Nonlinear Multiobjective Optimization

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Author: Kaisa Miettinen
Publisher: Springer Science & Business Media
ISBN: 1461555639
Size: 30.46 MB
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Nonlinear Multiobjective Optimization by Kaisa Miettinen

Original Title: Nonlinear Multiobjective Optimization

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.

Multi Objective Optimization Problems

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Author: Fran Sérgio Lobato
Publisher: Springer
ISBN: 3319585657
Size: 33.85 MB
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Multi Objective Optimization Problems by Fran Sérgio Lobato

Original Title: Multi Objective Optimization Problems

This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.

Theory Of Multiobjective Optimization

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Author: Yoshikazu Sawaragi
Publisher: Elsevier
ISBN: 9780080958668
Size: 11.42 MB
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Theory Of Multiobjective Optimization by Yoshikazu Sawaragi

Original Title: Theory Of Multiobjective Optimization

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; and methods 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 particular branches, 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

Non Convex Multi Objective Optimization

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Author: Panos M. Pardalos
Publisher: Springer
ISBN: 3319610074
Size: 25.79 MB
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Non Convex Multi Objective Optimization by Panos M. Pardalos

Original Title: Non Convex Multi Objective Optimization

Recent results on non-convex multi-objective optimization problems and methods are presented in this book, with particular attention to expensive black-box objective functions. Multi-objective optimization methods facilitate designers, engineers, and researchers to make decisions on appropriate trade-offs between various conflicting goals. A variety of deterministic and stochastic multi-objective optimization methods are developed in this book. Beginning with basic concepts and a review of non-convex single-objective optimization problems; this book moves on to cover multi-objective branch and bound algorithms, worst-case optimal algorithms (for Lipschitz functions and bi-objective problems), statistical models based algorithms, and probabilistic branch and bound approach. Detailed descriptions of new algorithms for non-convex multi-objective optimization, their theoretical substantiation, and examples for practical applications to the cell formation problem in manufacturing engineering, the process design in chemical engineering, and business process management are included to aide researchers and graduate students in mathematics, computer science, engineering, economics, and business management.

Nonlinear Multiobjective Optimization

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Author: Claus Hillermeier
Publisher: Birkhäuser
ISBN: 3034882807
Size: 69.25 MB
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Nonlinear Multiobjective Optimization by Claus Hillermeier

Original Title: Nonlinear Multiobjective Optimization

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.

Multiobjective Optimization

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Author: Jürgen Branke
Publisher: Springer
ISBN: 3540889086
Size: 17.63 MB
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Multiobjective Optimization by Jürgen Branke

Original Title: Multiobjective Optimization

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.

Multiobjective Optimization Behavioral And Computational Considerations

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Author: Jeffrey L. Ringuest
Publisher: Springer Science & Business Media
ISBN: 146153612X
Size: 10.79 MB
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Multiobjective Optimization Behavioral And Computational Considerations by Jeffrey L. Ringuest

Original Title: Multiobjective Optimization Behavioral And Computational Considerations

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.

Sequential Approximate Multiobjective Optimization Using Computational Intelligence

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Author: Hirotaka Nakayama
Publisher: Springer Science & Business Media
ISBN: 3540889108
Size: 29.11 MB
Format: PDF
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Sequential Approximate Multiobjective Optimization Using Computational Intelligence by Hirotaka Nakayama

Original Title: Sequential Approximate Multiobjective Optimization Using Computational Intelligence

Many kinds of practical problems such as engineering design, industrial m- agement and ?nancial investment have multiple objectives con?icting with eachother. Thoseproblemscanbeformulatedasmultiobjectiveoptimization. In multiobjective optimization, there does not necessarily a unique solution which minimizes (or maximizes) all objective functions. We usually face to the situation in which if we want to improve some of objectives, we have to give up other objectives. Finally, we pay much attention on how much to improve some of objectives and instead how much to give up others. This is called “trade-o?. ” Note that making trade-o? is a problem of value ju- ment of decision makers. One of main themes of multiobjective optimization is how to incorporate value judgment of decision makers into decision s- port systems. There are two major issues in value judgment (1) multiplicity of value judgment and (2) dynamics of value judgment. The multiplicity of value judgment is treated as trade-o? analysis in multiobjective optimi- tion. On the other hand, dynamics of value judgment is di?cult to treat. However, it is natural that decision makers change their value judgment even in decision making process, because they obtain new information during the process. Therefore, decision support systems are to be robust against the change of value judgment of decision makers. To this aim, interactive p- grammingmethodswhichsearchasolutionwhileelicitingpartialinformation on value judgment of decision makers have been developed. Those methods are required to perform ?exibly for decision makers’ attitude.

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