Abstract i
Acknowledgements vi
1 Introduction 1
1.1..... Simulation-Based Optimization 1
1.1.1 Simulation-Based Optimization Methods................................................ ........ 4
1.1.2 White Noise vs. Common Random Numbers........................................... ..... 10
1.2..... Bayesian Analysis in Simulation 12
1.2.1 Selecting the Best System .......................................................................... 14
1.2.2 Constructing Bayesian Posterior Estimations........................................ ..... 16
1.2.3 The Bayesian Method for Selecting the Best System . . 20
1.3..... The Two-Phase Optimization Framework 21
1.3.1 The WISOPT Structure ................................................................................ 23
1.3.2 Introduction to the Methodologies.............................................................. ..... 25
1.4..... Outline of the Thesis ..................................................................................................... 33
2 The Phase I Methods
2.1 Classification-Based Global Search
2.1.1 The Idea of Classification-Based Global Search
36
38 38
2.1.2 A Voting Scheme to Assemble Multiple Classifiers ... 40
2.1.3 Handling Imbalanced Dataset.................................................................... ...... 43
2.1.4 General Procedure.......................................................................................... ...... 47
2.1.5 Numerical Examples..................................................................................... ...... 47
2.2..... The Noisy DIRECT Algorithm 51
2.2.1 The DIRECT Optimization Algorithm...................................................... ...... 53
2.2.2 Modifications................................................................................................... ...... 58
2.2.3 Numerical Examples..................................................................................... ...... 65
2.3 The Phase Transition Module ..................................................................................... ...... 73
3 Phase II Methods 80
3.1 The Deterministic UOBYQA Algorithm ................................................................. ..... 81
3.1.1 The Core Algorithm ..................................................................................... ..... 82
3.1.2 Interpolating Quadratic Model Properties ............................................ ..... 85
3.2..... The VNSP-UOBYQA Algorithm 86
3.2.1 The Bayesian VNSP Scheme....................................................................... ..... 89
3.2.2 Convergence Analysis of the Algorithm .................................................... ... 103
3.2.3 Numerical Results ...................................................................................... ... 111
3.3..... The Noisy UOBYQA Algorithm 118
3.3.1 Modifications................................................................................................... 119
3.3.2 Numerical Results ...................................................................................... 128
4 Applications 136
4.1 The Wisconsin Breast Cancer Epidemiology Simulation .... 137
4.1.1 Introduction .................................................................................................... 137
4.1.2 Methods and Results .................................................................................... 139
4.2..... The Coaxial Antenna Design in Microwave Ablation 145
4.2.1 Introduction .................................................................................................... 145
4.2.2 Methods ........................................................................................................... 148
4.2.3 Results ............................................................................................................. 154
4.2.4 Conclusions ..................................................................................................... 162
4.3 Ambulance Base Problem .......................................................................................... 164
5 Monte Carlo Simulation Efficiency in Neuro-Dynamic Pro-
gramming 168
gramming 168
5.1 Introduction ..................................................................................................................... 169
5.2 Evaluating Rollout Policy Accuracy ............................................................................ 178
5.2.1 Bayesian Posterior Estimation .................................................................. 180
5.2.2 Computing the PCS....................................................................................... 181
5.3..... Allocating Simulation Resource 184
5.3.1 The Resource Allocation Scheme .............................................................. 184
5.3.2 Special Case - Finite State Space............................................................... 186
5.3.3 An Extension - Group Similar M by Policy................................................ 188
5.4 A Fractionated Radiotherapy Problem ................................................................... 190
5.5 Conclusions....................................................................................................................... 197
6 Conclusions 198
A User Guide to WISOPT 203
Bibliography 214
Tags
MCA Notes