Nonlinear Multiobjective Optimization
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Nonlinear Multiobjective Optimization
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Author : Kaisa Miettinen
language : en
Publisher: Springer Science & Business Media
Release Date : 1999
Nonlinear Multiobjective Optimization written by Kaisa Miettinen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Business & Economics categories.
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.
Nonlinear Multiobjective Optimization
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Author : Claus Hillermeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Nonlinear Multiobjective Optimization written by Claus Hillermeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Arguably, many industrial optimization problems are of the multiobjective type. The present work, after providing a survey of the state of the art in multiobjective optimization, gives new insight into this important mathematical field by consequently taking up the viewpoint of differential geometry. This approach, unprecedented in the literature, very naturally results in a generalized homotopy method for multiobjective optimization which is theoretically well-founded and numerically efficient. The power of the new method is demonstrated by solving two real-life problems of industrial optimization. The book presents recent results obtained by the author and is aimed at mathematicians, scientists, students and practitioners interested in optimization and numerical homotopy methods.
Nonlinear Multiobjective Optimization
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Author : Kaisa Miettinen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Multiobjective Optimization written by Kaisa Miettinen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Business & Economics categories.
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.
Nonlinear Multiobjective Optimization
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Author : Kaisa Miettinen
language : en
Publisher:
Release Date : 1998-09-01
Nonlinear Multiobjective Optimization written by Kaisa Miettinen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09-01 with categories.
Multiobjective Optimization
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Author : Jürgen Branke
language : en
Publisher: Springer
Release Date : 2008-10-18
Multiobjective Optimization written by Jürgen Branke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-18 with Computers categories.
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.
Theory Of Multiobjective Optimization
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Author : Yoshikazu Sawaragi
language : en
Publisher: Elsevier
Release Date : 1985-09-19
Theory Of Multiobjective Optimization written by Yoshikazu Sawaragi and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-09-19 with Mathematics categories.
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 matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression. - Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering
Fuzzy Sets And Interactive Multiobjective Optimization
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Author : Masatoshi Sakawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Fuzzy Sets And Interactive Multiobjective Optimization written by Masatoshi Sakawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Mathematics categories.
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.
Genetic Algorithms And Fuzzy Multiobjective Optimization
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Author : Masatoshi Sakawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Genetic Algorithms And Fuzzy Multiobjective Optimization written by Masatoshi Sakawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Business & Economics categories.
Since the introduction of genetic algorithms in the 1970s, an enormous number of articles together with several significant monographs and books have been published on this methodology. As a result, genetic algorithms have made a major contribution to optimization, adaptation, and learning in a wide variety of unexpected fields. Over the years, many excellent books in genetic algorithm optimization have been published; however, they focus mainly on single-objective discrete or other hard optimization problems under certainty. There appears to be no book that is designed to present genetic algorithms for solving not only single-objective but also fuzzy and multiobjective optimization problems in a unified way. Genetic Algorithms And Fuzzy Multiobjective Optimization introduces the latest advances in the field of genetic algorithm optimization for 0-1 programming, integer programming, nonconvex programming, and job-shop scheduling problems under multiobjectiveness and fuzziness. In addition, the book treats a wide range of actual real world applications. The theoretical material and applications place special stress on interactive decision-making aspects of fuzzy multiobjective optimization for human-centered systems in most realistic situations when dealing with fuzziness. The intended readers of this book are senior undergraduate students, graduate students, researchers, and practitioners in the fields of operations research, computer science, industrial engineering, management science, systems engineering, and other engineering disciplines that deal with the subjects of multiobjective programming for discrete or other hard optimization problems under fuzziness. Real world research applications are used throughout the book to illustrate the presentation. These applications are drawn from complex problems. Examples include flexible scheduling in a machine center, operation planning of district heating and cooling plants, and coal purchase planning in an actual electric power plant.
Multicriteria Optimization
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Author : Matthias Ehrgott
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16
Multicriteria Optimization written by Matthias Ehrgott and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Business & Economics categories.
- Collection of results of multicriteria optimization, including nonlinear, linear and combinatorial optimization problems - Includes numerous illustrations, examples and problems
A Branch And Bound Algorithm For Multiobjective Mixed Integer Convex Optimization
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Author : Stefan Rocktäschel
language : en
Publisher: Springer Nature
Release Date : 2020-01-21
A Branch And Bound Algorithm For Multiobjective Mixed Integer Convex Optimization written by Stefan Rocktäschel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-21 with Mathematics categories.
Stefan Rocktäschel introduces a branch-and-bound algorithm that determines a cover of the efficient set of multiobjective mixed-integer convex optimization problems. He examines particular steps of this algorithm in detail and enhances the basic algorithm with additional modifications that ensure a more precise cover of the efficient set. Finally, he gives numerical results on some test instances.