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Multiobjective Linear Programming
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Book Synopsis Multiobjective Linear Programming by : Dinh The Luc
Download or read book Multiobjective Linear Programming written by Dinh The Luc and published by Springer. This book was released on 2015-07-31 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to the field of multiobjective optimization through problems with simple structures, namely those in which the objective function and constraints are linear. Fundamental notions as well as state-of-the-art advances are presented in a comprehensive way and illustrated with the help of numerous examples. Three of the most popular methods for solving multiobjective linear problems are explained, and exercises are provided at the end of each chapter, helping students to grasp and apply key concepts and methods to more complex problems. The book was motivated by the fact that the majority of the practical problems we encounter in management science, engineering or operations research involve conflicting criteria and therefore it is more convenient to formulate them as multicriteria optimization models, the solution concepts and methods of which cannot be treated using traditional mathematical programming approaches.
Book Synopsis Linear Multiobjective Programming by : M. Zeleny
Download or read book Linear Multiobjective Programming written by M. Zeleny and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1.1. The origin of the multiobjective problem and a short historical review The continuing search for a discovery of theories, tools and c- cepts applicable to decision-making processes has increased the complexity of problems eligible for analytical treatment. One of the more pertinent criticisms of current decision-making theory and practice is directed against the traditional approximation of multiple goal behavior of men and organizations by single, technically-convenient criterion. Reins- tementof the role of human judgment in more realistic, multiple goal se,ttings has been one of the ma~or recent developments in the literature. Consider the following simplified problem. There is a large number of people to be transported daily between two industrial areas and their adjacent residential areas. Given some budgetary and technological c- straints we would like to determine optimal transportation modes as well as the number of units of each to be scheduled for service. What is the optimal solution? Are we interested in the cheapest transportation? Do we want the fastest, the safest, the cleanest, the most profitable, the most durable? There are many criteria which are to be considered: travel times, consumer's cost, construction cost, operating cost, expected fatalities and injuries, probability of delays, etc.
Book Synopsis Multiobjective Linear and Integer Programming by : Carlos Henggeler Antunes
Download or read book Multiobjective Linear and Integer Programming written by Carlos Henggeler Antunes and published by Springer. This book was released on 2016-04-08 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book opens the door to multiobjective optimization for students in fields such as engineering, management, economics and applied mathematics. It offers a comprehensive introduction to multiobjective optimization, with a primary emphasis on multiobjective linear programming and multiobjective integer/mixed integer programming. A didactic book, it is mainly intended for undergraduate and graduate students, but can also be useful for researchers and practitioners. Further, it is accompanied by an interactive software package - developed by the authors for Windows platforms - which can be used for teaching and decision-making support purposes in multiobjective linear programming problems. Thus, besides the textbook’s coverage of the essential concepts, theory and methods, complemented with illustrative examples and exercises, the computational tool enables students to experiment and enhance their technical skills, as well as to capture the essential characteristics of real-world problems.
Book Synopsis Nonlinear Multiobjective Optimization by : Kaisa Miettinen
Download or read book Nonlinear Multiobjective Optimization written by Kaisa Miettinen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Problems with multiple objectives and criteria are generally known as multiple criteria optimization or multiple criteria decision-making (MCDM) problems. So far, these types of problems have typically been modelled and solved by means of linear programming. However, many real-life phenomena are of a nonlinear nature, which is why we need tools for nonlinear programming capable of handling several conflicting or incommensurable objectives. In this case, methods of traditional single objective optimization and linear programming are not enough; we need new ways of thinking, new concepts, and new methods - nonlinear multiobjective optimization. Nonlinear Multiobjective Optimization provides an extensive, up-to-date, self-contained and consistent survey, review of the literature and of the state of the art on nonlinear (deterministic) multiobjective optimization, its methods, its theory and its background. The amount of literature on multiobjective optimization is immense. The treatment in this book is based on approximately 1500 publications in English printed mainly after the year 1980. Problems related to real-life applications often contain irregularities and nonsmoothnesses. The treatment of nondifferentiable multiobjective optimization in the literature is rather rare. For this reason, this book contains material about the possibilities, background, theory and methods of nondifferentiable multiobjective optimization as well. This book is intended for both researchers and students in the areas of (applied) mathematics, engineering, economics, operations research and management science; it is meant for both professionals and practitioners in many different fields of application. The intention has been to provide a consistent summary that may help in selecting an appropriate method for the problem to be solved. It is hoped the extensive bibliography will be of value to researchers.
Book Synopsis Multiobjective Programming and Planning by : Jared L. Cohon
Download or read book Multiobjective Programming and Planning written by Jared L. Cohon and published by Courier Corporation. This book was released on 2013-01-18 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text takes a broad view of multiobjective programming, emphasizing the methods most useful for continuous problems. It reviews methods in the context of public decision-making problems. 1978 edition.
Book Synopsis Multi-Objective Combinatorial Optimization Problems and Solution Methods by : Mehdi Toloo
Download or read book Multi-Objective Combinatorial Optimization Problems and Solution Methods written by Mehdi Toloo and published by Academic Press. This book was released on 2022-02-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Objective Combinatorial Optimization Problems and Solution Methods discusses the results of a recent multi-objective combinatorial optimization achievement that considered metaheuristic, mathematical programming, heuristic, hyper heuristic and hybrid approaches. In other words, the book presents various multi-objective combinatorial optimization issues that may benefit from different methods in theory and practice. Combinatorial optimization problems appear in a wide range of applications in operations research, engineering, biological sciences and computer science, hence many optimization approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic and algebraic techniques. This book covers this important topic as computational optimization has become increasingly popular as design optimization and its applications in engineering and industry have become ever more important due to more stringent design requirements in modern engineering practice. Presents a collection of the most up-to-date research, providing a complete overview of multi-objective combinatorial optimization problems and applications Introduces new approaches to handle different engineering and science problems, providing the field with a collection of related research not already covered in the primary literature Demonstrates the efficiency and power of the various algorithms, problems and solutions, including numerous examples that illustrate concepts and algorithms
Book Synopsis Multiobjective Optimization: Behavioral and Computational Considerations by : Jeffrey L. Ringuest
Download or read book Multiobjective Optimization: Behavioral and Computational Considerations written by Jeffrey L. Ringuest and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Throughout the development of mathematical programming researchers have paid great attention to problems that are described by a single objective that can only be achieved subject to satisfying a set of restrictions or constraints. Recently, it has been recognized that the use of a single objective limits the applicability of In reality, many multiobjective mathematical programming models. situations exist and frequently these mUltiple objectives are in direct conflict. Research on multiobjective problems can be broken down into two broad categories: multiobjective optimization and multicriterion decision theory. Multiobjective optimization models are based on techniques such as linear programming. In general, the multiobjective optimization problem can be defined as finding a feasible alternative that yields the most preferred set of values for the objective functions. This problem differs from a single objective because subjective methods are required to determine which alternative is most preferred. A body of literature parallel to that m multiobjective optimization has been developing in the area of multicriterion decision theory. These models are based on classical decision analysis, particularly utility theory. One focus of this research has been the development and testing of procedures for estimating multiattribute utility functions that are consistent with rational decision maker behavior. A utility function provides a model of a decision maker's choice among alternatives. This literature is directly xii MULTIOBJECTIVE OPTIMIZATION applicable to multiobjective optimization and provides much needed insight into the subjective character of that problem.
Book Synopsis Fuzzy Sets and Interactive Multiobjective Optimization by : Masatoshi Sakawa
Download or read book Fuzzy Sets and Interactive Multiobjective Optimization written by Masatoshi Sakawa and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main characteristics of the real-world decision-making problems facing humans today are multidimensional and have multiple objectives including eco nomic, environmental, social, and technical ones. Hence, it seems natural that the consideration of many objectives in the actual decision-making process re quires multiobjective approaches rather than single-objective. One ofthe major systems-analytic multiobjective approaches to decision-making under constraints is multiobjective optimization as a generalization of traditional single-objective optimization. Although multiobjective optimization problems differ from single objective optimization problems only in the plurality of objective functions, it is significant to realize that multiple objectives are often noncom mensurable and conflict with each other in multiobjective optimization problems. With this ob servation, in multiobjective optimization, the notion of Pareto optimality or effi ciency has been introduced instead of the optimality concept for single-objective optimization. However, decisions with Pareto optimality or efficiency are not uniquely determined; the final decision must be selected from among the set of Pareto optimal or efficient solutions. Therefore, the question is, how does one find the preferred point as a compromise or satisficing solution with rational pro cedure? This is the starting point of multiobjective optimization. To be more specific, the aim is to determine how one derives a compromise or satisficing so lution of a decision maker (DM), which well represents the subjective judgments, from a Pareto optimal or an efficient solution set.
Book Synopsis Fuzzy Stochastic Multiobjective Programming by : Masatoshi Sakawa
Download or read book Fuzzy Stochastic Multiobjective Programming written by Masatoshi Sakawa and published by Springer Science & Business Media. This book was released on 2011-02-03 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although studies on multiobjective mathematical programming under uncertainty have been accumulated and several books on multiobjective mathematical programming under uncertainty have been published (e.g., Stancu-Minasian (1984); Slowinski and Teghem (1990); Sakawa (1993); Lai and Hwang (1994); Sakawa (2000)), there seems to be no book which concerns both randomness of events related to environments and fuzziness of human judgments simultaneously in multiobjective decision making problems. In this book, the authors are concerned with introducing the latest advances in the field of multiobjective optimization under both fuzziness and randomness on the basis of the authors’ continuing research works. Special stress is placed on interactive decision making aspects of fuzzy stochastic multiobjective programming for human-centered systems under uncertainty in most realistic situations when dealing with both fuzziness and randomness. Organization of each chapter is briefly summarized as follows: Chapter 2 is devoted to mathematical preliminaries, which will be used throughout the remainder of the book. Starting with basic notions and methods of multiobjective programming, interactive fuzzy multiobjective programming as well as fuzzy multiobjective programming is outlined. In Chapter 3, by considering the imprecision of decision maker’s (DM’s) judgment for stochastic objective functions and/or constraints in multiobjective problems, fuzzy multiobjective stochastic programming is developed. In Chapter 4, through the consideration of not only the randomness of parameters involved in objective functions and/or constraints but also the experts’ ambiguous understanding of the realized values of the random parameters, multiobjective programming problems with fuzzy random variables are formulated. In Chapter 5, for resolving conflict of decision making problems in hierarchical managerial or public organizations where there exist two DMs who have different priorities in making decisions, two-level programming problems are discussed. Finally, Chapter 6 outlines some future research directions.
Book Synopsis Multiobjective Optimization by : Jürgen Branke
Download or read book Multiobjective Optimization written by Jürgen Branke and published by Springer. This book was released on 2008-10-18 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiobjective optimization deals with solving problems having not only one, but multiple, often conflicting, criteria. Such problems can arise in practically every field of science, engineering and business, and the need for efficient and reliable solution methods is increasing. The task is challenging due to the fact that, instead of a single optimal solution, multiobjective optimization results in a number of solutions with different trade-offs among criteria, also known as Pareto optimal or efficient solutions. Hence, a decision maker is needed to provide additional preference information and to identify the most satisfactory solution. Depending on the paradigm used, such information may be introduced before, during, or after the optimization process. Clearly, research and application in multiobjective optimization involve expertise in optimization as well as in decision support. This state-of-the-art survey originates from the International Seminar on Practical Approaches to Multiobjective Optimization, held in Dagstuhl Castle, Germany, in December 2006, which brought together leading experts from various contemporary multiobjective optimization fields, including evolutionary multiobjective optimization (EMO), multiple criteria decision making (MCDM) and multiple criteria decision aiding (MCDA). This book gives a unique and detailed account of the current status of research and applications in the field of multiobjective optimization. It contains 16 chapters grouped in the following 5 thematic sections: Basics on Multiobjective Optimization; Recent Interactive and Preference-Based Approaches; Visualization of Solutions; Modelling, Implementation and Applications; and Quality Assessment, Learning, and Future Challenges.
Book Synopsis Multi-Objective Optimization in Theory and Practice I: Classical Methods by : Andre A. Keller
Download or read book Multi-Objective Optimization in Theory and Practice I: Classical Methods written by Andre A. Keller and published by Bentham Science Publishers. This book was released on 2017-12-13 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multi-Objective Optimization in Theory and Practice is a traditional two-part approach to solving multi-objective optimization (MOO) problems namely the use of classical methods and evolutionary algorithms. This first book is devoted to classical methods including the extended simplex method by Zeleny and preference-based techniques. This part covers three main topics through nine chapters. The first topic focuses on the design of such MOO problems, their complexities including nonlinearities and uncertainties, and optimality theory. The second topic introduces the founding solving methods including the extended simplex method to linear MOO problems and weighting objective methods. The third topic deals with particular structures of MOO problems, such as mixed-integer programming, hierarchical programming, fuzzy logic programming, and bimatrix games. Multi-Objective Optimization in Theory and Practice is a user-friendly book with detailed, illustrated calculations, examples, test functions, and small-size applications in Mathematica® (among other mathematical packages) and from scholarly literature. It is an essential handbook for students and teachers involved in advanced optimization courses in engineering, information science, and mathematics degree programs.
Book Synopsis Multiple Objective and Goal Programming by : Tadeusz Trzaskalik
Download or read book Multiple Objective and Goal Programming written by Tadeusz Trzaskalik and published by Springer Science & Business Media. This book was released on 2013-06-05 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is dedicated to multi-objective methods in decision making. The first part which is devoted to theoretical aspects, covers a broad range of multi-objective methods such as multiple linear programming, vector optimisation, fuzzy goal programming, data envelopment analysis, game theory, and dynamic programming. The reader who is interested in practical applications, will find in the remaining parts a variety of approaches applied in numerous fields including production planning, logistics, marketing, and finance.
Book Synopsis Advances in Operational Research in the Balkans by : Nenad Mladenović
Download or read book Advances in Operational Research in the Balkans written by Nenad Mladenović and published by Springer. This book was released on 2019-07-24 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents recent theoretical and practical advances in operational research (OR). The papers focus on a number of key areas including combinatorial optimization, integer programming, heuristics, and mathematical programming. In addition, this volume highlights OR applications in different areas such as financial decision making, marketing, e-business, project management, scheduling, traffic and transportation. The chapters are based on papers presented at the 13th Balkan Conference on Operations Research (BALCOR). BALCOR is an established biennial conference. The selected papers promote international collaboration among researchers and practitioners, with a particular focus on the Balkan countries.
Book Synopsis Operations Research. Optimization With Matlab. Multiobjective, Quadratic and Mixed Programming by : Perez C.
Download or read book Operations Research. Optimization With Matlab. Multiobjective, Quadratic and Mixed Programming written by Perez C. and published by . This book was released on 2017-08-16 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. Optimization includes finding "best available" values of some objective function given a defined domain (or input), including a variety of different types of objective functions and different types of domains.Adding more than one objective to an optimization problem adds complexity. For example, to optimize a structural design, one would desire a design that is both light and rigid. When two objectives conflict, a trade-off must be created. There may be one lightest design, one stiffest design, and an infinite number of designs that are some compromise of weight and rigidity. The set of trade-off designs that cannot be improved upon according to one criterion without hurting another criterion is known as the Pareto set. The curve created plotting weight against stiffness of the best designs is known as the Pareto frontier.A design is judged to be "Pareto optimal" (equivalently, "Pareto efficient" or in the Pareto set) if it is not dominated by any other design: If it is worse than another design in some respects and no better in any respect, then it is dominated and is not Pareto optimal. The choice among "Pareto optimal" solutions to determine the "favorite solution" is delegated to the decision maker. In other words, defining the problem as multi-objective optimization signals that some information is missing: desirable objectives are given but combinations of them are not rated relative to each other. In some cases, the missing information can be derived by interactive sessions with the decision maker.Multi-objective optimization problems have been generalized further into vector optimization problems where the (partial) ordering is no longer given by the Pareto ordering.Optimization problems are often multi-modal; that is, they possess multiple good solutions. They could all be globally good or there could be a mix of globally good and locally good solutions. Obtaining all (or at least some of) the multiple solutions is the goal of a multi-modal optimizer.Classical optimization techniques due to their iterative approach do not perform satisfactorily when they are used to obtain multiple solutions, since it is not guaranteed that different solutions will be obtained even with different starting points in multiple runs of the algorithm. Evolutionary algorithms, however, are a very popular approach to obtain multiple solutions in a multi-modal optimization task.This book develops the following topics:* "Multiobjective Optimization Algorithms" * "Using fminimax with a Simulink Model" * "Signal Processing Using fgoalattain" * "Generate and Plot a Pareto Front" * "Linear Programming Algorithms" * "Maximize Long-Term Investments Using Linear Programming" * "Mixed-Integer Linear Programming Algorithms" * "Tuning Integer Linear Programming" * "Mixed-Integer Linear Programming Basics" * "Optimal Dispatch of Power Generators" * "Mixed-Integer Quadratic Programming Portfolio Optimization" * "Quadratic Programming Algorithms"* "Quadratic Minimization with Bound Constraints" * "Quadratic Minimization with Dense, Structured Hessian"* "Large Sparse Quadratic Program with Interior Point Algorithm" * "Least-Squares (Model Fitting) Algorithms" * "lsqnonlin with a Simulink Model" * "Nonlinear Least Squares With and Without Jacobian" * "Linear Least Squares with Bound Constraints" * "Optimization App with the lsqlin Solver" * "Maximize Long-Term Investments Using Linear Programming" * "Jacobian Multiply Function with Linear Least Squares" * "Nonlinear Curve Fitting with lsqcurvefit" * "Fit a Model to Complex-Valued Data" * "Systems of Equations" * "Nonlinear Equations with Analytic Jacobian" * "Nonlinear Equations with Jacobian" * "Nonlinear Equations with Jacobian Sparsity Pattern"* "Nonlinear Systems with Constraints" * "Parallel Computing for Optimization"
Book Synopsis Multi-Objective Programming and Goal Programming by : Tetsuzo Tanino
Download or read book Multi-Objective Programming and Goal Programming written by Tetsuzo Tanino and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the Fifth International Conference on Multi-Objective Programming and Goal Programming: Theory & Appli cations (MOPGP'02) held in Nara, Japan on June 4-7, 2002. Eighty-two people from 16 countries attended the conference and 78 papers (including 9 plenary talks) were presented. MOPGP is an international conference within which researchers and prac titioners can meet and learn from each other about the recent development in multi-objective programming and goal programming. The participants are from different disciplines such as Optimization, Operations Research, Math ematical Programming and Multi-Criteria Decision Aid, whose common in terest is in multi-objective analysis. The first MOPGP Conference was held at Portsmouth, United Kingdom, in 1994. The subsequent conferenes were held at Torremolinos, Spain in 1996, at Quebec City, Canada in 1998, and at Katowice, Poland in 2000. The fifth conference was held at Nara, which was the capital of Japan for more than seventy years in the eighth century. During this Nara period the basis of Japanese society, or culture established itself. Nara is a beautiful place and has a number of historic monuments in the World Heritage List. The members of the International Committee of MOPGP'02 were Dylan Jones, Pekka Korhonen, Carlos Romero, Ralph Steuer and Mehrdad Tamiz.
Book Synopsis Evolutionary Algorithms for Solving Multi-Objective Problems by : Carlos Coello Coello
Download or read book Evolutionary Algorithms for Solving Multi-Objective Problems written by Carlos Coello Coello and published by Springer Science & Business Media. This book was released on 2007-08-26 with total page 810 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is a second edition of Evolutionary Algorithms for Solving Multi-Objective Problems, significantly expanded and adapted for the classroom. The various features of multi-objective evolutionary algorithms are presented here in an innovative and student-friendly fashion, incorporating state-of-the-art research. The book disseminates the application of evolutionary algorithm techniques to a variety of practical problems. It contains exhaustive appendices, index and bibliography and links to a complete set of teaching tutorials, exercises and solutions.
Book Synopsis Multiobjective Optimization by : Yann Collette
Download or read book Multiobjective Optimization written by Yann Collette and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text offers many multiobjective optimization methods accompanied by analytical examples, and it treats problems not only in engineering but also operations research and management. It explains how to choose the best method to solve a problem and uses three primary application examples: optimization of the numerical simulation of an industrial process; sizing of a telecommunication network; and decision-aid tools for the sorting of bids.
