Multicriteria Optimization
Decision makers in many areas, from industry to engineering and the social sector, face an increasing need to consider multiple, conflicting objectives in their decision processes. In many cases these real world decision problems can be formulated as mult
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Matthias Ehrgott
Multicriteria Optimization Second edition With 88 Figures and 12 Tables
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Dr. habil. Matthias Ehrgott, Associate Professor The University of Auckland Department of Engineering Science School of Engineering Private Bag 92019 70 Symonds Street Level 3 Auckland 1001 New Zealand [email protected]
Originally published as volume 491 in the series: Lecture Notes in Economics and Mathematical Systems
Cataloging-in-Publication Data Library of Congress Control Number: 2005924730
ISBN 3-540-21398-8 Springer Berlin Heidelberg New York Bibliographic information published by Die Deutsche Bibliothek. Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic dat is available in the Internet at http://dnb.ddb.de 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 permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com ° Springer Berlin ´ Heidelberg 2005 Printed in Germany 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. Hardcover-Design: Erich Kirchner, Heidelberg SPIN 10996973
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Preface
Life is about decisions. Decisions, no matter if made by a group or an individual, usually involve several conflicting objectives. The observation that real world problems have to be solved optimally according to criteria, which prohibit an “ideal” solution – optimal for each decision-maker under each of the criteria considered – has led to the development of multicriteria optimization. From its first roots, which where laid by Pareto at the end of the 19th century the discipline has prospered and grown, especially during the last three decades. Today, many decision support systems incorporate methods to deal with conflicting objectives. The foundation for such systems is a mathematical theory of optimization under multiple objectives. Fully aware of the fact that there have been excellent textbooks on the topic before, I do not claim that this is a better text, but it has a considerably different focus. Some of the available books develop the mathematical background in great depth, such as Sawaragi et al. (1985); G¨ opfert and Nehse (1990); Jahn (1986). Others focus on a specific structure of the problems covered as Zeleny (1974); Steuer (1985); Miettinen (199
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