1 Introduction 1
1.1 Motivation . . . 1
1.2 Main contributions . . . 4
1.3 Structure of the thesis . . . 7
2 Background 9 2.1 Introduction . . . 9
2.2 Combinatorial optimization . . . 10
2.3 Quadratic assignment problem . . . 11
2.4 Examples of real world QAP applications . . . 12
2.4.1 Hospital layout problem . . . 12
2.4.2 Keyboard layout problem . . . 12
2.4.3 Backboard wiring problem . . . 14
2.4.4 Turbine balancing problem . . . 14
2.4.5 Other QAP applications . . . 14
2.5 Computational complexity . . . 15
2.6 Solving the QAP . . . 18
2.6.1 Exact algorithms . . . 19
2.6.2 Approximate algorithms . . . 20
2.7 Iterative improvement algorithms for the QAP . . . 22
2.8 Metaheuristics . . . 26
2.8.1 Simulated Annealing . . . 27
2.8.2 Tabu Search . . . 29
vi Contents
2.8.3 Iterated Local Search . . . 30
2.8.4 Ant Colony Optimization . . . 32
2.8.5 Evolutionary Algorithms . . . 35
2.9 Multi-objective QAP . . . 36
2.10 SLS algorithms for multi-objective combinatorial optimization problems . . . 39
2.11 Conclusions . . . 40
3 Experimental design 41 3.1 Introduction . . . 41
3.2 Analysis of QAP instances . . . 41
3.2.1 Characterization of QAP instances . . . 42
3.2.2 Search space analysis of the QAP . . . 43
3.3 Publicly available instances . . . 45
3.3.1 QAPLIB instances . . . 46
3.3.2 Drezner’s and Taillard’s instances . . . 47
3.3.3 Microarray instances . . . 49
3.3.4 QAP instances with known optimal solutions. . . 51
3.4 Generated instances. . . 51
3.4.1 Structured flow matrix . . . 53
3.4.2 Euclidean distance matrix . . . 53
3.4.3 Grid distance matrix . . . 54
3.4.4 Random distance matrix . . . 55
3.4.5 Search space analysis of generated instances . . . 55
3.5 Parameter tuning - F-Race and Iterated F-Race . . . 56
3.6 Conclusions . . . 60
4 New Algorithm Variants 61
4.1 Introduction . . . 61
4.2 Hierarchical Iterated Local Search . . . 62
4.2.1 Algorithm: Hierarchical Iterated Local Search . . . 63
4.2.2 Benchmark instances . . . 65
4.2.3 Choice of local search. . . 65
4.2.4 Experimental study of HILS combinations . . . 66
4.2.5 Performance comparison of HILS and ILS variants. . . 66
4.2.6 Comparison of HILS, ILS-ES, ILSts, and RoTS . . . . 70
4.2.7 HILS(3) . . . 71
4.2.8 Discussion . . . 72
4.3 Comparison of SA and TS . . . 74
4.3.1 Algorithms . . . 75
4.3.2 Benchmark instances . . . 76
4.3.3 Experimental results . . . 77
4.3.4 Discussion . . . 84
4.4 Conclusions . . . 85
5 Stochastic Local Search algorithms for the QAP 87 5.1 Introduction . . . 87
5.2 SLS algorithms for the QAP . . . 88
5.2.1 Simulated Annealing . . . 88
5.2.2 Tabu Search . . . 89
5.2.3 Iterated Local Search . . . 92
5.2.4 Ant Colony Optimization . . . 96
5.2.5 Evolutionary Algorithms . . . 97
viii Contents
5.3 Experimental setup . . . 101
5.4 Performance comparison on benchmarks . . . 103
5.4.1 QAPLIB instances . . . 103
5.4.2 Taillard’s instances . . . 104
5.4.3 Microarray instances . . . 107
5.4.4 Drezner’s instances . . . 111
5.5 Tuning results . . . 111
5.5.1 Results of tuning Simulated Annealing . . . 113
5.5.2 Results of tuning Robust Tabu Search . . . 114
5.5.3 Results of tuning Iterated Local Search . . . 115
5.5.4 Results of tuning MMAS . . . 118
5.5.5 Results of tuning Evolutionary Algorithms . . . 119
5.5.6 Results of tuning Hierarchical ILS . . . 120
5.6 Default vs. tuned parameter settings . . . 120
5.7 Overall performance comparison . . . 123
5.8 Additional performance comparison on ES instances . . . 131
5.9 General result of algorithms . . . 139
5.10 Conclusions . . . 139
6 SLS algorithms for bi-objective QAP 141 6.1 Introduction . . . 141
6.2 Bi-objective QAP . . . 141
6.3 bQAP Instances. . . 142
6.4 Performance of SLS algorithms for MOP . . . 143
6.4.1 Empirical attainment function . . . 144
6.4.2 Hypervolume indicator . . . 146
6.5 SLS Algorithms for multi-objective combinatorial optimization
problems . . . 146
6.6 SLS Algorithms for bQAP . . . 148
6.6.1 Two-phase Local Search . . . 149
6.6.2 Pareto Local Search . . . 151
6.6.3 Multi Objective Ant Colony Optimization . . . 152
6.6.4 Strength Pareto Evolutionary Algorithm 2 . . . 153
6.7 Hybrid TPLS-PLS algorithms . . . 153
6.8 Experimental results . . . 157
6.9 Conclusions . . . 163
7 Conclusions 167 7.1 Contributions . . . 167
7.2 Future work . . . 171
Bibliography 173
