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Carlos A. Coello Coello, Gary B. Lamont and David A. Van Veldhuizen Evolutionary Algorithms for Solving Multi-Objective Problems Second Edition

Genetic and Evolutionary Computation Series Series Editors David E. Goldberg Consulting Editor IlliGAL, Dept. of General Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801 USA Email: deg@uiuc.edu John R. Koza Consulting Editor Medical Informatics Stanford University Stanford, CA 94305-5479 USA Email: john@johnkoza.com Selected titles from this series: Markus Brameier, Wolfgang Banzhaf Linear Genetic Programming, 2007 ISBN 978-0-387-31029-9 Nikolay Y. Nikolaev, Hitoshi Iba Adaptive Learning of Polynomial Networks, 2006 ISBN 978-0-387-31239-2 Tetsuya Higuchi, Yong Liu, Xin Yao Evolvable Hardware, 2006 ISBN 978-0-387-24386-3 David E. Goldberg The Design of Innovation: Lessons from and for Competent Genetic Algorithms, 2002 ISBN 978-1-4020-7098-3 John R. Koza, Martin A. Keane, Matthew J. Streeter, William Mydlowec, Jessen Yu, Guido Lanza Genetic Programming IV: Routine Human-Computer Machine Intelligence ISBN: 978-1-4020-7446-2 (hardcover), 2003; ISBN: 978-0-387-25067-0 (softcover), 2005 Carlos A. Coello Coello, David A. Van Veldhuizen, Gary B. Lamont Evolutionary Algorithms for Solving Multi-Objective Problems, 2002 ISBN: 978-0-306- 46762-2 Lee Spector Automatic Quantum Computer Programming: A Genetic Programming Approach ISBN: 978-1-4020-789 William B. Langdon Genetic Programming and D Programming! 1998 ISBN: 978-0-7923-8135-8 For a complete listing of books in this series, go to http://www.springer.com ata Structures: Genetic Programming + Data Structures = Automatic 4-1 (hardcover), 2004; ISBN 978-0-387-36496-4 (softcover), 2007

Carlos A. Coello Coello Gary B. Lamont David A. Van Veldhuizen Evolutionary Algorithms for Solving Multi-Objective Problems Second Edition

Carlos A. Coello Coello CINVESTAV-IPN Depto. de Computación Av. Instituto Politécnico Nacional No. 2508 Col. San Pedro Zacatenco México, D.F. 07360 MEXICO ccoello@cs.cinvestav.mx Gary B. Lamont Department of Electrical and Computer Engineering Graduate School of Engineering Air Force Institute of Technology 2950 Hobson Way WPAFB, Dayton, OH 45433-7765 lamont@afit.af.mil David A. Van Veldhuizen QHQ AMC/A9 402 Scott Dr., No. 3L3 Scott AFB, IL 62225-5307 dvanveldhuizen@jieee.orrgr Series Editors: David E. Goldberg Consulting Editor IlliGAL, Dept. of General Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801 USA deg@uiuc.edu John R. Koza Consulting Editor Medical Informatics Stanford University Stanford, CA 94305-5479 USA john@johnkoza.com Library of Congress Control Number: 2007930239 ISBN 978-0-387-33254-3 e-ISBN 978-0-387-36797-2 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. 9 8 7 6 5 4 3 2 1 springer.com g r g r g r g

to our wives

Preface to the Second Edition The response of the multiobjective optimization community to our ﬁrst edi- tion in 2002 was extremely enthusiastic. Many have indicated their use of our monograph to gain insight to the interdisciplinary nature of multiobjective op- timization employing evolutionary algorithms. Others are appreciative for our providing them a foundation for associated contemporary multiobjective evo- lutionary algorithm (MOEA) research. We appreciate these warm comments along with readers’ suggestions for improvements. In that vein, we have sig- niﬁcantly extended and modiﬁed our previous material using contemporary literature resulting in this new edition, which is extended into a textbook. In addition to new classroom exercises contained in each chapter, the MOEA discussion questions and possible research directions are updated. The ﬁrst edition presented an organized variety of MOEA topics based on fundamental principles derived from single-objective evolutionary algorithm (EA) optimization and multiobjective problem (MOP) domains. Yet, many new developments occurred in the intervening years. New MOEA structures were proposed with new operators and therefore better search techniques. The explosion of successful MOEA applications continues to be reported in the literature. Statistical testing methods for evaluating results now oﬀers improved analysis of comparative techniques, innovative metrics, and better visualization tools. The continuing development of MOEA activity in the- ory, algorithmic innovations, and MOEA practice calls for these new concepts to be integrated into our generic MOEA text. Note that the continuing im- provement (speed, memory, etc.) of computer hardware provides computa- tional platforms that permit larger search spaces to be addressed at higher eﬃciencies using both serial and parallel processing. This phenomenon, in conjunction with user-friendly software interfacing tools, permits an increas- ing number of scientists and engineers to explore the use of MOEAs in their particular multiobjective problem domains. With this new edition, we continue to provide an interdisciplinary com- puter science and computer engineering text that considers other academic ﬁelds such as operations research, industrial engineering, and management

VIII Preface to the Second Edition state-of-the-art concepts and discussions of open research topics. science. Examples from all these disciplines, as well as all engineering areas in general, are discussed and addressed as to their fundamental unique prob- lem domain characteristics and their solutions using MOEAs. An expanded reference list is included with suggestions of further reading for both the stu- dent and practitioner. As in the previous edition, this book addresses MOEA development and applications issues through the following features: • The text is meant to be both a textbook and a self-contained reference. The book provides all the necessary elements to guide a newcomer in the design, implementation, validation, and application of MOEAs in either the classroom or the ﬁeld. • Researchers in the ﬁeld beneﬁt from the book’s comprehensive review of • The book is also written for graduate students in computer science, com- puter engineering, operations research, management science, and other scientiﬁc and engineering disciplines, who are interested in multiobjective optimization using evolutionary algorithms. • The book is also for professionals interested in developing practical applica- tions of evolutionary algorithms to real-world multiobjective optimization problems. • Each chapter is complemented by discussion questions and several ideas meant to trigger novel research paths. Supplementary reading is strongly suggested for deepening MOEA understanding. • Key features include MOEA classiﬁcations and explanations, MOEA ap- plications and techniques, MOEA test function suites, and MOEA perfor- mance measurements. • We created a website for this book at: http://www.cs.cinvestav.mx/~emoobook which contains considerable material supporting this second edition. This site contains all the appendices of the book (which have been removed from the original monograph due to space limitations), as well as public- domain software, tutorial slides, and additional sources of contemporary MOEA information. This new synergistic text is markedly improved from the ﬁrst edition. New material is integrated providing more detail, which leads to a realignment of material. Old chapters were modiﬁed and a new one was added. As before, the various features of MOEAs continue to be discussed in an innovative and unique fashion, with detailed customized forms suggested for a variety of applications. The ﬂow of material in each chapter is intended to present a natural and comprehensive development of MOEAs from basic concepts to complex applications. Chapter 1 presents and motivates MOP and MOEA terminology and the nomenclature used in successive chapters including a lengthy discussion on the

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