Plain text is unavailable for this page.

HANDBOOK OF METAHEURISTICS

INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE Frederick S. Hillier, Series Editor Stanford University Weyant, J. / ENERGY AND ENVIRONMENTAL POLICY MODELING Shanthikumar, J.G. & Sumita, U. / APPLIED PROBABILITY AND STOCHASTIC PROCESSES Liu, B. & Esogbue, A.O. / DECISION CRITERIA AND OPTIMAL INVENTORY PROCESSES Gal, T., Stewart, T.J., Hanne, T. / MULTICRITERIA DECISION MAKING: Advances in MCDM Models, Algorithms, Theory, and Applications Fox, B.L. / STRATEGIES FOR QUASI-MONTE CARLO Hall, R.W. / HANDBOOK OF TRANSPORTATION SCIENCE Grassman, W.K. / COMPUTATIONAL PROBABILITY Pomerol, J.-C. & Barba-Romero, S. / MULTICRITERION DECISION IN MANAGEMENT Axs��ter, S. / INVENTORY CONTROL Wolkowicz, H., Saigal, R., & Vandenberghe, L. / HANDBOOK OF SEMI-DEFINITE PROGRAMMING: Theory, Algorithms, and Applications Hobbs, B.F. & Meier, P. / ENERGY DECISIONS AND THE ENVIRONMENT: A Guide to the Use of Multicriteria Methods Dar-El, E. / HUMAN LEARNING: From Learning Curves to Learning Organizations Armstrong, J.S. / PRINCIPLES OF FORECASTING: A Handbook for Researchers and Practitioners Balsamo, S., Person��, V., & Onvural, R. / ANALYSIS OF QUEUEING NETWORKS WITH BLOCKING Bouyssou, D. et al. / EVALUATION AND DECISION MODELS: A Critical Perspective Hanne, T. / INTELLIGENT STRATEGIES FOR META MULTIPLE CRITERIA DECISION MAKING Saaty, T. & Vargas, L. / MODELS, METHODS, CONCEPTS and APPLICATIONS OF THE ANALYTIC HIERARCHY PROCESS Chatterjee, K. & Samuelson, W. / GAME THEORY AND BUSINESS APPLICATIONS Hobbs, B. et al. / THE NEXT GENERATION OF ELECTRIC POWER UNIT COMMITMENT MODELS Vanderbei, R.J. / LINEAR PROGRAMMING: Foundations and Extensions, 2nd Ed. Kimms, A. / MATHEMATICAL PROGRAMMING AND FINANCIAL OBJECTIVES FOR SCHEDULING PROJECTS Baptiste, P., Le Pape, C. & Nuijten, W. / CONSTRAINT-BASED SCHEDULING Feinberg, E. & Shwartz, A. / HANDBOOK OF MARKOV DECISION PROCESSES: Methods and Applications Ram��k, J. & Vlach, M. / GENERALIZED CONCAVITY IN FUZZY OPTIMIZATION AND DECISION ANALYSIS Song, J. & Yao, D. / SUPPLY CHAIN STRUCTURES: Coordination, Information and Optimization Kozan, E. & Ohuchi, A. / OPERATIONS RESEARCH/MANAGEMENT SCIENCE AT WORK Bouyssou et al. / AIDING DECISIONS WITH MULTIPLE CRITERIA: Essays in Honor of Bernard Roy Cox, Louis Anthony, Jr. / RISK ANALYSIS: Foundations, Models and Methods Dror, M., L���Ecuyer, P. & Szidarovszky, F. / MODELING UNCERTAINTY: An Examination of Stochastic Theory, Methods, and Applications Dokuchaev, N. / DYNAMIC PORTFOLIO STRATEGIES: Quantitative Methods and Empirical Rules for Incomplete Information Sarker, R., Mohammadian, M. & Yao, X. / EVOLUTIONARY OPTIMIZATION Demeulemeester, R. & Herroelen, W. / PROJECT SCHEDULING: A Research Handbook Gazis, D.C. / TRAFFIC THEORY Zhu, J. / QUANTITATIVE MODELS FOR PERFORMANCE EVALUATION AND BENCHMARKING Ehrgott, M. & Gandibleux, X. / MULTIPLE CRITERIA OPTIMIZATION: State of the Art Annotated Bibliographical Surveys Bienstock, D. / Potential Function Methods for Approx. Solving Linear Programming Problems Matsatsinis, N.F. & Siskos, Y. / INTELLIGENT SUPPORT SYSTEMS FOR MARKETING DECISIONS Alpern, S. & Gal, S. / THE THEORY OF SEARCH GAMES AND RENDEZVOUS Hall, R.W. / HANDBOOK OF TRANSPORTATION SCIENCE���2nd Ed.

HANDBOOK OF METAHEURISTICS edited by Fred Glover Leeds School of Business University of Colorado at Boulder Gary A. Kochenberger College of Business University of Colorado at Denver KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW

eBook ISBN: 0-306-48056-5 Print ISBN: 1-4020-7263-5 ��2003 Kluwer Academic Publishers New York, Boston, Dordrecht, London, Moscow Print ��2003 Kluwer Academic Publishers All rights reserved No part of this eBook may be reproduced or transmitted in any form or by any means, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline.com and Kluwer's eBookstore at: http://ebooks.kluweronline.com Dordrecht

To our wives, Diane and Ann, whose meta-patience and meta-support have sustained us through this effort!

This page intentionally left blank

CONTENTS List of Contributors Preface ix xi 1 Scatter Search and Path Relinking: Advances and Applications 1 Fred Glover, Manuel Laguna and Rafael Marti 2 An Introduction to Tabu Search 37 Michel Gendreau 3 Genetic Algorithms 55 Colin Reeves 4 Genetic Programming: Automatic Synthesis of Topologies and Numerical Parameters 83 John R. Koza 5 A Gentle Introduction to Memetic Algorithms 105 Pablo Moscato and Carlos Cotta 6 Variable Neighborhood Search 145 Pierre Hansen and Nenad 7 Guided Local Search 185 Christos Voudouris and Edward P.K. Tsang 8 Greedy Randomized Adaptive Search Procedures 219 Mauricio G.C. Resende and Celso C. Ribeiro 9 The Ant Colony Optimization Metaheuristic: Algorithms, Applications, and Advances 251 Marco Dorigo and Thomas St��tzle

viii Contents 10 The Theory and Practice of Simulated Annealing 287 Darrall Henderson, Sheldon H. Jacobson and Alan W. Johnson 11 Iterated Local Search 321 Helena R. Louren��o, Olivier C. Martin and Thomas St��tzle 12 Multi-Start Methods 355 Rafael Mart�� 13 Local Search and Constraint Programming 369 Filippo Focacci, Fran��ois Laburthe and Andrea Lodi 14 Constraint Satisfaction Eugene C. Freuder and Mark Wallace 405 15 Artificial Neural Networks for Combinatorial Optimization 429 Jean-Yves Potvin and Kate A. Smith 16 Hyper-heuristics: an Emerging Direction in Modern Search Technology 457 Edmund Burke, Graham Kendall, Jim Newall, Emma Hart, Peter Ross and Sonia Schulenburg 17 Parallel Strategies for Meta-heuristics 475 Teodor Gabriel Crainic and Michel Toulouse 18 Metaheuristic Class Libraries 515 Andreas Fink, Stefan Vo�� and David L. Woodruff 19 Asynchronous Teams Sarosh Talukdar, Sesh Murthy and Rama Akkiraju 537 Index 557

LIST OF CONTRIBUTORS Rama Akkiraju IBM T.J. Watson Labs E-mail: akkiraju@us.ibm.com Edmund Burke University of Nottingham E-mail: ekb@cs.nott.ac.uk Carlos Cotta Universidad de Malaga E-mail: ccottap@lcc.uma.es Teodor Gabriel Crainic University of Montreal E-mail: theo@crt.umontreal.ca Marco Dorigo Universite Libre de Bruxelles E-mail: mdorigo@ulb.ac.be Andreas Fink Universitat Braunschweig E-mail: a.fink@tu-bs.de Filippo Focacci ILOG S. A. E-mail: ffocacci@ilog.fr Eugene C. Freuder University of New Hampshire E-mail: ecf@cs.unh.edu Michel Gendreau University of Montreal E-mail: michelg@crt.umontreal.ca Fred Glover University of Colorado E-mail: fred.glover@colorado.edu Andrea Lodi University of Bologna E-mail: alodi@deis.unibo.it Manuel Laguna University of Colorado E-mail: manuel.laguna@Colorado.edu Fran��ois Laburthe Bouygues e-Lab E-mail: flaburthe@bouygues.com John R. Koza Stanford University E-mail: koza@stanford.edu Graham Kendall University of Nottingham E-mail: gxk@cs.nott.ac.uk Alan W. Johnson US Military Academy E-mail: aa2895@usma.edu Sheldon H. Jacobson University of Illinois E-mail: shj@uiuc.edu Darrall Henderson US Military Academy E-mail: darrall@stanfordalumni.org Emma Hart Napier University E-mail: emmah@dcs.napier.ac.uk Pierre Hansen University of Montreal E-mail: pierreh@crt.umontreal.ca

x List of Contributors Helena R. Louren��o Universitat Pompeu Fabra E-mail: helena.ramalhinho@econ.upf.es Rafael Mart�� Universitat de Valencia E-mail: rafael.marti@uv.es Olivier C. Martin Universite Paris-Sud E-mail: martino@ipno.in2p3.fr Nenad Serbian Academy of Science E-mail: nenad@mi.sanu.ac.yu Pablo Moscato Universidade Estadual de Campinas E-mail: moscato@densis.fee.unicamp.br Sesh Murthy IBM T.J. Watson Labs E-mail: murthy@watson.ibm.com Jim Newall University of Nottingham E-mail: jpn@cs.nott.ac.uk Jean-Yves Potvin University of Montreal E-mail: potvin@iro.unmontreal.ca Colin Reeves Coventry University E-mail: c.reeves@coventry.ac.uk Mauricio G.C. Resende AT&T Labs Research E-mail: mgcr@research.att.com Celso C. Ribeiro Catholic University of Rio de Janeiro E-mail: celso@inf.puc-rio.br Peter Ross Napier University E-mail: peter@dcs.napier.ac.uk David L. Woodruff University of California at Davis E-mail: dlwoodruff@ucdavis.edu Mark Wallace Imperial College E-mail: mgw@icparc.ic.ac.uk Cristos Voudouris BTexact Technologies E-mail: chris.voudouris@bt.com Stefan Vo�� Universitat Braunschweig E-mail: stefan.voss@tu-bs.de Edward P.K. Tsang University of Essex E-mail: edward@essex.ac.uk Michel Toulouse University of Manitoba E-mail: toulouse@cs.umanitoba.ca Sarosh Talukdar Carnegie Mellon University E-mail: talukdar@ece.cmu.edu Thomas St��tzle Darmstadt University of Technology E-mail: stuetzle@informatik. tu-darmstadt.de Kate A. Smith Monash University E-mail: kate.smith@infotech.monash. edu.au Sonia Schulenburg Napier University E-mail: s.schulenberg@napier.ac.uk

PREFACE Metaheuristics, in their original definition, are solution methods that orchestrate an interaction between local improvement procedures and higher level strategies to create a process capable of escaping from local optima and performing a robust search of a solution space. Over time, these methods have also come to include any procedures that employ strategies for overcoming the trap of local optimality in complex solution spaces, especially those procedures that utilize one or more neighborhood structures as a means of defining admissible moves to transition from one solution to another, or to build or destroy solutions in constructive and destructive processes. The degree to which neighborhoods are exploited varies according to the type of procedure. In the case of certain population-based procedures, such as genetic algo- rithms, neighborhoods are implicitly (and somewhat restrictively) defined by reference to replacing components of one solution with those of another, by variously chosen rules of exchange popularly given the name of ���crossover.��� In other population-based methods, based on the notion of path relinking, neighborhood structures are used in their full generality, including constructive and destructive neighborhoods as well as those for transitioning between (complete) solutions. Certain hybrids of classical evolution- ary approaches, which link them with local search, also use neighborhood structures more fully, though apart from the combination process itself. Meanwhile, ���single thread��� solution approaches, which do not undertake to manipulate multiple solutions simultaneously, run a wide gamut that not only manipulate diverse neighborhoods but incorporate numerous forms of strategies ranging from thoroughly randomized to thor- oughly deterministic, depending on the elements such as the phase of search or (in the case of memory-based methods) the history of the solution process.1 A number of the tools and mechanisms that have emerged from the creation of metaheuristic methods have proved to be remarkably effective, so much so that meta- heuristics have moved into the spotlight in recent years as the preferred line of attack for solving many types of complex problems, particularly those of a combinatorial nature. While metaheuristics are not able to certify the optimality of the solutions they find, exact procedures (which theoretically can provide such a certification, if allowed to run long enough)2 have often proved incapable of finding solutions whose 1 Methods based on incorporating collections of memory-based strategies, invoking forms of memory more flexible and varied than those used in approaches such as tree search and branch and bound, are sometimes grouped under the name Adaptive Memory Programming. This term, which originated in the tabu search literature where such adaptive memory strategies were first introduced and continue to be the primary focus, is also sometimes used to encompass other methods that have more recently adopted memory-based elements. 2Some types of problems seem quite amenable to exact methods, particularly to some of the methods embodied in the leading commercial software packages for mixed integer programming. Yet even by these approaches the ���length of time��� required to solve many problems exactly appears to exceed all reasonable measure, including in some cases measures of astronomical scale. It has been conjectured that metaheuristics

xii Preface quality is close to that obtained by the leading metaheuristics���particularly for real world problems, which often attain notably high levels of complexity. In addition, some of the more successful applications of exact methods have come about by incorporating metaheuristic strategies within them. These outcomes have motivated additional research and application of new and improved metaheuristic methodologies. This handbook is designed to provide the reader with a broad coverage of the con- cepts, themes and instrumentalities of this important and evolving area of optimization. In doing so, we hope to encourage an even wider adoption of metaheuristic methods for assisting in problem solving, and to stimulate research that may lead to additional innovations in metaheuristic procedures. The handbook consists of 19 chapters. Topics covered include Scatter Search, Tabu Search, Genetic Algorithms, Genetic Programming, Memetic Algorithms, Variable Neighborhood Search, Guided Local Search, GRASP, Ant Colony Optimization, Simu- lated Annealing, Iterated Local Search, Multi-Start Methods, Constraint Programming, Constraint Satisfaction, Neural Network Methods for Optimization, Hyper-Heuristics, Parallel Strategies for Metaheuristics, Metaheuristic Class Libraries, and A-Teams. This family of metaheuristic chapters, while not exhaustive of the many approaches that have sprung into existence in recent years, encompasses the critical strategic elements and their underlying ideas that represent the state-of-the-art of modern metaheuristics. This book is intended to provide the communities of both researchers and practi- tioners with a broadly applicable, up to date coverage of metaheuristic methodologies that have proven to be successful in a wide variety of problem settings, and that hold particular promise for success in the future. The various chapters serve as stand alone presentations giving both the necessary underpinnings as well as practical guides for implementation. The nature of metaheuristics invites an analyst to modify basic meth- ods in response to problem characteristics, past experiences, and personal preferences and the chapters in this handbook are designed to facilitate this process as well. The authors who have contributed to this volume represent leading figures from the metaheuristic community and are responsible for pioneering contributions to the fields they write about. Their collective work has significantly enriched the field of optimization in general and combinatorial optimization in particular. We are especially grateful to them for agreeing to provide the first-rate chapters that appear in this hand- book. We would also like to thank our graduate students, Gyung Yung and Rahul Patil, for their assistance. Finally, we would like to thank Gary Folven and Carolyn Ford of Kluwer Academic Publishers for their unwavering support and patience throughout this project. succeed where exact methods fail because of their ability to use strategies of greater flexibility than permitted to assure that convergence will inevitably be obtained.

Chapter 1 SCATTER SEARCH AND PATH RELINKING: ADVANCES AND APPLICATIONS Fred Glover and Manuel Laguna Leeds School of Business, Campus Box 419, University of Colorado, Boulder, CO 80309-0419, USA E-mail: Fred.Glover@Colorado.edu, Manuel.Laguna@Colorado.edu Rafael Marti Dpto. de Estad��stica e Investigaci��n Operativa, Facultad de Matem��ticas, Universitat de Valencia, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain E-mail: Rafael.Marti@uv.es Abstract Scatter search (SS) is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints, SS uses strategies for combining solution vectors that have proved effective in a variety of problem settings. Path relinking (PR) has been suggested as an approach to integrate intensification and diversification strategies in a search scheme. The approach may be viewed as an extreme (highly focused) instance of a strategy that seeks to incorporate attributes of high quality solutions, by creating inducements to favor these attributes in the moves selected. The goal of this paper is to examine SS and PR strategies that provide useful alternatives to more established search methods. We describe the features of SS and PR that set them apart from other evolutionary approaches, and that offer opportunities for creating increasingly more versatile and effective methods in the future. Specific applications are summarized to provide a clearer understanding of settings where the methods are being used. 1 INTRODUCTION Scatter search (SS), from the standpoint of metaheuristic classification, may be viewed as an evolutionary (population-based) algorithm that constructs solutions by combining others. It derives its foundations from strategies originally proposed for combining decision rules and constraints in the context of integer programming. The goal of this methodology is to enable the implementation of solution procedures that can derive new solutions from combined elements in order to yield better solutions than those procedures that base their combinations only on a set of original elements. For example, see the overview by Glover (1998).

F. Glover et al. 2 The antecedent strategies for combining decision rules were first introduced in the area of scheduling, as a means to obtain improved local decisions. Numerically weighted combinations of existing rules, suitably restructured so that their evaluations embodied a common metric, generated new rules (Glover, 1963). The approach was motivated by the conjecture that information about the relative desirability of alternative choices is captured in different forms by different rules, and that this information can be exploited more effectively when integrated than when treated in isolation (i.e., by choosing selection rules one at a time). Empirical outcomes disclosed that the decision rules created from such combination strategies produced better outcomes than standard applications of local decision rules. The strategy of creating combined rules also proved superior to a ���probabilistic learning approach��� that used stochastic selection of rules at different junctures, but without the integration effect provided by the combined rules (Crowston et al., 1963). The associated procedures for combining constraints likewise employed a mech- anism of generating weighted combinations. In this case, nonnegative weights were introduced to create new constraint inequalities, called surrogate constraints, in the context of integer and nonlinear programming (Glover, 1965, 1968). The approach isolated subsets of (original) constraints that were gauged to be most critical, relative to trial solutions that were obtained based on the surrogate constraints. This critical sub- set was used to produce new weights that reflected the degree to which the component constraints were satisfied or violated. In addition, the resulting surrogate constraints served as source constraints for deriving new inequalities (cutting planes) which in turn provide material for creating further surrogate constraints. Path relinking has been suggested as an approach to integrate intensification and diversification strategies (Glover and Laguna, 1997) in the context of tabu search. This approach generates new solutions by exploring trajectories that connect high- quality solutions, by starting from one of these solutions and generating a path in the neighborhood space that leads toward the other solutions. Recent applications of both methods (and of selected component strategies within them) that have proved highly successful are: The Linear Ordering Problem (Campos, Laguna and Mart��) The Bipartite Drawing Problem (Laguna and Mart��) The Graph Coloring Problem (Hamiez and Hao) Capacitated Multicommodity Network Design (Ghamlouche, Crainic and Gendreau) The Maximum Clique Problem (Cavique, Rego and Themido) Assigning Proctor to Exams (Ramalhinho, Laguna and Mart��) Periodic Vehicle Loading (Delgado, Laguna and Pacheco) Job Shop Scheduling (Nowicki and Smutnicki) The Arc Routing Problem (Greistorfer) Resource Constrained Project Scheduling (Valls, Quintanilla and Ballest��n) Multiple Criteria Scatter Search (Beausoleil) Meta-Heuristic Use of Scatter Search via OptQuest (Hill)