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SIMULATION-BASED OPTIMIZATION


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 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

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