ISBN: 3-540-66367-3
TITLE: Integer Optimization by Local Search
AUTHOR: Walser, Joachim P.
TOC:

1. Introduction 1
1.1 Integer Optimization and Heuristics 1
1.2 Integer Local Search 5
1.3 Experimental Results 7
1.4 Research Contributions 9
2. Frameworks for Combinatorial Optimization 11
2.1 Integer Programming Branch- and- Bound 11
2.2 Finite Domain Constraint Programming 13
2.3 Local Search 15
2.3.1 Meta- heuristics 16
2.3.2 RISC and CISC Local Search 17
2.3.3 Local Search for SAT 18
2.3.4 Application Domains of SAT Local Search 20
2.4 Modeling Languages 21
2.5 Search Relaxations and Integer Local Search 21
3. Local Search for Integer Constraints 25
3.1 Over- Constrained Integer Programs 25
3.1.1 Definition 27
3.1.2 Relation to Integer Linear Programs 28
3.1.3 Constraint-Bounds 31
3.2 Integer Local Search: Wsat(oip) 32
3.2.1 The Score 33
3.2.2 The Main Loop 34
3.2.3 Move Selection and Tabu Search Extensions 34
3.3 Combinations with Linear Programming. 37
3.3.1 Bounds from LP Relaxations 37
3.3.2 Initialization by Rounding LP Solutions 38
3.3.3 Search Space Reduction Using LP Reduced Costs 40
3.3.4 Implementation Issues 41
3.4 A Graphical Interpretation 43
3.5 Related Work 47
3.5.1 Integer Programming Heuristics 48
3.5.2 Local Search in Constraint Satisfaction 51
3.6 Summary 51
4. Case Studies Methodology 53
4.1 Optimization in Practice: Criteria of Success 53
4.1.1 Scaling with Increasing Problem Size 54
4.1.2 Scaling with Increasing Constrainedness 55
4.1.3 Flexibility and Residual Robustness 56
4.2 The Problem Class Selection 56
4.3 The Empirical Comparisons 57
5. Time-Tabling and Sports Scheduling 59
5.1 The Progressive Party Problem 59
5.1.1 Problem Description and Formulation 60
5.1.2 Experimental Results and Comparison 62
5.2 The ACC Basketball Scheduling Problem 64
5.2.1 Double Round Robin Scheduling 65
5.2.2 Problem Specification of ACC97/98 66
5.2.3 Integer Local Search Formulation 68
5.2.4 Redundant Constraints 71
5.2.5 Previous (Multi- stage) Approaches 72
5.2.6 Experimental Results under Varied Constrainedness 73
5.2.7 Minimal Distortion Mirroring 76
5.3 Conclusions 78
6. Covering and Assignment 81
6.1 Radar Surveillance Covering 81
6.1.1 Problem Description and Formulation 81
6.1.2 Experimental Results under Varied Problem Size 83
6.2 Course Assignment 87
6.2.1 Problem Description and Formulation 87
6.2.2 Experimental Results under Varied Problem Size 89
6.2.3 A Related Application: Reviewer Assignment 91
6.3 Conclusions 93
7. Capacitated Production Planning 95
7.1 Capacitated Lot- Sizing 96
7.2 Integer Local Search Formulation 98
7.3 Mixed Integer Programming Formulation 99
7.3.1 Lagrangean Relaxation Approach 100
7.3.2 Restricting the Problem 101
7.4 Experimental Results 101
7.4.1 Comparison of Results 101
7.4.2 Lower Bounds 104
7.5 Conclusions 105
8. Extensions 107
8.1 Current Limitations 107
8.2 An Alternative Scoring Scheme 108
8.3 Future Research 111
8.4 Conclusions 112
A. A Complete AMPL Model for ACC97/98 115
References 122
Index 135
END
