Heuristic Search. The Emerging Science of Problem Solving

221 Pages·2017·1.588 MB·english

by  Saïd Salhi

SaïdSalhi
Heuristic Search
The Emerging Science of Problem Solving
SaïdSalhi
CentreforLogistics&HeuristicOptimisation
KentBusinessSchool,UniversityofKent
Canterbury,UnitedKingdom
ISBN978-3-319-49354-1 ISBN978-3-319-49355-8 (eBook)
DOI10.1007/978-3-319-49355-8
LibraryofCongressControlNumber:2016957033
©TheEditor(s)(ifapplicable)andTheAuthor(s)2017
ThisPalgraveMacmillanimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Preface
This monograph aims to provide an overview of heuristic search in
general, to present the basic steps of the most popular heuristics and to
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stress the hidden dif culties as well as the challenging opportunities
presented to researchers and practitioners when faced with complex
combinatorial and global optimisation problems. Heuristic search,
which is a combination of several attributes ranging from mathematical
logictoexperience,isanartandascienceatthesametime.Someofthese
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heuristics are inspired from natural and biological evolution, arti cial
intelligence and even music. Their applications are now widely used in
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engineering, nance, management, sport and medicine among others.
This book is written in an informal way so that students and
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non-specialists will nd it easy to read and will get interested in this
exciting decision science-based subject. Throughout the text, comments
and observations will be added to keep an open mind on how these
approaches are conceived, analysed and applied. Each chapter starts with
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a brief introduction and nishes with a small summary to provide the
reader with the opportunity to read the chapter in its entirety, or just the
overview.
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At rst glance, these methods present themselves as simple and easy,
but once the experience kicks in, the researcher and/or practitioner will
start to appreciate that their implementation is harder than expected,
challenging and probably addictive, if you permit me to use this word.
By the end of this book the reader will acquire the basic philosophy of
these exciting andlively methodologies,and astrong foundation to build
on when designing and analysing his/her own techniques.
Itisalso worthmentioningthatheuristicsearch isconsideredas agrey
research area that is not as structured as classical research, and hence
considered by some as less rigorous. Meanwhile, others like myself take
fl
theoppositeviewofembracingitduetoits exibilityandsoftboundaries
that make the science even more exciting and rewarding.
This book is suitable as an introductory and general book on heuristic
search for combinatorial and global optimisation for research students at
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the master s and doctoral levels in Operational Research, Computer
Science, Engineering and Medicine. Consultants and analysts in
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problem-solving and decision-making will also nd this book to be a
practical addition to their analysis tool kit while being useful and easy to
read and understand.
Centre for Logistics & Heuristic Optimisation Saïd Salhi
Kent Business School
University of Kent
Canterbury, UK
Contents
1 Introduction 1
1.1 Introduction 1
1.2 The Optimisation Problem 3
1.3 Possible Methodological Approaches 4
1.4 Need for Heuristics 8
1.5 Some Characteristics of Heuristics 9
1.6 Complexity and Performance of Heuristics 11
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1.7 A Possible Heuristic Classi cation 16
1.8 Summary 16
References 17
2 Improvement-Only Heuristics 19
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2.1 Neighbourhood De nition and Examples 19
2.2 Basic Descent or Hill Climbing Method 23
2.3 Classical Multi-Start 27
2.4 GRASP 28
2.5 Simple Composite Heuristics 30
2.6 A Multi-Level Composite Heuristic 32
2.7 Variable Neighbourhood Search 34
2.8 Problem Perturbation Heuristics 38
2.9 Other Improving Only Methods 41
2.10 Summary 45
References 45
3 Not Necessary Improving Heuristics 49
3.1 Simulated Annealing 49
3.2 TA Heuristics 58
3.3 Tabu Search (TS) 61
3.4 Summary 74
References 74
4 Population-Based Heuristics 77
4.1 Genetic Algorithms 77
4.2 Scatter Search 90
4.3 Harmony Search 92
4.4 Differential Evolution 97
4.5 Ant Colonies 103
4.6 The Bees Algorithm 111
4.7 Particle Swarm Optimisation 115
4.8 A Brief on Other Population-Based Approaches 118
4.9 Summary 124
References 125
5 Hybridisation Search 129
5.1 Hybridisation of Heuristics with Heuristics 129
5.2 Integrating Heuristics Within Exact Methods 135
5.3 Integration of ILP Within Heuristics/Metaheuristics 146
5.4 Data Mining Hybridisation Search 149
5.5 Summary 152
References 153
6 Implementation Issues 157
6.1 Data Structure 157
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6.2 Duplication Identi cation 162
6.3 Approximation Effect on Cost Function Evaluation 164
6.4 Reduction Tests/Neighbourhood Reduction 165
6.5 Parameters Estimation/Adaptive Search 169
6.6 Constraint Handling via SO 171
6.7 Impact of Parallelisation 173
6.8 Fuzzy Logic 179
6.9 Dealing with Multiple Objectives 181
6.10 Summary 186
References 187
7 Applications, Conclusion and Research Challenges 189
7.1 Real-Life Applications 189
7.2 Conclusion 197
7.3 Research Challenges 199
References 205
Index 211
Algorithms
Algorithm1.1 APossibleRecursiveMethodologicalApproach 6
Algorithm2.1 TheBasicDescentMethod 23
Algorithm2.2 ABasicGRASP 29
Algorithm2.3 ABasicCompositeHeuristic 30
Algorithm2.4 ABasicMulti-levelHeuristic 33
Algorithm2.5 ABasicVNSHeuristic 35
Algorithm3.1 ABasicSAHeuristic 51
Algorithm3.2 ABasicTAHeuristic 58
Algorithm3.3 ABasicTSHeuristic 63
Algorithm4.1 ABasicGeneticAlgorithm 78
Algorithm4.2 ABasicScatterSearchHeuristic 91
Algorithm4.3 BasicHarmonySearchHeuristic 95
Algorithm4.4 ABasicDifferentialEvolutionHeuristic 99
Algorithm4.5 ABasicASHeuristic 106
Algorithm4.6 ABasicBeesAlgorithm 112
Algorithm4.7 TheABCAlgorithm 114
Algorithm4.8 ABasicPSOHeuristic 117
Figures
Fig.1.1 Aheuristicclassification 17
Fig.2.1 Localoptimalityrepresentationofacontinuousfunction 27
Fig.2.2 Apossibletourimprovement 31
Fig.2.3 Moretourimprovement 31
Fig.4.1 Abinaryencodingofthefivefacilitiesexample 79
Fig.4.2 Anintegerencodingofthefivefacilitiesexample 79
Fig.4.3 Injectionofchromosomesandnew-generationcomposition 88
Fig.5.1 Arepresentationoftheimprovementhyper-heuristics 133
Fig.5.2 PrincipleofLagrangeanrelaxationheuristics 137
Fig.5.3 IntegratingheuristicpowerwithinB&B 144
Fig.5.4 Datamininghybridisationsearchheuristics 151
Fig.5.5 Adynamicdataminingapproach(degreeof
focusvsiterations) 152
Fig.6.1 TwoneighbourhoodreductionsfortheVRP 168
Fig.6.2 Exchangeofinformationbetweenthemaster
andtheslaveprocessors 174
Fig.6.3 Fuzzyquality 180
Fig.6.4 Paretocurve,heuristicsolutionsandtheidealpoint 183
Fig.6.5 MoveselectionfromSctoS2NðScÞinbi-objective
optimisation 185
Table
Table3.1 Theeffectoftheinitialsolutionwhenusingboth
SAandDM 53