objective linear function by a weighted combination of the given objectives. It requires the specification of a set of weights, which is not straightforward and can be time consuming. In this work we present both mathematical and software ingredients necessary to solve LMOLP problems using a recently introduced computational methodology (allowing one to work numerically with infinities and infinitesimals) based on the concept of grossone. The ultimate goal of such an attempt is an implementation of a simplex-like algorithm, able to solve the original LMOLP problem by solving only one single-objective problem and without the need to specify finite weights. The expected advantages are therefore obvious.
C-program LINOP for the evaluation of film dosemeters by linear optimization. User manual
International Nuclear Information System (INIS)
Kragh, P.
1995-11-01
Linear programming results in an optimal measuring value for film dosemeters. The Linop program was developed to be used for linear programming. The program permits the evaluation and control of film dosemeters and of all other multi-component dosemeters. This user manual for the Linop program contains the source program, a description of the program and installation and use instructions. The data sets with programs and examples are available upon request. (orig.) [de
Landman, Bruce M
2014-01-01
Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems. For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an "inequality" version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdős-Ginzberg-Ziv theorem, and t...
A linear programming approach for placement of applicants to academic programs
Kassa, Biniyam Asmare
2013-01-01
This paper reports a linear programming approach for placement of applicants to study programs developed and implemented at the college of Business & Economics, Bahir Dar University, Bahir Dar, Ethiopia. The approach is estimated to significantly streamline the placement decision process at the college by reducing required man hour as well as the time it takes to announce placement decisions. Compared to the previous manual system where only one or two placement criteria were considered, the ...
Linear Optimization of Frequency Spectrum Assignments Across System
2016-03-01
selection tools, frequency allocation, transmission optimization, electromagnetic maneuver warfare, electronic protection, assignment model 15. NUMBER ...Characteristics Modeled ...............................................................29 Table 10. Antenna Systems Modeled , Number of Systems and...surveillance EW early warning GAMS general algebraic modeling system GHz gigahertz IDE integrated development environment ILP integer linear program
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…
Approximate labeling via graph cuts based on linear programming.
Komodakis, Nikos; Tziritas, Georgios
2007-08-01
A new framework is presented for both understanding and developing graph-cut-based combinatorial algorithms suitable for the approximate optimization of a very wide class of Markov Random Fields (MRFs) that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the \\alpha-expansion algorithm, which is included merely as a special case. Moreover, contrary to \\alpha-expansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, for example, even for MRFs with nonmetric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete MRFs with an arbitrary potential function. These bounds prove to be very tight in practice (that is, very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low-level vision tasks, such as stereo matching, image restoration, image completion, and optical flow estimation, as well as on synthetic problems.
Flow discharge prediction in compound channels using linear genetic programming
Azamathulla, H. Md.; Zahiri, A.
2012-08-01
SummaryFlow discharge determination in rivers is one of the key elements in mathematical modelling in the design of river engineering projects. Because of the inundation of floodplains and sudden changes in river geometry, flow resistance equations are not applicable for compound channels. Therefore, many approaches have been developed for modification of flow discharge computations. Most of these methods have satisfactory results only in laboratory flumes. Due to the ability to model complex phenomena, the artificial intelligence methods have recently been employed for wide applications in various fields of water engineering. Linear genetic programming (LGP), a branch of artificial intelligence methods, is able to optimise the model structure and its components and to derive an explicit equation based on the variables of the phenomena. In this paper, a precise dimensionless equation has been derived for prediction of flood discharge using LGP. The proposed model was developed using published data compiled for stage-discharge data sets for 394 laboratories, and field of 30 compound channels. The results indicate that the LGP model has a better performance than the existing models.
Periodic inventory system in cafeteria using linear programming
Usop, Mohd Fais; Ishak, Ruzana; Hamdan, Ahmad Ridhuan
2017-11-01
Inventory management is an important factor in running a business. It plays a big role of managing the stock in cafeteria. If the inventories are failed to be managed wisely, it will affect the profit of the cafeteria. Therefore, the purpose of this study is to find the solution of the inventory management in cafeteria. Most of the cafeteria in Malaysia did not manage their stock well. Therefore, this study is to propose a database system of inventory management and to develop the inventory model in cafeteria management. In this study, new database system to improve the management of the stock in a weekly basis will be provided using Linear Programming Model to get the optimal range of the inventory needed for selected categories. Data that were collected by using the Periodic Inventory System at the end of the week within three months period being analyzed by using the Food Stock-take Database. The inventory model was developed from the collected data according to the category of the inventory in the cafeteria. Results showed the effectiveness of using the Periodic Inventory System and will be very helpful to the cafeteria management in organizing the inventory. Moreover, the findings in this study can reduce the cost of operation and increased the profit.
Near-Regular Structure Discovery Using Linear Programming
Huang, Qixing
2014-06-02
Near-regular structures are common in manmade and natural objects. Algorithmic detection of such regularity greatly facilitates our understanding of shape structures, leads to compact encoding of input geometries, and enables efficient generation and manipulation of complex patterns on both acquired and synthesized objects. Such regularity manifests itself both in the repetition of certain geometric elements, as well as in the structured arrangement of the elements. We cast the regularity detection problem as an optimization and efficiently solve it using linear programming techniques. Our optimization has a discrete aspect, that is, the connectivity relationships among the elements, as well as a continuous aspect, namely the locations of the elements of interest. Both these aspects are captured by our near-regular structure extraction framework, which alternates between discrete and continuous optimizations. We demonstrate the effectiveness of our framework on a variety of problems including near-regular structure extraction, structure-preserving pattern manipulation, and markerless correspondence detection. Robustness results with respect to geometric and topological noise are presented on synthesized, real-world, and also benchmark datasets. © 2014 ACM.
Storage and distribution/Linear programming for storage operations
Energy Technology Data Exchange (ETDEWEB)
Coleman, D
1978-07-15
The techniques of linear programing to solve storage problems as applied in a tank farm tie-in with refinery throughput operation include: (1) the time-phased model which works on storage and refinery operations input parameters, e.g., production, distribution, cracking, etc., and is capable of representing product stockpiling in slack periods to meet future peak demands, and investigating alternative strategies such as exchange deals and purchase and leasing of additional storage, and (2) the Monte Carlo simulation method, which inputs parameters, e.g., arrival of crude products at refinery, tankage size, likely demand for products, etc., as probability distributions rather than single values, and is capable of showing the average utilization of facilities, potential bottlenecks, investment required to achieve an increase in utilization, and to enable the user to predict total investment, cash flow, and profit emanating from the original financing decision. The increasing use of computer techniques to solve refinery and storage problems is attributed to potential savings resulting from more effective planning, reduced computer costs, ease of access and more usable software. Diagrams.
Pilkey, W. D.; Chen, Y. H.
1974-01-01
An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.
NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program
Chermakani, Deepak Ponvel
2012-01-01
We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the time parameter that tends to positive infinity. The number of variables, constraints, and rational linear functions in the objective, of the real-variable problem is bounded by a polynomial ...
Linear programming model can explain respiration of fermentation products
Möller, Philip; Liu, Xiaochen; Schuster, Stefan
2018-01-01
Many differentiated cells rely primarily on mitochondrial oxidative phosphorylation for generating energy in the form of ATP needed for cellular metabolism. In contrast most tumor cells instead rely on aerobic glycolysis leading to lactate to about the same extent as on respiration. Warburg found that cancer cells to support oxidative phosphorylation, tend to ferment glucose or other energy source into lactate even in the presence of sufficient oxygen, which is an inefficient way to generate ATP. This effect also occurs in striated muscle cells, activated lymphocytes and microglia, endothelial cells and several mammalian cell types, a phenomenon termed the “Warburg effect”. The effect is paradoxical at first glance because the ATP production rate of aerobic glycolysis is much slower than that of respiration and the energy demands are better to be met by pure oxidative phosphorylation. We tackle this question by building a minimal model including three combined reactions. The new aspect in extension to earlier models is that we take into account the possible uptake and oxidation of the fermentation products. We examine the case where the cell can allocate protein on several enzymes in a varying distribution and model this by a linear programming problem in which the objective is to maximize the ATP production rate under different combinations of constraints on enzymes. Depending on the cost of reactions and limitation of the substrates, this leads to pure respiration, pure fermentation, and a mixture of respiration and fermentation. The model predicts that fermentation products are only oxidized when glucose is scarce or its uptake is severely limited. PMID:29415045
Optimizing Biorefinery Design and Operations via Linear Programming Models
Energy Technology Data Exchange (ETDEWEB)
Talmadge, Michael; Batan, Liaw; Lamers, Patrick; Hartley, Damon; Biddy, Mary; Tao, Ling; Tan, Eric
2017-03-28
The ability to assess and optimize economics of biomass resource utilization for the production of fuels, chemicals and power is essential for the ultimate success of a bioenergy industry. The team of authors, consisting of members from the National Renewable Energy Laboratory (NREL) and the Idaho National Laboratory (INL), has developed simple biorefinery linear programming (LP) models to enable the optimization of theoretical or existing biorefineries. The goal of this analysis is to demonstrate how such models can benefit the developing biorefining industry. It focuses on a theoretical multi-pathway, thermochemical biorefinery configuration and demonstrates how the biorefinery can use LP models for operations planning and optimization in comparable ways to the petroleum refining industry. Using LP modeling tools developed under U.S. Department of Energy's Bioenergy Technologies Office (DOE-BETO) funded efforts, the authors investigate optimization challenges for the theoretical biorefineries such as (1) optimal feedstock slate based on available biomass and prices, (2) breakeven price analysis for available feedstocks, (3) impact analysis for changes in feedstock costs and product prices, (4) optimal biorefinery operations during unit shutdowns / turnarounds, and (5) incentives for increased processing capacity. These biorefinery examples are comparable to crude oil purchasing and operational optimization studies that petroleum refiners perform routinely using LPs and other optimization models. It is important to note that the analyses presented in this article are strictly theoretical and they are not based on current energy market prices. The pricing structure assigned for this demonstrative analysis is consistent with $4 per gallon gasoline, which clearly assumes an economic environment that would favor the construction and operation of biorefineries. The analysis approach and examples provide valuable insights into the usefulness of analysis tools for
Linear programming model can explain respiration of fermentation products.
Möller, Philip; Liu, Xiaochen; Schuster, Stefan; Boley, Daniel
2018-01-01
Many differentiated cells rely primarily on mitochondrial oxidative phosphorylation for generating energy in the form of ATP needed for cellular metabolism. In contrast most tumor cells instead rely on aerobic glycolysis leading to lactate to about the same extent as on respiration. Warburg found that cancer cells to support oxidative phosphorylation, tend to ferment glucose or other energy source into lactate even in the presence of sufficient oxygen, which is an inefficient way to generate ATP. This effect also occurs in striated muscle cells, activated lymphocytes and microglia, endothelial cells and several mammalian cell types, a phenomenon termed the "Warburg effect". The effect is paradoxical at first glance because the ATP production rate of aerobic glycolysis is much slower than that of respiration and the energy demands are better to be met by pure oxidative phosphorylation. We tackle this question by building a minimal model including three combined reactions. The new aspect in extension to earlier models is that we take into account the possible uptake and oxidation of the fermentation products. We examine the case where the cell can allocate protein on several enzymes in a varying distribution and model this by a linear programming problem in which the objective is to maximize the ATP production rate under different combinations of constraints on enzymes. Depending on the cost of reactions and limitation of the substrates, this leads to pure respiration, pure fermentation, and a mixture of respiration and fermentation. The model predicts that fermentation products are only oxidized when glucose is scarce or its uptake is severely limited.
Very Low-Cost Nutritious Diet Plans Designed by Linear Programming.
Foytik, Jerry
1981-01-01
Provides procedural details of Linear Programing, developed by the U.S. Department of Agriculture to devise a dietary guide for consumers that minimizes food costs without sacrificing nutritional quality. Compares Linear Programming with the Thrifty Food Plan, which has been a basis for allocating coupons under the Food Stamp Program. (CS)
Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems
Directory of Open Access Journals (Sweden)
Bambang Riyanto
2005-11-01
Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.
Wouda, H.E.; Beek, van P.; Vorst, van der J.G.A.J.; Tacke, H.
2002-01-01
Between 1995 and 1998 Nutricia acquired a number of dairy companies in Hungary. Each of these companies produced a wide variety of products for its regional market. Although alterations had been made to the production system in the last few years, production and transportation costs were still
Frost, Susan A.; Bodson, Marc; Acosta, Diana M.
2009-01-01
The Next Generation (NextGen) transport aircraft configurations being investigated as part of the NASA Aeronautics Subsonic Fixed Wing Project have more control surfaces, or control effectors, than existing transport aircraft configurations. Conventional flight control is achieved through two symmetric elevators, two antisymmetric ailerons, and a rudder. The five effectors, reduced to three command variables, produce moments along the three main axes of the aircraft and enable the pilot to control the attitude and flight path of the aircraft. The NextGen aircraft will have additional redundant control effectors to control the three moments, creating a situation where the aircraft is over-actuated and where a simple relationship does not exist anymore between the required effector deflections and the desired moments. NextGen flight controllers will incorporate control allocation algorithms to determine the optimal effector commands and attain the desired moments, taking into account the effector limits. Approaches to solving the problem using linear programming and quadratic programming algorithms have been proposed and tested. It is of great interest to understand their relative advantages and disadvantages and how design parameters may affect their properties. In this paper, we investigate the sensitivity of the effector commands with respect to the desired moments and show on some examples that the solutions provided using the l2 norm of quadratic programming are less sensitive than those using the l1 norm of linear programming.
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 a...... 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....
Quasi-greedy systems of integer translates
DEFF Research Database (Denmark)
Nielsen, Morten; Sikic, Hrvoje
We consider quasi-greedy systems of integer translates in a finitely generated shift invariant subspace of L2(Rd), that is systems for which the thresholding approximation procedure is well behaved. We prove that every quasi-greedy system of integer translates is also a Riesz basis for its closed...
Quasi-greedy systems of integer translates
DEFF Research Database (Denmark)
Nielsen, Morten; Sikic, Hrvoje
2008-01-01
We consider quasi-greedy systems of integer translates in a finitely generated shift-invariant subspace of L2(Rd), that is systems for which the thresholding approximation procedure is well behaved. We prove that every quasi-greedy system of integer translates is also a Riesz basis for its closed...
Positive integer solutions of certain diophantine equations
Indian Academy of Sciences (India)
BIJAN KUMAR PATEL
2018-03-19
Mar 19, 2018 ... integer solutions. They also found all the positive integer solutions of the given equations in terms of Fibonacci and Lucas numbers. Another interesting number sequence which is closely related to the sequence of. Fibonacci numbers is the sequence of balancing numbers. In 1999, Behera et al. [1] intro-.
Analysis misconception of integers in microteaching activities
Setyawati, R. D.; Indiati, I.
2018-05-01
This study view to analyse student misconceptions on integers in microteaching activities. This research used qualitative research design. An integers test contained questions from eight main areas of integers. The Integers material test includes (a) converting the image into fractions, (b) examples of positive numbers including rational numbers, (c) operations in fractions, (d) sorting fractions from the largest to the smallest, and vice versa; e) equate denominator, (f) concept of ratio mark, (g) definition of fraction, and (h) difference between fractions and parts. The results indicated an integers concepts: (1) the students have not been able to define concepts well based on the classification of facts in organized part; (2) The correlational concept: students have not been able to combine interrelated events in the form of general principles; and (3) theoretical concepts: students have not been able to use concepts that facilitate in learning the facts or events in an organized system.
Fleming, P.
1985-01-01
A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a non-linear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer-aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer.
Sensitivity analysis of linear programming problem through a recurrent neural network
Das, Raja
2017-11-01
In this paper we study the recurrent neural network for solving linear programming problems. To achieve optimality in accuracy and also in computational effort, an algorithm is presented. We investigate the sensitivity analysis of linear programming problem through the neural network. A detailed example is also presented to demonstrate the performance of the recurrent neural network.
Schmitt, M. A.; And Others
1994-01-01
Compares traditional manure application planning techniques calculated to meet agronomic nutrient needs on a field-by-field basis with plans developed using computer-assisted linear programming optimization methods. Linear programming provided the most economical and environmentally sound manure application strategy. (Contains 15 references.) (MDH)
Fundamental solution of the problem of linear programming and method of its determination
Petrunin, S. V.
1978-01-01
The idea of a fundamental solution to a problem in linear programming is introduced. A method of determining the fundamental solution and of applying this method to the solution of a problem in linear programming is proposed. Numerical examples are cited.
DEFF Research Database (Denmark)
Ren, Jingzheng; Dong, Liang; Sun, Lu
2015-01-01
in this model, and the price of the resources, the yield of grain and the market demands were regarded as interval numbers instead of constants. An interval linear programming was developed, and a method for solving interval linear programming was presented. An illustrative case was studied by the proposed...
The essential multiobjectivity of linear programming | Stewart | ORiON
African Journals Online (AJOL)
It is argued that any non-trivial real world problems involve multiple objectives. The simplistic approach of combining objectives in linear form can generate highly misleading and biased results, and is poor operational research practice. Such biases are illustrated by means of a simple example, and it is demonstrated that ...
International Nuclear Information System (INIS)
Cullen, D.E.
1979-01-01
Program LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form (i.e., removes points not needed for linear interpolability). The main advantage of the code is that it allows subsequent codes to consider only linear-linear data. A listing of the source deck is available on request
Effective radiological safety program for electron linear accelerators
International Nuclear Information System (INIS)
Swanson, W.P.
1980-10-01
An outline is presented of some of the main elements of an electron accelerator radiological safety program. The discussion includes types of accelerator facilities, types of radiations to be anticipated, activity induced in components, air and water, and production of toxic gases. Concepts of radiation shielding design are briefly discussed and organizational aspects are considered as an integral part of the overall safety program
Portfolio optimization by using linear programing models based on genetic algorithm
Sukono; Hidayat, Y.; Lesmana, E.; Putra, A. S.; Napitupulu, H.; Supian, S.
2018-01-01
In this paper, we discussed the investment portfolio optimization using linear programming model based on genetic algorithms. It is assumed that the portfolio risk is measured by absolute standard deviation, and each investor has a risk tolerance on the investment portfolio. To complete the investment portfolio optimization problem, the issue is arranged into a linear programming model. Furthermore, determination of the optimum solution for linear programming is done by using a genetic algorithm. As a numerical illustration, we analyze some of the stocks traded on the capital market in Indonesia. Based on the analysis, it is shown that the portfolio optimization performed by genetic algorithm approach produces more optimal efficient portfolio, compared to the portfolio optimization performed by a linear programming algorithm approach. Therefore, genetic algorithms can be considered as an alternative on determining the investment portfolio optimization, particularly using linear programming models.
Shen, Peiping; Zhang, Tongli; Wang, Chunfeng
2017-01-01
This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.
Zhao, Yingfeng; Liu, Sanyang
2016-01-01
We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.
International Nuclear Information System (INIS)
Zavaljevski, N.
1985-01-01
Proposed optimization procedure is fast due to application of linear programming. Non-linear constraints which demand iterative application of linear programming are slowing down the calculation. Linearization can be done by different procedures starting from simple empirical rules for fuel in-core management to complicated general perturbation theory with higher order of corrections. A mathematical model was formulated for optimization of improved fuel cycle. A detailed algorithm for determining minimum of fresh fuel at the beginning of each fuel cycle is shown and the problem is linearized by first order perturbation theory and it is optimized by linear programming. Numerical illustration of the proposed method was done for the experimental reactor mostly for saving computer time
AN INTEGER PROGRAMMING MODEL FOR HIERARCHICAL WORKFORCE
Directory of Open Access Journals (Sweden)
BANU SUNGUR
2013-06-01
Full Text Available The model presented in this paper is based on the model developed by Billionnet for the hierarchical workforce problem. In Billionnet’s Model, while determining the workers’ weekly costs, weekly working hours of workers are not taken into consideration. In our model, the weekly costs per worker are reduced in proportion to the working hours per week. Our model is illustrated on the Billionnet’s Example. The models in question are compared and evaluated on the basis of the results obtained from the example problem. A reduction is achieved in the total cost by the proposed model.
Parallel Integer Factorization Using Quadratic Forms
National Research Council Canada - National Science Library
McMath, Stephen S
2005-01-01
Factorization is important for both practical and theoretical reasons. In secure digital communication, security of the commonly used RSA public key cryptosystem depends on the difficulty of factoring large integers...
A linear programming approach for placement of applicants to academic programs.
Kassa, Biniyam Asmare
2013-01-01
This paper reports a linear programming approach for placement of applicants to study programs developed and implemented at the college of Business & Economics, Bahir Dar University, Bahir Dar, Ethiopia. The approach is estimated to significantly streamline the placement decision process at the college by reducing required man hour as well as the time it takes to announce placement decisions. Compared to the previous manual system where only one or two placement criteria were considered, the new approach allows the college's management to easily incorporate additional placement criteria, if needed. Comparison of our approach against manually constructed placement decisions based on actual data for the 2012/13 academic year suggested that about 93 percent of the placements from our model concur with the actual placement decisions. For the remaining 7 percent of placements, however, the actual placements made by the manual system display inconsistencies of decisions judged against the very criteria intended to guide placement decisions by the college's program management office. Overall, the new approach proves to be a significant improvement over the manual system in terms of efficiency of the placement process and the quality of placement decisions.
Bruhn, Peter; Geyer-Schulz, Andreas
2002-01-01
In this paper, we introduce genetic programming over context-free languages with linear constraints for combinatorial optimization, apply this method to several variants of the multidimensional knapsack problem, and discuss its performance relative to Michalewicz's genetic algorithm with penalty functions. With respect to Michalewicz's approach, we demonstrate that genetic programming over context-free languages with linear constraints improves convergence. A final result is that genetic programming over context-free languages with linear constraints is ideally suited to modeling complementarities between items in a knapsack problem: The more complementarities in the problem, the stronger the performance in comparison to its competitors.
International Nuclear Information System (INIS)
Hutchinson, W.
1983-04-01
The report takes the form of a user guide to a computer program using linear programming techniques to aid the assignment and scheduling of radioactive wastes for disposal to sea. The program is aimed at the identification of 'optimum' amounts of each waste stream for disposal to sea without violating specific constraints values and/or fairness parameters. (author)
COMPUTING VERTICES OF INTEGER PARTITION POLYTOPES
Directory of Open Access Journals (Sweden)
A. S. Vroublevski
2015-01-01
Full Text Available The paper describes a method of generating vertices of the polytopes of integer partitions that was used by the authors to calculate all vertices and support vertices of the partition polytopes for all n ≤ 105 and all knapsack partitions of n ≤ 165. The method avoids generating all partitions of n. The vertices are determined with the help of sufficient and necessary conditions; in the hard cases, the well-known program Polymake is used. Some computational aspects are exposed in more detail. These are the algorithm for checking the criterion that characterizes partitions that are convex combinations of two other partitions; the way of using two combinatorial operations that transform the known vertices to the new ones; and employing the Polymake to recognize a limited number (for small n of partitions that need three or more other partitions for being convexly expressed. We discuss the computational results on the numbers of vertices and support vertices of the partition polytopes and some appealing problems these results give rise to.
adapta~k>n -11 of the surrogate memods for linear programming ...
African Journals Online (AJOL)
2005-08-02
Aug 2, 2005 ... inequality problem is made uj~ of the primal and dual optimal solutions for the given primal ... KEYWORDS: Linear Programming, Duality Theory, Surrogate Methods. ..... replaces x and the process IS repeated with the new x.
Development of demand functions and their inclusion in linear programming forecasting models
International Nuclear Information System (INIS)
Chamberlin, J.H.
1976-05-01
The purpose of the paper is to present a method for including demand directly within a linear programming model, and to use this method to analyze the effect of the Liquid Metal Fast Breeder Reactor upon the nuclear energy system
An introduction to fuzzy linear programming problems theory, methods and applications
Kaur, Jagdeep
2016-01-01
The book presents a snapshot of the state of the art in the field of fully fuzzy linear programming. The main focus is on showing current methods for finding the fuzzy optimal solution of fully fuzzy linear programming problems in which all the parameters and decision variables are represented by non-negative fuzzy numbers. It presents new methods developed by the authors, as well as existing methods developed by others, and their application to real-world problems, including fuzzy transportation problems. Moreover, it compares the outcomes of the different methods and discusses their advantages/disadvantages. As the first work to collect at one place the most important methods for solving fuzzy linear programming problems, the book represents a useful reference guide for students and researchers, providing them with the necessary theoretical and practical knowledge to deal with linear programming problems under uncertainty.
Fuzzy Multi Objective Linear Programming Problem with Imprecise Aspiration Level and Parameters
Directory of Open Access Journals (Sweden)
Zahra Shahraki
2015-07-01
Full Text Available This paper considers the multi-objective linear programming problems with fuzzygoal for each of the objective functions and constraints. Most existing works deal withlinear membership functions for fuzzy goals. In this paper, exponential membershipfunction is used.
International Nuclear Information System (INIS)
Ureba, A.; Palma, B. A.; Leal, A.
2011-01-01
Develop a more efficient method of optimization in relation to time, based on linear programming designed to implement a multi objective penalty function which also permits a simultaneous solution integrated boost situations considering two white volumes simultaneously.
Portfolio selection problem: a comparison of fuzzy goal programming and linear physical programming
Directory of Open Access Journals (Sweden)
Fusun Kucukbay
2016-04-01
Full Text Available Investors have limited budget and they try to maximize their return with minimum risk. Therefore this study aims to deal with the portfolio selection problem. In the study two criteria are considered which are expected return, and risk. In this respect, linear physical programming (LPP technique is applied on Bist 100 stocks to be able to find out the optimum portfolio. The analysis covers the period April 2009- March 2015. This period is divided into two; April 2009-March 2014 and April 2014 – March 2015. April 2009-March 2014 period is used as data to find an optimal solution. April 2014-March 2015 period is used to test the real performance of portfolios. The performance of the obtained portfolio is compared with that obtained from fuzzy goal programming (FGP. Then the performances of both method, LPP and FGP are compared with BIST 100 in terms of their Sharpe Indexes. The findings reveal that LPP for portfolio selection problem is a good alternative to FGP.
Arc-Search Infeasible Interior-Point Algorithm for Linear Programming
Yang, Yaguang
2014-01-01
Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the propo...
Diet models with linear goal programming: impact of achievement functions.
Gerdessen, J C; de Vries, J H M
2015-11-01
Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost constraints. Results derived from GP models are usually very sensitive to the type of achievement function that is chosen.This paper aims to provide a methodological insight into several achievement functions. It describes the extended GP (EGP) achievement function, which enables the decision maker to use either a MinSum achievement function (which minimizes the sum of the unwanted deviations) or a MinMax achievement function (which minimizes the largest unwanted deviation), or a compromise between both. An additional advantage of EGP models is that from one set of data and weights multiple solutions can be obtained. We use small numerical examples to illustrate the 'mechanics' of achievement functions. Then, the EGP achievement function is demonstrated on a diet problem with 144 foods, 19 nutrients and several types of palatability constraints, in which the nutritional constraints are modeled with fuzzy sets. Choice of achievement function affects the results of diet models. MinSum achievement functions can give rise to solutions that are sensitive to weight changes, and that pile all unwanted deviations on a limited number of nutritional constraints. MinMax achievement functions spread the unwanted deviations as evenly as possible, but may create many (small) deviations. EGP comprises both types of achievement functions, as well as compromises between them. It can thus, from one data set, find a range of solutions with various properties.
Multi-Objective Fuzzy Linear Programming In Agricultural Production Planning
Directory of Open Access Journals (Sweden)
H.M.I.U. Herath
2015-08-01
Full Text Available Abstract Modern agriculture is characterized by a series of conflicting optimization criteria that obstruct the decision-making process in the planning of agricultural production. Such criteria are usually net profit total cost total production etc. At the same time the decision making process in the agricultural production planning is often conducted with data that accidentally occur in nature or that are fuzzy not deterministic. Such data are the yields of various crops the prices of products and raw materials demand for the product the available quantities of production factors such as water labor etc. In this paper a fuzzy multi-criteria mathematical programming model is presented. This model is applied in a region of 10 districts in Sri Lanka where paddy is cultivated under irrigated and rain fed water in the two main seasons called Yala and Maha and the optimal production plan is achieved. This study was undertaken to find out the optimal allocation of land for paddy to get a better yield while satisfying the two conflicting objectives profit maximizing and cost minimizing subjected to the utilizing of water constraint and the demand constraint. Only the availability of land constraint is considered as a crisp in nature while objectives and other constraints are treated as fuzzy. It is observed that the MOFLP is an effective method to handle more than a single objective occurs in an uncertain vague environment.
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…
FSILP: fuzzy-stochastic-interval linear programming for supporting municipal solid waste management.
Li, Pu; Chen, Bing
2011-04-01
Although many studies on municipal solid waste management (MSW management) were conducted under uncertain conditions of fuzzy, stochastic, and interval coexistence, the solution to the conventional linear programming problems of integrating fuzzy method with the other two was inefficient. In this study, a fuzzy-stochastic-interval linear programming (FSILP) method is developed by integrating Nguyen's method with conventional linear programming for supporting municipal solid waste management. The Nguyen's method was used to convert the fuzzy and fuzzy-stochastic linear programming problems into the conventional linear programs, by measuring the attainment values of fuzzy numbers and/or fuzzy random variables, as well as superiority and inferiority between triangular fuzzy numbers/triangular fuzzy-stochastic variables. The developed method can effectively tackle uncertainties described in terms of probability density functions, fuzzy membership functions, and discrete intervals. Moreover, the method can also improve upon the conventional interval fuzzy programming and two-stage stochastic programming approaches, with advantageous capabilities that are easily achieved with fewer constraints and significantly reduces consumption time. The developed model was applied to a case study of municipal solid waste management system in a city. The results indicated that reasonable solutions had been generated. The solution can help quantify the relationship between the change of system cost and the uncertainties, which could support further analysis of tradeoffs between the waste management cost and the system failure risk. Copyright © 2010 Elsevier Ltd. All rights reserved.
Study and program implementation of transient curves' piecewise linearization
International Nuclear Information System (INIS)
Shi Yang; Zu Hongbiao
2014-01-01
Background: Transient curves are essential for the stress analysis of related equipment in nuclear power plant (NPP). The actually operating data or the design transient data of a NPP usually consist of a large number of data points with very short time intervals. To simplify the analysis, transient curves are generally piecewise linearized in advance. Up to now, the piecewise linearization of transient curves is accomplished manually, Purpose: The aim is to develop a method for the piecewise linearization of transient curves, and to implement it by programming. Methods: First of all, the fitting line of a number of data points was obtained by the least square method. The segment of the fitting line is set while the accumulation error of linearization exceeds the preset limit with the increasing number of points. Then the linearization of subsequent data points was begun from the last point of the preceding curve segment to get the next segment in the same way, and continue until the final data point involved. Finally, averaging of junction points is taken for the segment connection. Results: A computer program named PLTC (Piecewise Linearization for Transient Curves) was implemented and verified by the linearization of the standard sine curve and typical transient curves of a NPP. Conclusion: The method and the PLTC program can be well used to the piecewise linearization of transient curves, with improving efficiency and precision. (authors)
A Nutritional Analysis of the Food Basket in BIH: A Linear Programming Approach
Directory of Open Access Journals (Sweden)
Arnaut-Berilo Almira
2017-04-01
Full Text Available This paper presents linear and goal programming optimization models for determining and analyzing the food basket in Bosnia and Herzegovina (BiH in terms of adequate nutritional needs according to World Health Organization (WHO standards and World Bank (WB recommendations. A linear programming (LP model and goal linear programming model (GLP are adequate since price and nutrient contents are linearly related to food weight. The LP model provides information about the minimal value and the structure of the food basket for an average person in BiH based on nutrient needs. GLP models are designed to give us information on minimal deviations from nutrient needs if the budget is fixed. Based on these results, poverty analysis can be performed. The data used for the models consisted of 158 food items from the general consumption of the population of BiH according to COICOP classifications, with average prices in 2015 for these products.
The Computer Program LIAR for Beam Dynamics Calculations in Linear Accelerators
International Nuclear Information System (INIS)
Assmann, R.W.; Adolphsen, C.; Bane, K.; Raubenheimer, T.O.; Siemann, R.H.; Thompson, K.
2011-01-01
Linear accelerators are the central components of the proposed next generation of linear colliders. They need to provide acceleration of up to 750 GeV per beam while maintaining very small normalized emittances. Standard simulation programs, mainly developed for storage rings, do not meet the specific requirements for high energy linear accelerators. We present a new program LIAR ('LInear Accelerator Research code') that includes wakefield effects, a 6D coupled beam description, specific optimization algorithms and other advanced features. Its modular structure allows to use and to extend it easily for different purposes. The program is available for UNIX workstations and Windows PC's. It can be applied to a broad range of accelerators. We present examples of simulations for SLC and NLC.
Linearized Programming of Memristors for Artificial Neuro-Sensor Signal Processing.
Yang, Changju; Kim, Hyongsuk
2016-08-19
A linearized programming method of memristor-based neural weights is proposed. Memristor is known as an ideal element to implement a neural synapse due to its embedded functions of analog memory and analog multiplication. Its resistance variation with a voltage input is generally a nonlinear function of time. Linearization of memristance variation about time is very important for the easiness of memristor programming. In this paper, a method utilizing an anti-serial architecture for linear programming is proposed. The anti-serial architecture is composed of two memristors with opposite polarities. It linearizes the variation of memristance due to complimentary actions of two memristors. For programming a memristor, additional memristor with opposite polarity is employed. The linearization effect of weight programming of an anti-serial architecture is investigated and memristor bridge synapse which is built with two sets of anti-serial memristor architecture is taken as an application example of the proposed method. Simulations are performed with memristors of both linear drift model and nonlinear model.
Micosoft Excel Sensitivity Analysis for Linear and Stochastic Program Feed Formulation
Sensitivity analysis is a part of mathematical programming solutions and is used in making nutritional and economic decisions for a given feed formulation problem. The terms, shadow price and reduced cost, are familiar linear program (LP) terms to feed formulators. Because of the nonlinear nature of...
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.
International program on linear electric motors. CIGGT report No. 92-1
Energy Technology Data Exchange (ETDEWEB)
Dawson, G.E.; Eastham, A.R.; Parker, J.H.
1992-12-31
The International Program for Linear Electric Motors (LEM) was begun in April 1989 to communicate and coordinate activities with centers of expertise in Germany, Canada, and Japan; to provide for the assessment and support of the planning of technological developments and for dissemination of information to researchers, service operators, and policy makers; and to ensure that full advantage can be taken if opportunities for technology transfer occur. This report documents the work done under the program, including standardizing linear induction motor (LIM) design characteristics; test procedures and measurement methods; rating; database for design data; criteria for evaluation of designs; computer programs for modelling performance; and a design study for an agreed application.
A statistical mechanical approach to restricted integer partition functions
Zhou, Chi-Chun; Dai, Wu-Sheng
2018-05-01
The main aim of this paper is twofold: (1) suggesting a statistical mechanical approach to the calculation of the generating function of restricted integer partition functions which count the number of partitions—a way of writing an integer as a sum of other integers under certain restrictions. In this approach, the generating function of restricted integer partition functions is constructed from the canonical partition functions of various quantum gases. (2) Introducing a new type of restricted integer partition functions corresponding to general statistics which is a generalization of Gentile statistics in statistical mechanics; many kinds of restricted integer partition functions are special cases of this restricted integer partition function. Moreover, with statistical mechanics as a bridge, we reveal a mathematical fact: the generating function of restricted integer partition function is just the symmetric function which is a class of functions being invariant under the action of permutation groups. Using this approach, we provide some expressions of restricted integer partition functions as examples.
Object matching using a locally affine invariant and linear programming techniques.
Li, Hongsheng; Huang, Xiaolei; He, Lei
2013-02-01
In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.
Weighted thinned linear array design with the iterative FFT technique
CSIR Research Space (South Africa)
Du Plessis, WP
2011-09-01
Full Text Available techniques utilise simulated annealing [3]?[5], [10], mixed integer linear programming [7], genetic algorithms [9], and a hyrid approach combining a genetic algorithm and a local optimiser [8]. The iterative Fourier technique (IFT) developed by Keizer [2... algorithm being well- suited to obtaining low CTRs. Test problems from the literature are considered, and the results obtained with the IFT considerably exceed those achieved with other algorithms. II. DESCRIPTION OF THE ALGORITHM A flowchart describing...
Development and adjustment of programs for solving systems of linear equations
International Nuclear Information System (INIS)
Fujimura, Toichiro
1978-03-01
Programs for solving the systems of linear equations have been adjusted and developed in expanding the scientific subroutine library SSL. The principal programs adjusted are based on the congruent method, method of product form of the inverse, orthogonal method, Crout's method for sparse system, and acceleration of iterative methods. The programs developed are based on the escalator method, direct parallel residue method and block tridiagonal method for band system. Described are usage of the programs developed and their future improvement. FORTRAN lists with simple examples in tests of the programs are also given. (auth.)
DESIGN OF EDUCATIONAL PROBLEMS ON LINEAR PROGRAMMING USING SYSTEMS OF COMPUTER MATHEMATICS
Directory of Open Access Journals (Sweden)
Volodymyr M. Mykhalevych
2013-11-01
Full Text Available From a perspective of the theory of educational problems a problem of substitution in the conditions of ICT use of one discipline by an educational problem of another discipline is represented. Through the example of mathematical problems of linear programming it is showed that a student’s method of operation in the course of an educational problem solving is determinant in the identification of an educational problem in relation to a specific discipline: linear programming, informatics, mathematical modeling, methods of optimization, automatic control theory, calculus etc. It is substantiated the necessity of linear programming educational problems renovation with the purpose of making students free of bulky similar arithmetic calculations and notes which often becomes a barrier to a deeper understanding of key ideas taken as a basis of algorithms used by them.
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...
A quantum architecture for multiplying signed integers
International Nuclear Information System (INIS)
Alvarez-Sanchez, J J; Alvarez-Bravo, J V; Nieto, L M
2008-01-01
A new quantum architecture for multiplying signed integers is presented based on Booth's algorithm, which is well known in classical computation. It is shown how a quantum binary chain might be encoded by its flank changes, giving the final product in 2's-complement representation.
Accommodation of practical constraints by a linear programming jet select. [for Space Shuttle
Bergmann, E.; Weiler, P.
1983-01-01
An experimental spacecraft control system will be incorporated into the Space Shuttle flight software and exercised during a forthcoming mission to evaluate its performance and handling qualities. The control system incorporates a 'phase space' control law to generate rate change requests and a linear programming jet select to compute jet firings. Posed as a linear programming problem, jet selection must represent the rate change request as a linear combination of jet acceleration vectors where the coefficients are the jet firing times, while minimizing the fuel expended in satisfying that request. This problem is solved in real time using a revised Simplex algorithm. In order to implement the jet selection algorithm in the Shuttle flight control computer, it was modified to accommodate certain practical features of the Shuttle such as limited computer throughput, lengthy firing times, and a large number of control jets. To the authors' knowledge, this is the first such application of linear programming. It was made possible by careful consideration of the jet selection problem in terms of the properties of linear programming and the Simplex algorithm. These modifications to the jet select algorithm may by useful for the design of reaction controlled spacecraft.
Method for solving fully fuzzy linear programming problems using deviation degree measure
Institute of Scientific and Technical Information of China (English)
Haifang Cheng; Weilai Huang; Jianhu Cai
2013-01-01
A new ful y fuzzy linear programming (FFLP) prob-lem with fuzzy equality constraints is discussed. Using deviation degree measures, the FFLP problem is transformed into a crispδ-parametric linear programming (LP) problem. Giving the value of deviation degree in each constraint, the δ-fuzzy optimal so-lution of the FFLP problem can be obtained by solving this LP problem. An algorithm is also proposed to find a balance-fuzzy optimal solution between two goals in conflict: to improve the va-lues of the objective function and to decrease the values of the deviation degrees. A numerical example is solved to il ustrate the proposed method.
A novel recurrent neural network with finite-time convergence for linear programming.
Liu, Qingshan; Cao, Jinde; Chen, Guanrong
2010-11-01
In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.
Fault detection and initial state verification by linear programming for a class of Petri nets
Rachell, Traxon; Meyer, David G.
1992-01-01
The authors present an algorithmic approach to determining when the marking of a LSMG (live safe marked graph) or a LSFC (live safe free choice) net is in the set of live safe markings M. Hence, once the marking of a net is determined to be in M, then if at some time thereafter the marking of this net is determined not to be in M, this indicates a fault. It is shown how linear programming can be used to determine if m is an element of M. The worst-case computational complexity of each algorithm is bounded by the number of linear programs necessary to compute.
DEFF Research Database (Denmark)
Bresolin, Davide; Goranko, Valentin; Montanari, Angelo
2009-01-01
Interval temporal logics are based on interval structures over linearly (or partially) ordered domains, where time intervals, rather than time instants, are the primitive ontological entities. In this paper we introduce and study Right Propositional Neighborhood Logic over natural numbers...... with integer constraints for interval lengths, which is a propositional interval temporal logic featuring a modality for the 'right neighborhood' relation between intervals and explicit integer constraints for interval lengths. We prove that it has the bounded model property with respect to ultimately periodic...
BEAMPATH: a program library for beam dynamics simulation in linear accelerators
International Nuclear Information System (INIS)
Batygin, Y.K.
1992-01-01
A structured programming technique was used to develop software for space charge dominated beams investigation in linear accelerators. The method includes hierarchical program design using program independent modules and a flexible combination of modules to provide a most effective version of structure for every specific case of simulation. A modular program BEAMPATH was developed for 2D and 3D particle-in-cell simulation of beam dynamics in a structure containing RF gaps, radio-frequency quadrupoles (RFQ), multipole lenses, waveguides, bending magnets and solenoids. (author) 5 refs.; 2 figs
Cellular Automata Rules and Linear Numbers
Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika
2012-01-01
In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.
International Nuclear Information System (INIS)
Reibel, R.R.; Barber, Z.W.; Fischer, J.A.; Tian, M.; Babbitt, W.R.
2004-01-01
Linear sideband chirped (LSC) programming is introduced as a means of configuring spatial-spectral holographic gratings for optical coherent transient processors. Similar to linear frequency chirped programming, LSC programming allows the use of broadband integrated electro-optic phase modulators to produce chirps instead of using elaborate broadband chirped lasers. This approach has several advantages including the ability to use a stabilized laser for the optical carrier as well as stable, reproducible chirped optical signals when the modulator is driven digitally. Using LSC programming, we experimentally demonstrate broadband true-time delay as a proof of principle for the optical control of phased array radars. Here both cw phase modulated and binary phase shift keyed probe signals are true-time delayed with bandwidths of 1 GHz and delay resolutions better than 60 ps
Directory of Open Access Journals (Sweden)
Chandra Nagasuma R
2009-02-01
Full Text Available Abstract Background A genetic network can be represented as a directed graph in which a node corresponds to a gene and a directed edge specifies the direction of influence of one gene on another. The reconstruction of such networks from transcript profiling data remains an important yet challenging endeavor. A transcript profile specifies the abundances of many genes in a biological sample of interest. Prevailing strategies for learning the structure of a genetic network from high-dimensional transcript profiling data assume sparsity and linearity. Many methods consider relatively small directed graphs, inferring graphs with up to a few hundred nodes. This work examines large undirected graphs representations of genetic networks, graphs with many thousands of nodes where an undirected edge between two nodes does not indicate the direction of influence, and the problem of estimating the structure of such a sparse linear genetic network (SLGN from transcript profiling data. Results The structure learning task is cast as a sparse linear regression problem which is then posed as a LASSO (l1-constrained fitting problem and solved finally by formulating a Linear Program (LP. A bound on the Generalization Error of this approach is given in terms of the Leave-One-Out Error. The accuracy and utility of LP-SLGNs is assessed quantitatively and qualitatively using simulated and real data. The Dialogue for Reverse Engineering Assessments and Methods (DREAM initiative provides gold standard data sets and evaluation metrics that enable and facilitate the comparison of algorithms for deducing the structure of networks. The structures of LP-SLGNs estimated from the INSILICO1, INSILICO2 and INSILICO3 simulated DREAM2 data sets are comparable to those proposed by the first and/or second ranked teams in the DREAM2 competition. The structures of LP-SLGNs estimated from two published Saccharomyces cerevisae cell cycle transcript profiling data sets capture known
A novel approach based on preference-based index for interval bilevel linear programming problem
Aihong Ren; Yuping Wang; Xingsi Xue
2017-01-01
This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrain...
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.
The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.
Pang, Haotian; Liu, Han; Vanderbei, Robert
2014-02-01
We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.
Mass Optimization of Battery/Supercapacitors Hybrid Systems Based on a Linear Programming Approach
Fleury, Benoit; Labbe, Julien
2014-08-01
The objective of this paper is to show that, on a specific launcher-type mission profile, a 40% gain of mass is expected using a battery/supercapacitors active hybridization instead of a single battery solution. This result is based on the use of a linear programming optimization approach to perform the mass optimization of the hybrid power supply solution.
Optimal local dimming for LED-backlit LCD displays via linear programming
DEFF Research Database (Denmark)
Shu, Xiao; Wu, Xiaolin; Forchhammer, Søren
2012-01-01
and the attenuations of LCD pixels. The objective is to minimize the distortion in luminance reproduction due to the leakage of LCD and the coarse granularity of the LED lights. The optimization problem is formulated as one of linear programming, and both exact and approximate algorithms are proposed. Simulation...
Linear Programming Approaches for Power Savings in Software-defined Networks
Moghaddam, F.A.; Grosso, P.
2016-01-01
Software-defined networks have been proposed as a viable solution to decrease the power consumption of the networking component in data center networks. Still the question remains on which scheduling algorithms are most suited to achieve this goal. We propose 4 different linear programming
Velazquez-Marti, B.; Annevelink, E.
2009-01-01
Much bio-energy can be obtained from wood pruning operations in forests and fruit orchards. Several spatial studies have been carried out for biomass surveys, and many linear programming models have been developed to model the logistics of bio-energy chains. These models can assist in determining
Discounted semi-Markov decision processes : linear programming and policy iteration
Wessels, J.; van Nunen, J.A.E.E.
1975-01-01
For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal
Fuzzy chance constrained linear programming model for scrap charge optimization in steel production
DEFF Research Database (Denmark)
Rong, Aiying; Lahdelma, Risto
2008-01-01
the uncertainty based on fuzzy set theory and constrain the failure risk based on a possibility measure. Consequently, the scrap charge optimization problem is modeled as a fuzzy chance constrained linear programming problem. Since the constraints of the model mainly address the specification of the product...
Visual, Algebraic and Mixed Strategies in Visually Presented Linear Programming Problems.
Shama, Gilli; Dreyfus, Tommy
1994-01-01
Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.)…
Discounted semi-Markov decision processes : linear programming and policy iteration
Wessels, J.; van Nunen, J.A.E.E.
1974-01-01
For semi-Markov decision processes with discounted rewards we derive the well known results regarding the structure of optimal strategies (nonrandomized, stationary Markov strategies) and the standard algorithms (linear programming, policy iteration). Our analysis is completely based on a primal
Eric J. Gustafson; L. Jay Roberts; Larry A. Leefers
2006-01-01
Forest management planners require analytical tools to assess the effects of alternative strategies on the sometimes disparate benefits from forests such as timber production and wildlife habitat. We assessed the spatial patterns of alternative management strategies by linking two models that were developed for different purposes. We used a linear programming model (...
Nutrient density score of typical Indonesian foods and dietary formulation using linear programming.
Jati, Ignasius Radix A P; Vadivel, Vellingiri; Nöhr, Donatus; Biesalski, Hans Konrad
2012-12-01
The present research aimed to analyse the nutrient density (ND), nutrient adequacy score (NAS) and energy density (ED) of Indonesian foods and to formulate a balanced diet using linear programming. Data on typical Indonesian diets were obtained from the Indonesian Socio-Economic Survey 2008. ND was investigated for 122 Indonesian foods. NAS was calculated for single nutrients such as Fe, Zn and vitamin A. Correlation analysis was performed between ND and ED, as well as between monthly expenditure class and food consumption pattern in Indonesia. Linear programming calculations were performed using the software POM-QM for Windows version 3. Republic of Indonesia, 2008. Public households (n 68 800). Vegetables had the highest ND of the food groups, followed by animal-based foods, fruits and staple foods. Based on NAS, the top ten food items for each food group were identified. Most of the staple foods had high ED and contributed towards daily energy fulfillment, followed by animal-based foods, vegetables and fruits. Commodities with high ND tended to have low ED. Linear programming could be used to formulate a balanced diet. In contrast to staple foods, purchases of fruit, vegetables and animal-based foods increased with the rise of monthly expenditure. People should select food items based on ND and NAS to alleviate micronutrient deficiencies in Indonesia. Dietary formulation calculated using linear programming to achieve RDA levels for micronutrients could be recommended for different age groups of the Indonesian population.
Huitzing, Hiddo A.
2004-01-01
This article shows how set covering with item sampling (SCIS) methods can be used in the analysis and preanalysis of linear programming models for test assembly (LPTA). LPTA models can construct tests, fulfilling a set of constraints set by the test assembler. Sometimes, no solution to the LPTA model exists. The model is then said to be…
An Interactive Method to Solve Infeasibility in Linear Programming Test Assembling Models
Huitzing, Hiddo A.
2004-01-01
In optimal assembly of tests from item banks, linear programming (LP) models have proved to be very useful. Assembly by hand has become nearly impossible, but these LP techniques are able to find the best solutions, given the demands and needs of the test to be assembled and the specifics of the item bank from which it is assembled. However,…
Secret Message Decryption: Group Consulting Projects Using Matrices and Linear Programming
Gurski, Katharine F.
2009-01-01
We describe two short group projects for finite mathematics students that incorporate matrices and linear programming into fictional consulting requests presented as a letter to the students. The students are required to use mathematics to decrypt secret messages in one project involving matrix multiplication and inversion. The second project…
Research and evaluation of the effectiveness of e-learning in the case of linear programming
Directory of Open Access Journals (Sweden)
Ljiljana Miletić
2016-04-01
Full Text Available The paper evaluates the effectiveness of the e-learning approach to linear programming. The goal was to investigate how proper use of information and communication technologies (ICT and interactive learning helps to improve high school students’ understanding, learning and retention of advanced non-curriculum material. The hypothesis was that ICT and e-learning is helpful in teaching linear programming methods. In the first phase of the research, a module of lessons for linear programming (LP was created using the software package Loomen Moodle and other interactive software packages such as Geogebra. In the second phase, the LP module was taught as a short course to two groups of high school students. These two groups of students were second-grade students in a Croatian high school. In Class 1, the module was taught using ICT and e-learning, while the module was taught using classical methods in Class 2. The action research methodology was an integral part in delivering the course to both student groups. The sample student groups were carefully selected to ensure that differences in background knowledge and learning potential were statistically negligible. Relevant data was collected while delivering the course. Statistical analysis of the collected data showed that the student group using the e-learning method produced better results than the group using a classical learning method. These findings support previous results on the effectiveness of e-learning, and also establish a specific approach to e-learning in linear programming.
Korman, Jonathan; McCann, Robert J.; Seis, Christian
2013-01-01
A new approach to linear programming duality is proposed which relies on quadratic penalization, so that the relation between solutions to the penalized primal and dual problems becomes affine. This yields a new proof of Levin's duality theorem for capacity-constrained optimal transport as an infinite-dimensional application.
The effect of workload constraints in linear programming models for production planning
Jansen, M.M.; Kok, de A.G.; Adan, I.J.B.F.
2011-01-01
Linear programming (LP) models for production planning incorporate a model of the manufacturing system that is necessarily deterministic. Although these deterministic models are the current state-of-the-art, it should be recognized that they are used in an environment that is inherently stochastic.
A linear programming model of diet choice of free-living beavers
Nolet, BA; VanderVeer, PJ; Evers, EGJ; Ottenheim, MM
1995-01-01
Linear programming has been remarkably successful in predicting the diet choice of generalist herbivores. We used this technique to test the diet choice of free-living beavers (Castor fiber) in the Biesbosch (The Netherlands) under different Foraging goals, i.e. maximization of intake of energy,
Cooke, C. H.
1975-01-01
STICAP (Stiff Circuit Analysis Program) is a FORTRAN 4 computer program written for the CDC-6400-6600 computer series and SCOPE 3.0 operating system. It provides the circuit analyst a tool for automatically computing the transient responses and frequency responses of large linear time invariant networks, both stiff and nonstiff (algorithms and numerical integration techniques are described). The circuit description and user's program input language is engineer-oriented, making simple the task of using the program. Engineering theories underlying STICAP are examined. A user's manual is included which explains user interaction with the program and gives results of typical circuit design applications. Also, the program structure from a systems programmer's viewpoint is depicted and flow charts and other software documentation are given.
Dyehouse, Melissa; Bennett, Deborah; Harbor, Jon; Childress, Amy; Dark, Melissa
2009-01-01
Logic models are based on linear relationships between program resources, activities, and outcomes, and have been used widely to support both program development and evaluation. While useful in describing some programs, the linear nature of the logic model makes it difficult to capture the complex relationships within larger, multifaceted…
International Nuclear Information System (INIS)
Aref'ev, A.V.; Blokhov, M.V.; Gerasimov, V.F.
1981-01-01
A program of physical investigations and the corresponding requirements to accelerated beam parameters are discussed in brief. The state and working capacity of separate units and the accelerator as a whole for the 8-year operating period are analyzed. The aim and principal program points of linear electron accelerator modernization are defined. The program of accelerator modernization assumes: electron beam energy increase up to 100-120 MeV; mounting of three additional accelerating sections; clystron efficiency increase; development of a highly reliable modulator; stabilized power supply sources; a system of synchronous start-up; a focusing system; a beam separation system and etc [ru
Linear programming models and methods of matrix games with payoffs of triangular fuzzy numbers
Li, Deng-Feng
2016-01-01
This book addresses two-person zero-sum finite games in which the payoffs in any situation are expressed with fuzzy numbers. The purpose of this book is to develop a suite of effective and efficient linear programming models and methods for solving matrix games with payoffs in fuzzy numbers. Divided into six chapters, it discusses the concepts of solutions of matrix games with payoffs of intervals, along with their linear programming models and methods. Furthermore, it is directly relevant to the research field of matrix games under uncertain economic management. The book offers a valuable resource for readers involved in theoretical research and practical applications from a range of different fields including game theory, operational research, management science, fuzzy mathematical programming, fuzzy mathematics, industrial engineering, business and social economics. .
User's Guide to the Weighted-Multiple-Linear Regression Program (WREG version 1.0)
Eng, Ken; Chen, Yin-Yu; Kiang, Julie.E.
2009-01-01
Streamflow is not measured at every location in a stream network. Yet hydrologists, State and local agencies, and the general public still seek to know streamflow characteristics, such as mean annual flow or flood flows with different exceedance probabilities, at ungaged basins. The goals of this guide are to introduce and familiarize the user with the weighted multiple-linear regression (WREG) program, and to also provide the theoretical background for program features. The program is intended to be used to develop a regional estimation equation for streamflow characteristics that can be applied at an ungaged basin, or to improve the corresponding estimate at continuous-record streamflow gages with short records. The regional estimation equation results from a multiple-linear regression that relates the observable basin characteristics, such as drainage area, to streamflow characteristics.
SLFP: a stochastic linear fractional programming approach for sustainable waste management.
Zhu, H; Huang, G H
2011-12-01
A stochastic linear fractional programming (SLFP) approach is developed for supporting sustainable municipal solid waste management under uncertainty. The SLFP method can solve ratio optimization problems associated with random information, where chance-constrained programming is integrated into a linear fractional programming framework. It has advantages in: (1) comparing objectives of two aspects, (2) reflecting system efficiency, (3) dealing with uncertainty expressed as probability distributions, and (4) providing optimal-ratio solutions under different system-reliability conditions. The method is applied to a case study of waste flow allocation within a municipal solid waste (MSW) management system. The obtained solutions are useful for identifying sustainable MSW management schemes with maximized system efficiency under various constraint-violation risks. The results indicate that SLFP can support in-depth analysis of the interrelationships among system efficiency, system cost and system-failure risk. Copyright © 2011 Elsevier Ltd. All rights reserved.
What Else Is Decidable about Integer Arrays?
Habermehl, Peter; Iosif, Radu; Vojnar, Tomáš
2008-01-01
International audience; We introduce a new decidable logic for reasoning about infinite arrays of integers. The logic is in the ∃ * ∀ * first-order fragment and allows (1) Presburger constraints on existentially quantified variables, (2) difference constraints as well as periodicity constraints on universally quantified indices, and (3) difference constraints on values. In particular, using our logic, one can express constraints on consecutive elements of arrays (e.g. ∀i. 0 ≤ i < n → a[i + 1]...
Fractional and integer charges from Levinson's theorem
International Nuclear Information System (INIS)
Farhi, E.; Graham, N.; Jaffe, R.L.; Weigel, H.
2001-01-01
We compute fractional and integer fermion quantum numbers of static background field configurations using phase shifts and Levinson's theorem. By extending fermionic scattering theory to arbitrary dimensions, we implement dimensional regularization in a (1+1)-dimensional gauge theory. We demonstrate that this regularization procedure automatically eliminates the anomaly in the vector current that a naive regulator would produce. We also apply these techniques to bag models in one and three dimensions
Integer factoring and modular square roots
Czech Academy of Sciences Publication Activity Database
Jeřábek, Emil
2016-01-01
Roč. 82, č. 2 (2016), s. 380-394 ISSN 0022-0000 R&D Projects: GA AV ČR IAA100190902; GA ČR GBP202/12/G061 Institutional support: RVO:67985840 Keywords : integer factoring * quadratic residue * PPA Subject RIV: BA - General Mathematics Impact factor: 1.678, year: 2016 http://www.sciencedirect.com/science/article/pii/S0022000015000768
On the price of integer charge quarks
International Nuclear Information System (INIS)
Okun, L.B.; Voloshin, M.B.; Zakharov, V.I.
1979-01-01
Implication of the integer charge quark (ICQ) model with a broken SU(3)xU(1) gauge symmetry for interactions in the leptonic sector were discussed. In this model there should be very large deviations of e + e - →μ + μ - annihilation processes in the GeV region from the standard QED behaviour. Such deviations seem to be completely excluded by existing data. Therefore it is concluded that the ICQ model is ruled out
Quadratic Sieve integer factorization using Hadoop
Ghebregiorgish, Semere Tsehaye
2012-01-01
Master's thesis in Computer Science Integer factorization problem is one of the most important parts in the world of cryptography. The security of the widely-used public-key cryptographic algorithm, RSA [1], and the Blum Blum Shub cryptographic pseudorandom number generator [2] heavily depend on the presumed difficulty of factoring a number to its prime constituents. As the size of the number to be factored gets larger, the difficulty of the problem increases enormously. Thi...
Guo, Sangang
2017-09-01
There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.
Stability of multi-objective bi-level linear programming problems under fuzziness
Directory of Open Access Journals (Sweden)
Abo-Sinna Mahmoud A.
2013-01-01
Full Text Available This paper deals with multi-objective bi-level linear programming problems under fuzzy environment. In the proposed method, tentative solutions are obtained and evaluated by using the partial information on preference of the decision-makers at each level. The existing results concerning the qualitative analysis of some basic notions in parametric linear programming problems are reformulated to study the stability of multi-objective bi-level linear programming problems. An algorithm for obtaining any subset of the parametric space, which has the same corresponding Pareto optimal solution, is presented. Also, this paper established the model for the supply-demand interaction in the age of electronic commerce (EC. First of all, the study uses the individual objectives of both parties as the foundation of the supply-demand interaction. Subsequently, it divides the interaction, in the age of electronic commerce, into the following two classifications: (i Market transactions, with the primary focus on the supply demand relationship in the marketplace; and (ii Information service, with the primary focus on the provider and the user of information service. By applying the bi-level programming technique of interaction process, the study will develop an analytical process to explain how supply-demand interaction achieves a compromise or why the process fails. Finally, a numerical example of information service is provided for the sake of illustration.
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
The use of linear programming in optimization of HDR implant dose distributions
International Nuclear Information System (INIS)
Jozsef, Gabor; Streeter, Oscar E.; Astrahan, Melvin A.
2003-01-01
The introduction of high dose rate brachytherapy enabled optimization of dose distributions to be used on a routine basis. The objective of optimization is to homogenize the dose distribution within the implant while simultaneously satisfying dose constraints on certain points. This is accomplished by varying the time the source dwells at different locations. As the dose at any point is a linear function of the dwell times, a linear programming approach seems to be a natural choice. The dose constraints are inherently linear inequalities. Homogeneity requirements are linearized by minimizing the maximum deviation of the doses at points inside the implant from a prescribed dose. The revised simplex method was applied for the solution of this linear programming problem. In the homogenization process the possible source locations were chosen as optimization points. To avoid the problem of the singular value of the dose at a source location from the source itself we define the 'self-contribution' as the dose at a small distance from the source. The effect of varying this distance is discussed. Test cases were optimized for planar, biplanar and cylindrical implants. A semi-irregular, fan-like implant with diverging needles was also investigated. Mean central dose calculation based on 3D Delaunay-triangulation of the source locations was used to evaluate the dose distributions. The optimization method resulted in homogeneous distributions (for brachytherapy). Additional dose constraints--when applied--were satisfied. The method is flexible enough to include other linear constraints such as the inclusion of the centroids of the Delaunay-triangulation for homogenization, or limiting the maximum allowable dwell time
Linear programming to build food-based dietary guidelines: Romanian food baskets
DEFF Research Database (Denmark)
Parlesak, Alexandr; Robertson, Aileen; Hondru, Gabriela
approach using linear programming methodology to design national dietary recommendations which aim to prevent both NCDs and micronutrient deficiencies and still be affordable by low income groups. This new approach is applied within the context of food availability in Romania in 2014. Eating the same food...... every day is unrealistic and too monotonous to be maintained, so this novel approach is used to select a wide range of diverse foods that can be recommended for a period of up to, for example, one month. The following are the key findings of this report. • The simplest version of the Romanian food.......65 lei (~€ 4.46) for a day. • Key nutrients, primarily vitamin D, calcium, potassium and iron, were found to control the overall price. • The least expensive basket (one day’s rations) is monotonous and the linear programming approach is used to select a wide range of foods that can be recommended...
International Nuclear Information System (INIS)
Shimizu, Yoshiaki
1981-01-01
A mathematical procedure is proposed to make a radioactive waste management plan comprehensively. Since such planning is relevant to some different goals in management, decision making has to be formulated as a multiobjective optimization problem. A mathematical programming method was introduced to make a decision through an interactive manner which enables us to assess the preference of decision maker step by step among the conflicting objectives. The reference system taken as an example is the radioactive waste management system at the Research Reactor Institute of Kyoto University (KUR). Its linear model was built based on the experience in the actual management at KUR. The best-compromise model was then formulated as a multiobjective linear programming by the aid of the computational analysis through a conventional optimization. It was shown from the numerical results that the proposed approach could provide some useful informations to make an actual management plan. (author)
Visualizing measurement for 3D smooth density distributions by means of linear programming
International Nuclear Information System (INIS)
Tayama, Norio; Yang, Xue-dong
1994-01-01
This paper is concerned with a theoretical possibility of a new visualizing measurement method based on an optimum 3D reconstruction from a few selected projections. A theory of optimum 3D reconstruction by a linear programming is discussed, utilizing a few projections for sampled 3D smooth-density-distribution model which satisfies the condition of the 3D sampling theorem. First by use of the sampling theorem, it is shown that we can set up simultaneous simple equations which corresponds to the case of the parallel beams. Then we solve the simultaneous simple equations by means of linear programming algorithm, and we can get an optimum 3D density distribution images with minimum error in the reconstruction. The results of computer simulation with the algorithm are presented. (author)
Ren, Jingzheng; Dong, Liang; Sun, Lu; Goodsite, Michael Evan; Tan, Shiyu; Dong, Lichun
2015-01-01
The aim of this work was to develop a model for optimizing the life cycle cost of biofuel supply chain under uncertainties. Multiple agriculture zones, multiple transportation modes for the transport of grain and biofuel, multiple biofuel plants, and multiple market centers were considered in this model, and the price of the resources, the yield of grain and the market demands were regarded as interval numbers instead of constants. An interval linear programming was developed, and a method for solving interval linear programming was presented. An illustrative case was studied by the proposed model, and the results showed that the proposed model is feasible for designing biofuel supply chain under uncertainties. Copyright © 2015 Elsevier Ltd. All rights reserved.
Refining and end use study of coal liquids II - linear programming analysis
Energy Technology Data Exchange (ETDEWEB)
Lowe, C.; Tam, S.
1995-12-31
A DOE-funded study is underway to determine the optimum refinery processing schemes for producing transportation fuels that will meet CAAA regulations from direct and indirect coal liquids. The study consists of three major parts: pilot plant testing of critical upgrading processes, linear programming analysis of different processing schemes, and engine emission testing of final products. Currently, fractions of a direct coal liquid produced form bituminous coal are being tested in sequence of pilot plant upgrading processes. This work is discussed in a separate paper. The linear programming model, which is the subject of this paper, has been completed for the petroleum refinery and is being modified to handle coal liquids based on the pilot plant test results. Preliminary coal liquid evaluation studies indicate that, if a refinery expansion scenario is adopted, then the marginal value of the coal liquid (over the base petroleum crude) is $3-4/bbl.
International Nuclear Information System (INIS)
Romeijn, H Edwin; Ahuja, Ravindra K; Dempsey, James F; Kumar, Arvind; Li, Jonathan G
2003-01-01
We present a novel linear programming (LP) based approach for efficiently solving the intensity modulated radiation therapy (IMRT) fluence-map optimization (FMO) problem to global optimality. Our model overcomes the apparent limitations of a linear-programming approach by approximating any convex objective function by a piecewise linear convex function. This approach allows us to retain the flexibility offered by general convex objective functions, while allowing us to formulate the FMO problem as a LP problem. In addition, a novel type of partial-volume constraint that bounds the tail averages of the differential dose-volume histograms of structures is imposed while retaining linearity as an alternative approach to improve dose homogeneity in the target volumes, and to attempt to spare as many critical structures as possible. The goal of this work is to develop a very rapid global optimization approach that finds high quality dose distributions. Implementation of this model has demonstrated excellent results. We found globally optimal solutions for eight 7-beam head-and-neck cases in less than 3 min of computational time on a single processor personal computer without the use of partial-volume constraints. Adding such constraints increased the running times by a factor of 2-3, but improved the sparing of critical structures. All cases demonstrated excellent target coverage (>95%), target homogeneity (<10% overdosing and <7% underdosing) and organ sparing using at least one of the two models
Directory of Open Access Journals (Sweden)
Weihua Jin
2013-01-01
Full Text Available This paper proposes a genetic-algorithms-based approach as an all-purpose problem-solving method for operation programming problems under uncertainty. The proposed method was applied for management of a municipal solid waste treatment system. Compared to the traditional interactive binary analysis, this approach has fewer limitations and is able to reduce the complexity in solving the inexact linear programming problems and inexact quadratic programming problems. The implementation of this approach was performed using the Genetic Algorithm Solver of MATLAB (trademark of MathWorks. The paper explains the genetic-algorithms-based method and presents details on the computation procedures for each type of inexact operation programming problems. A comparison of the results generated by the proposed method based on genetic algorithms with those produced by the traditional interactive binary analysis method is also presented.
DEFF Research Database (Denmark)
Cetin, Bilge Kartal; Prasad, Neeli R.; Prasad, Ramjee
2011-01-01
In wireless sensor networks, one of the key challenge is to achieve minimum energy consumption in order to maximize network lifetime. In fact, lifetime depends on many parameters: the topology of the sensor network, the data aggregation regime in the network, the channel access schemes, the routing...... protocols, and the energy model for transmission. In this paper, we tackle the routing challenge for maximum lifetime of the sensor network. We introduce a novel linear programming approach to the maximum lifetime routing problem. To the best of our knowledge, this is the first mathematical programming...
A new neural network model for solving random interval linear programming problems.
Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza
2017-05-01
This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.
CiOpt: a program for optimization of the frequency response of linear circuits
Miró Sans, Joan Maria; Palà Schönwälder, Pere
1991-01-01
An interactive personal-computer program for optimizing the frequency response of linear lumped circuits (CiOpt) is presented. CiOpt has proved to be an efficient tool in improving designs where the inclusion of more accurate device models distorts the desired frequency response, as well as in device modeling. The outputs of CiOpt are the element values which best match the obtained and the desired frequency response. The optimization algorithms used (the Fletcher-Powell and Newton's methods,...
Roslee Rajikan; Nurul Izza Ahmad Zaidi; Siti Masitah Elias; Suzana Shahar; Zahara Abd Manaf; Noor Aini Md Yusoff
2017-01-01
Differences in socioeconomic profile may influences healthy food choices, particularly among individuals with low socioeconomic status. Thus, high-energy dense foods become the preferences compared to high nutritional content foods due to their cheaper price. The present study aims to develop healthy and palatable diet at the minimum cost based on Malaysian Dietary Guidelines 2010 and Recommended Nutrient Intake 2005 via linear programming. A total of 96 female adults from low socioeconomic f...
A linear programming approach to characterizing norm bounded uncertainty from experimental data
Scheid, R. E.; Bayard, D. S.; Yam, Y.
1991-01-01
The linear programming spectral overbounding and factorization (LPSOF) algorithm, an algorithm for finding a minimum phase transfer function of specified order whose magnitude tightly overbounds a specified nonparametric function of frequency, is introduced. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation).