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Ant Colony Optimization Marco Dorigo and Thomas Stützle Ant Colony Optimization Ant Colony.qxd 6/9/04 12:15 PM Page 1 Ant Colony Optimization Marco Dorigo and Thomas Stützle Optimization Ant Colony The complex social behaviors of ants have been much studied by science, and computer scientists are now finding that these behavior patterns can provide models for solving difficult combinatorial optimization problems. The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic Ant Colony technique based on ant behavior. This book presents an overview of this rapidly growing field, from its theoretical inception to practical applications, including descriptions of many available ACO algorithms and their uses. The book first describes the translation of observed ant behavior into working optimization algorithms. The ant Optimization colony metaheuristic is then introduced and viewed in the general context of combinatorial optimization. This is followed by a detailed description and guide to all major ACO algorithms and a report on current theoretical findings. The book surveys ACO applications now in use, including routing, assignment, scheduling, subset, machine learning, and bioin- formatics problems. AntNet, an ACO algorithm designed for the network routing problem, is described in detail. The authors conclude by summarizing the progress in the field and outlining future research directions. Each chapter ends Marco Dorigo and Thomas Stützle with bibliographic material, bullet points setting out important ideas covered in the chapter, and exercises. Ant Colony Optimization will be of interest to academic and industry researchers, graduate students, and practitioners who wish to learn how to implement ACO algorithms. Marco Dorigo is research director of the IRIDIA lab at the Université Libre de Bruxelles and the inventor of the ant colony optimization metaheuristic for combinatorial optimization problems. He has received the Marie Curie Excellence Award for his research work on ant colony optimization and ant algorithms. He is the coauthor of Robot Shaping (MIT Dorigo and Stützle Press, 1998) and Swarm Intelligence. Thomas Stützle is Assistant Professor in the Computer Science Department at Darmstadt University of Technology. A Bradford Book “Marco Dorigo and Thomas Stützle impressively demonstrate that the importance of ant behavior reaches far beyond the sociobiological domain. Ant Colony Optimization presents the most successful algorithmic techniques to be developed on the basis of ant behavior. This book will certainly open the gates for new experimental work on decision making, division of labor, and communication; moreover, it will also inspire all those studying patterns of self-organization.” Bert Hölldobler, Professor of Behavioral Physiology and Sociobiology, Biozentrum, University of Würzburg, Germany “Inspired by the remarkable ability of social insects to solve problems, Dorigo and Stützle introduce highly creative new technological design principles for seeking optimized solutions to extremely difficult real-world problems, such as network routing and task scheduling. This is essential reading not only for those working in artificial intelligence and optimization, but for all of us who find the interface between biology and technology fascinating.” Iain D. Couzin, Princeton University and University of Oxford The MIT Press Massachusetts Institute of Technology Cambridge, Massachusetts 02142 http://mitpress.mit.edu 0-262-04219-3 ,!7IA2G2-aecbjc!:t;K;k;K;k Ant Colony Optimization Ant Colony Optimization Marco Dorigo Thomas Stu¨tzle A Bradford Book The MIT Press Cambridge, Massachusetts London, England 6 2004 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Times New Roman on 3B2 by Asco Typesetters, Hong Kong. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Dorigo, Marco. Ant colony optimization / Marco Dorigo, Thomas Stu¨tzle. p. cm. ‘‘A Bradford book.’’ Includes bibliographical references (p. ). ISBN 0-262-04219-3 (alk. paper) 1. Mathematical optimization. 2. Ants–Behavior–Mathematical models. I. Stu¨tzle, Thomas. II. Title. QA402.5.D64 2004 519.6—dc22 2003066629 10 987654321 To Serena and Roberto To Maria Jose´ and Alexander Contents Preface ix Acknowledgments xiii 1 From Real to Artificial Ants 1 1.1 Ants’ Foraging Behavior and Optimization 1 1.2 Toward Artificial Ants 7 1.3 Artificial Ants and Minimum Cost Paths 9 1.4 Bibliographical Remarks 21 1.5 Things to Remember 22 1.6 Thought and Computer Exercises 23 2The Ant Colony Optimization Metaheuristic 25 2.1 Combinatorial Optimization 25 2.2 The ACO Metaheuristic 33 2.3 How Do I Apply ACO? 38 2.4 Other Metaheuristics 46 2.5 Bibliographical Remarks 60 2.6 Things to Remember 61 2.7 Thought and Computer Exercises 63 3Ant Colony Optimization Algorithms for the Traveling Salesman Problem 65 3.1 The Traveling Salesman Problem 65 3.2 ACO Algorithms for the TSP 67 3.3 Ant System and Its Direct Successors 69 3.4 Extensions of Ant System 76 3.5 Parallel Implementations 82 3.6 Experimental Evaluation 84 3.7 ACO Plus Local Search 92 3.8 Implementing ACO Algorithms 99 3.9 Bibliographical Remarks 114 3.10 Things to Remember 117 3.11 Computer Exercises 117 4Ant Colony Optimization Theory 121 4.1 Theoretical Considerations on ACO 121 4.2 The Problem and the Algorithm 123 4.3 Convergence Proofs 127 viii Contents 4.4 ACO and Model-Based Search 138 4.5 Bibliographical Remarks 149 4.6 Things to Remember 150 4.7 Thought and Computer Exercises 151 5Ant Colony Optimization for NP-Hard Problems 153 5.1 Routing Problems 153 5.2 Assignment Problems 159 5.3 Scheduling Problems 167 5.4 Subset Problems 181 5.5 Application of ACO to Other NP-Hard Problems 190 5.6 Machine Learning Problems 204 5.7 Application Principles of ACO 211 5.8 Bibliographical Remarks 219 5.9 Things to Remember 220 5.10 Computer Exercises 221 6AntNet: An ACO Algorithm for Data Network Routing 223 6.1 The Routing Problem 223 6.2 The AntNet Algorithm 228 6.3 The Experimental Settings 238 6.4 Results 243 6.5 AntNet and Stigmergy 252 6.6 AntNet, Monte Carlo Simulation, and Reinforcement Learning 254 6.7 Bibliographical Remarks 257 6.8 Things to Remember 258 6.9 Computer Exercises 259 7Conclusions and Prospects for the Future 261 7.1 What Do We Know about ACO? 261 7.2 Current Trends in ACO 263 7.3 Ant Algorithms 271 Appendix: Sources of Information about the ACO Field 275 References 277 Index 301 Preface Ants exhibit complex social behaviors that have long since attracted the attention of human beings. Probably one of the most noticeable behaviors visible to us is the for- mation of so-called ant streets. When we were young, several of us may have stepped on such an ant highway or may have placed some obstacle in its way just to see how the ants would react to such disturbances. We may have also wondered where these ant highways lead to or even how they are formed. This type of question may be- come less urgent for most of us as we grow older and go to university, studying other subjects like computer science, mathematics, and so on. However, there are a con- siderable number of researchers, mainly biologists, who study the behavior of ants in detail. One of the most surprising behavioral patterns exhibited by ants is the ability of certain ant species to find what computer scientists call shortest paths. Biologists have shown experimentally that this is possible by exploiting communication based only on pheromones, an odorous chemical substance that ants may deposit and smell. It is this behavioral pattern that inspired computer scientists to develop algo- rithms for the solution of optimization problems. The first attempts in this direction appeared in the early ’90s and can be considered as rather ‘‘toy’’ demonstrations, though important for indicating the general validity of the approach. Since then, these and similar ideas have attracted a steadily increasing amount of research—and ant colony optimization (ACO) is one outcome of these research e¤orts. In fact, ACO algorithms are the most successful and widely recognized algorithmic tech- niques based on ant behaviors. Their success is evidenced by the extensive array of dif- ferent problems to which they have been applied, and moreover by the fact that ACO algorithms are for many problems among the currently top-performing algorithms. Overview of the Book This book introduces the rapidly growing field of ant colony optimization. It gives a broad overview of many aspects of ACO, ranging from a detailed description of the ideas underlying ACO, to the definition of how ACO can generally be applied to a wide range of combinatorial optimization problems, and describes many of the avail- able ACO algorithms and their main applications. The book is divided into seven chapters and is organized as follows. Chapter 1 explains how ants find shortest paths under controlled experimental conditions, and illustrates how the observation of this behavior has been translated into working optimization algorithms. x Preface In chapter 2, the ACO metaheuristic is introduced and put into the general context of combinatorial optimization. Basic notions of complexity theory, such as NP- hardness, are given and other major metaheuristics are briefly overviewed. Chapter 3 is dedicated to the in-depth description of all the major ACO algorithms currently available in the literature. This description, which is developed using the traveling salesman problem as a running example, is completed by a guide to imple- menting the algorithms. A short description of a basic C implementation, as well as pointers to the public software available at www.aco-metaheuristic.org/aco-code/, is given.
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