Scatter Search: Methodology and Implementations in C

300 Pages·2003·16.144 MB·English

by  Manuel Laguna, Rafael Martí (auth.)

Scatter Search
Methodology and Implementations in C
OPERATIONS RESEARCH/COMPUTER SCIENCE
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OlcJahoma State University Universitiit Hamburg
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Scatter Search
Methodology and Implementations in C
Manuel Laguna
University of Colorado
Rafael Marti
University of Valencia
a...
"
Springer Science+ Business Media, LLC
Library of Congress Cataloging-in-Publication Data
A C.I.P. Catalogue record for this book is available from the Library ofCongress.
Laguna, Manuel and Marti, Rafael/ SCATTER SEARCH: Methodology and
Implementations in C
ISBN 978-1-4613-5027-9 ISBN 978-1-4615-0337-8 (eBook)
DOI 10.1007/978-1-4615-0337-8
Copyright © 2003 Springer Science+Business Media N ew York
Originally published by Kluwer Academic Publishers in 2003
All rights reserved. No part of this work may be reproduced, stored in a retrieval
system, or transmitted in any form or by any means, electronic, mechanical,
photocopying, microfilming, recording, or otherwise, without the written
permission from the Publisher, with the exception of any material supplied
specifically for the purpose of being entered and executed on a computer system,
for exclusive use by the purchaser of the work.
Permission for books published in Europe: [email protected]
Permissions for books published in the United States of America: [email protected]
Printed on acid-free paper.
To Sofia and Fabian, my limitless source of happiness and inspiration
M.L.
A Mila, por la paz, y sobre todo, por la guerra que me da
R.M.
Contents
Foreword xi
Preface xv
Acknowledgments xvii
1. INTRODUCTION
1. Historical Background 4
1.1. Original Proposal - 1977 4
1.2. Scatter I Tabu Search Hybrid - 1990 6
1.3. Scatter Search Template - 1998 8
2. Basic Design 11
2.1. Summary of Notation 14
3. C Code Conventions 16
2. TUTORIAL: Unconstrained Nonlinear Optimization 23
1. Diversification Generation Method 24
1.1. Computer Code 26
2. Improvement Method 28
2.1. Computer Code 29
3. Reference Set Update Method 31
3.1. Computer Code 33
4. Subset Generation Method 37
4.1. Computer Code 38
5. Combination Method 39
5.1. Computer Code 40
6. Overall Procedure 41
6.1. Computer Code 44
viii Scatter Search
7. Summary of C Functions 46
3. TUTORIAL: 0-1 Knapsack Problems 49
1. Diversification Generation Method 50
1.1. Computer Code 52
2. Improvement Method 55
2.1. Computer Code 57
3. Reference Set Update Method 59
3.1. Computer Code 61
4. Subset Generation Method 62
5. Combination Method 63
5.1. Computer Code 64
6. Overall Procedure 65
6.1. Computer Code 66
7. Summary of C Functions 67
4. TUTORIAL: linear Ordering Problem 69
1. The Linear Ordering Problem 69
2. Diversification Generation Method 71
2.1. Computer Code 74
3. Improvement Method 76
3.1. Computer Code 79
4. Reference Set Update Method 82
5. Combination Method 83
5.1. Computer Code 85
6. Summary of C Functions 86
S. ADVANCED SCATTER SEARCH DESIGNS 89
1. Reference Set 90
1.1. Dynamic Updating 91
1.2. Rebuilding and Multi-Tier Update 93
1.2.1. Rebuilding 94
1.2.2. 2-Tier Update 95
1.2.3. 3-Tier Update 99
1.3. Solution Duplication and Diversity Control 102
1.3.1. Minimum Diversity Test 103
1.3.2. Hashing 105
2. Subset Generation 107
3. Specialized Combination Methods 112
3.1. Variable Number of Solutions 114
3.2. Binary Variables 116
4. Diversification Generation 118
4.1. Experimental Design 118
4.2. GRASP Constructions 120
Contents ix
6. USE OF MEMORY IN SCATTER SEARCH 123
1. Tabu Search 124
2. Explicit Memory 128
3. Attributive Memory 130
3.1. Diversification 131
3.1.1. Computer Code 133
3.2. Intensification 135
3.2.1. Computer Code 136
3.3. Reference Set 138
7. CONNECTIONS WITH OTHER POPULATION-BASED
APPROACHES 141
1. Genetic Algorithms 142
1.1. SS and GA Comparison 146
1.1.1. Improvement Method 149
1.1.2. Combination Method 150
1.1.3. Computational Testing 154
2. Path Relinking 160
2.1. Simultaneous Relinking 166
2.2. Dealing with Infeasibility 167
2.3. Extrapolated Relinking 168
2.4. Multiple Guiding Solutions 170
2.5. Constructive Neighborhoods 172
2.6. Vocabulary Building 173
2.7. Computer Code 177
3. Intensification and Diversification 180
8. SCATTER SEARCH APPLICATIONS 185
1. Neural Network Training 185
1.1. Computer Code 187
2. Multi-Objective Bus Routing 189
3. Arc Crossing Minimization in Graphs 191
4. Maximum Clique 193
5. Graph Coloring 195
6. Periodic Vehicle Loading 197
7. Capacitated Multicommodity Network Design 198
8. Job-Shop Scheduling 201
9. Capacitated Chinese Postman Problem 202
9.1. Testing Population Designs 204
10. Vehicle Routing 206
11. Binary Mixed Integer Programming 208
11.1. Pivot Based Search with Branch and Bound 208
11.2. Generate Diverse Solutions 210
x Scatter Search
12. Iterated Re-start Procedures 212
13. Parallelization for the P-Median 215
14. OptQuest Application 217
9. COMMERCIAL SCATTER SEARCH IMPLEMENTATION 219
1. General OCL Design 223
2. Constraints and Requirements 225
3. OCL Functionality 227
3.1. Defining Constraints and Requirements 232
3.2. Boundary Search Strategy 235
4. Computational Experiments 239
5. Conclusions 245
6. Appendix 246
10. EXPERIENCES AND FUTURE DIRECTIONS 255
1. Experiences and Findings 256
1.1. Diversification Generation 256
1.2. Improvement Method 258
1.3. Reference Set Update Method 260
1.4. Subset Generation Method 263
1.5. Combination Method 264
2. Multi-Objective Scatter Search 266
2.1. Independent Sampling Technique 269
2.2. Criterion Selection Technique 269
2.3. Aggregation Selection Technique 270
2.4. Pareto Sampling 270
3. Maximum Diversity Problem 271
4. Implications for Future Developments 274
REFERENCES 277
INDEX 285
Foreword
The book Scatter Search by Manuel Laguna and Rafael Mart! represents
a long-awaited "missing link" in the literature of evolutionary methods.
Scatter Search (SS)-together with its generalized form called Path
Relinking-constitutes the only evolutionary approach that embraces a
collection of principles from Tabu Search (TS), an approach popularly
regarded to be divorced from evolutionary procedures. The TS perspective,
which is responsible for introducing adaptive memory strategies into the
metaheuristic literature (at purposeful level beyond simple inheritance
mechanisms), may at first seem to be at odds with population-based
approaches. Yet this perspective equips SS with a remarkably effective
foundation for solving a wide range of practical problems. The successes
documented by Scatter Search come not so much from the adoption of
adaptive memory in the range of ways proposed in Tabu Search (except
where, as often happens, SS is advantageously coupled with TS), but from
the use of strategic ideas initially proposed for exploiting adaptive memory,
which blend harmoniously with the structure of Scatter Search.
From a historical perspective, the dedicated use of heuristic strategies
both to guide the process of combining solutions and to enhance the quality
of offspring has been heralded as a key innovation in evolutionary methods,
giving rise to what are sometimes called "hybrid" (or "memetic")
evolutionary procedures. The underlying processes have been introduced
into the mainstream of evolutionary methods (such as genetic algorithms, for
example) by a series of gradual steps beginning in the late 1980s. Yet this
theme is an integral part of the SS methodology proposed a decade earlier,
and the form and scope of such heuristic strategies embedded in SS continue
to set it apart. Although there are points in common between SS and other