SIMULATION-BASED OPTIMIZATION

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Contents

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

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