Adaptive Scalarization Methods in Multiobjective Optimization
This book presents new adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarizations. With the help of sensitivity results an adaptive parameter control is developed so that high-quality approximations of t
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Editor: Johannes Jahn University of Erlangen-Nürnberg Department of Mathematics Martensstr. 3 91058 Erlangen Germany [email protected]
Vector Optimization The series Vector Optimization contains publications in various fields of optimization with vector-valued objective functions, such as multiobjective optimization, multi criteria decision making, set optimization, vector-valued game theory and border areas to financial mathematics, biosystems, semidefinite programming and multiobjective control theory. Studies of continuous, discrete, combinatorial and stochastic multiobjective models in interesting fields of operations research are also included. The series covers mathematical theory, methods and applications in economics and engineering. These publications being written in English are primarily monographs and multiple author works containing current advances in these fields.
Gabriele Eichfelder
Adaptive Scalarization Methods in Multiobjective Optimization
Author: Dr. Gabriele Eichfelder University of Erlangen-Nürnberg Department of Mathematics Martensstr. 3 91058 Erlangen Germany [email protected]
ISBN 978-3-540-79157-7
e-ISBN 978-3-540-79159-1
Library of Congress Control Number: 2008924782 © 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permissions for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg, Germany Printed on acid-free paper 987654321 springer.com
To my family, Paul, Sabine, Susanne, and Claudia, and especially to Tom.
Preface
In many areas in engineering, economics and science new developments are only possible by the application of modern optimization methods. The optimization problems arising nowadays in applications are mostly multiobjective, i. e. many competing objectives are aspired all at once. These optimization problems with a vector-valued objective function have in opposition to scalar-valued problems generally not only one minimal solution but the solution set is very large. Thus the development of efficient numerical methods for special classes of multiobjective optimization problems is, due to the complexity of the solution set, of special interest. This relevance is pointed out in many recent publications in application areas such
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