Stochastic Simulation Optimization : An Optimal Computing Budget Allocation.

By: Chen, Chun-HungContributor(s): Lee, Loo HaySeries: System Engineering and Operations Research SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2010Copyright date: ©2011Description: 1 online resource (246 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789814282659Subject(s): Systems engineering -- Simulation methods.;Stochastic processes.;Mathematical optimizationGenre/Form: Electronic books. Additional physical formats: Print version:: Stochastic Simulation Optimization : An Optimal Computing Budget AllocationDDC classification: 658.4 LOC classification: TA168 -- .C475 2011ebOnline resources: Click to View
Contents:
Intro -- Contents -- Foreword -- Preface -- Acknowledgments -- 1. Introduction to Stochastic Simulation Optimization -- 1.1 Introduction -- 1.2 Problem Definition -- 1.3 Classification -- 1.3.1. Design space is small -- 1.3.2. Design space is large -- 1.4 Summary -- 2. Computing Budget Allocation -- 2.1 Simulation Precision versus Computing Budget -- 2.2 Computing Budget Allocation for Comparison of Multiple Designs -- 2.3 Intuitive Explanations of Optimal Computing Budget Allocation -- 2.4 Computing Budget Allocation for Large Simulation Optimization -- 2.5 Roadmap -- 3. Selecting the Best from a Set of Alternative Designs -- 3.1 A Bayesian Framework for Simulation Output Modeling -- 3.2 Probability of Correct Selection -- 3.3 Maximizing the Probability of Correct Selection -- 3.3.1. Asymptotically optimal solution -- 3.3.2. OCBA simulation procedure -- 3.4 Minimizing the Total Simulation Cost -- 3.5 Non-Equal Simulation Costs -- 3.6 Minimizing Opportunity Cost -- 3.7 OCBA Derivation Based on Classical Model -- 4. Numerical Implementation and Experiments -- 4.1 Numerical Testing -- 4.1.1. OCBA algorithm -- 4.1.2. Different allocation procedures for comparison -- 4.1.3. Numerical experiments -- 4.2 Parameter Setting and Implementation of the OCBA Procedure -- 4.2.1. Initial number of simulation replications, n0 -- 4.2.2. One-time incremental computing budget, . -- 4.2.3. Rounding off Ni to integers -- 4.2.4. Variance -- 4.2.5. Finite computing budget and normality assumption -- 5. Selecting An Optimal Subset -- 5.1 Introduction and Problem Statement -- 5.2 Approximate Asymptotically Optimal Allocation Scheme -- 5.2.1. Determination of c value -- 5.2.2. Sequential allocation scheme -- 5.3 Numerical Experiments -- 5.3.1. Computing budget allocation procedures -- 5.3.2. Numerical results -- 6. Multi-objective Optimal Computing Budget Allocation.
6.1 Pareto Optimality -- 6.2 Multi-objective Optimal Computing Budget Allocation Problem -- 6.2.1. Performance index for measuring the dominance relationships and the quality of the selected Pareto set -- 6.2.1.1. A performance index to measure the degree of non-dominated for a design -- 6.2.1.2. Construction of the observed Pareto set -- 6.2.1.3. Evaluation of the observed Pareto set by two types of errors -- 6.2.2. Formulation for the multi-objective optimal computing budget allocation problem -- 6.3 Asymptotic Allocation Rule -- 6.4 A Sequential Allocation Procedure -- 6.5 Numerical Results -- 6.5.1. A 3-design case -- 6.5.2. Test problem with neutral spread designs -- 6.5.3. Test problem with steep spread designs -- 7. Large-Scale Simulation and Optimization -- 7.1 A General Framework of Integration of OCBA with Metaheuristics -- 7.2 Problems with Single Objective -- 7.2.1. Neighborhood random search (NRS) -- 7.2.2. Cross-entropy method (CE) -- 7.2.3. Population-based incremental learning (PBIL) -- 7.2.4. Nested partitions -- 7.3 Numerical Experiments -- 7.4 Multiple Objectives -- 7.4.1. Nested partitions -- 7.4.2. Evolutionary algorithm -- 7.5 Concluding Remarks -- 8. Generalized OCBA Framework and Other Related Methods -- 8.1 Optimal Computing Budget Allocation for Selecting the Best by Utilizing Regression Analysis (OCBA-OSD) -- 8.2 Optimal Computing Budget Allocation for Extended Cross-Entropy Method (OCBA-CE) -- 8.3 Optimal Computing Budget Allocation for Variance Reduction in Rare-event Simulation -- 8.4 Optimal Data Collection Budget Allocation (ODCBA) for Monte Carlo DEA -- 8.5 Other Related Works -- Appendix A: Fundamentals of Simulation -- A.1 What is Simulation? -- A.2 Steps in Developing A Simulation Model -- A.3 Concepts in Simulation Model Building -- A.4 Input Data Modeling -- A.5 Random Number and Variables Generation.
A.5.1. The Linear congruential generators (LCG) -- A.5.2. Random variate generation -- A.5.2.1. Inverse transform method -- A.5.2.2. Acceptance rejection method -- A.6 Output Analysis -- A.6.1. Output analysis for terminating simulation -- A.6.2. Output analysis for steady-state simulation -- A.7 Verification and Validation -- Appendix B: Basic Probability and Statistics -- B.1 Probability Distribution -- B.2 Some Important Statistical Laws -- B.3 Goodness of Fit Test -- Appendix C: Some Proofs in Chapter 6 -- C.1 Proof of Lemma 6.1 -- C.2 Proof of Lemma 6.2 -- C.3 Proof of Lemma 6.3 -- C.4 Proof of Lemma 6.5 (Asymptotic Allocation Rules) -- C.4.1. Determination of roles -- C.4.2. Allocation rules -- C.4.2.1. h ∈ SA, o ∈ SA -- C.4.2.2. d ∈ SB -- Appendix D: Some OCBA Source Codes -- References -- Index.
Summary: Key Features:This book explores a novel idea of optimal computing budget allocation in stochastic simulation optimization where the computational efficiency can be significantly enhanced, with the advantage of simulation modeling capability being preservedThis book covers both theoretic development and practical implementation guidelines.
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Intro -- Contents -- Foreword -- Preface -- Acknowledgments -- 1. Introduction to Stochastic Simulation Optimization -- 1.1 Introduction -- 1.2 Problem Definition -- 1.3 Classification -- 1.3.1. Design space is small -- 1.3.2. Design space is large -- 1.4 Summary -- 2. Computing Budget Allocation -- 2.1 Simulation Precision versus Computing Budget -- 2.2 Computing Budget Allocation for Comparison of Multiple Designs -- 2.3 Intuitive Explanations of Optimal Computing Budget Allocation -- 2.4 Computing Budget Allocation for Large Simulation Optimization -- 2.5 Roadmap -- 3. Selecting the Best from a Set of Alternative Designs -- 3.1 A Bayesian Framework for Simulation Output Modeling -- 3.2 Probability of Correct Selection -- 3.3 Maximizing the Probability of Correct Selection -- 3.3.1. Asymptotically optimal solution -- 3.3.2. OCBA simulation procedure -- 3.4 Minimizing the Total Simulation Cost -- 3.5 Non-Equal Simulation Costs -- 3.6 Minimizing Opportunity Cost -- 3.7 OCBA Derivation Based on Classical Model -- 4. Numerical Implementation and Experiments -- 4.1 Numerical Testing -- 4.1.1. OCBA algorithm -- 4.1.2. Different allocation procedures for comparison -- 4.1.3. Numerical experiments -- 4.2 Parameter Setting and Implementation of the OCBA Procedure -- 4.2.1. Initial number of simulation replications, n0 -- 4.2.2. One-time incremental computing budget, . -- 4.2.3. Rounding off Ni to integers -- 4.2.4. Variance -- 4.2.5. Finite computing budget and normality assumption -- 5. Selecting An Optimal Subset -- 5.1 Introduction and Problem Statement -- 5.2 Approximate Asymptotically Optimal Allocation Scheme -- 5.2.1. Determination of c value -- 5.2.2. Sequential allocation scheme -- 5.3 Numerical Experiments -- 5.3.1. Computing budget allocation procedures -- 5.3.2. Numerical results -- 6. Multi-objective Optimal Computing Budget Allocation.

6.1 Pareto Optimality -- 6.2 Multi-objective Optimal Computing Budget Allocation Problem -- 6.2.1. Performance index for measuring the dominance relationships and the quality of the selected Pareto set -- 6.2.1.1. A performance index to measure the degree of non-dominated for a design -- 6.2.1.2. Construction of the observed Pareto set -- 6.2.1.3. Evaluation of the observed Pareto set by two types of errors -- 6.2.2. Formulation for the multi-objective optimal computing budget allocation problem -- 6.3 Asymptotic Allocation Rule -- 6.4 A Sequential Allocation Procedure -- 6.5 Numerical Results -- 6.5.1. A 3-design case -- 6.5.2. Test problem with neutral spread designs -- 6.5.3. Test problem with steep spread designs -- 7. Large-Scale Simulation and Optimization -- 7.1 A General Framework of Integration of OCBA with Metaheuristics -- 7.2 Problems with Single Objective -- 7.2.1. Neighborhood random search (NRS) -- 7.2.2. Cross-entropy method (CE) -- 7.2.3. Population-based incremental learning (PBIL) -- 7.2.4. Nested partitions -- 7.3 Numerical Experiments -- 7.4 Multiple Objectives -- 7.4.1. Nested partitions -- 7.4.2. Evolutionary algorithm -- 7.5 Concluding Remarks -- 8. Generalized OCBA Framework and Other Related Methods -- 8.1 Optimal Computing Budget Allocation for Selecting the Best by Utilizing Regression Analysis (OCBA-OSD) -- 8.2 Optimal Computing Budget Allocation for Extended Cross-Entropy Method (OCBA-CE) -- 8.3 Optimal Computing Budget Allocation for Variance Reduction in Rare-event Simulation -- 8.4 Optimal Data Collection Budget Allocation (ODCBA) for Monte Carlo DEA -- 8.5 Other Related Works -- Appendix A: Fundamentals of Simulation -- A.1 What is Simulation? -- A.2 Steps in Developing A Simulation Model -- A.3 Concepts in Simulation Model Building -- A.4 Input Data Modeling -- A.5 Random Number and Variables Generation.

A.5.1. The Linear congruential generators (LCG) -- A.5.2. Random variate generation -- A.5.2.1. Inverse transform method -- A.5.2.2. Acceptance rejection method -- A.6 Output Analysis -- A.6.1. Output analysis for terminating simulation -- A.6.2. Output analysis for steady-state simulation -- A.7 Verification and Validation -- Appendix B: Basic Probability and Statistics -- B.1 Probability Distribution -- B.2 Some Important Statistical Laws -- B.3 Goodness of Fit Test -- Appendix C: Some Proofs in Chapter 6 -- C.1 Proof of Lemma 6.1 -- C.2 Proof of Lemma 6.2 -- C.3 Proof of Lemma 6.3 -- C.4 Proof of Lemma 6.5 (Asymptotic Allocation Rules) -- C.4.1. Determination of roles -- C.4.2. Allocation rules -- C.4.2.1. h ∈ SA, o ∈ SA -- C.4.2.2. d ∈ SB -- Appendix D: Some OCBA Source Codes -- References -- Index.

Key Features:This book explores a novel idea of optimal computing budget allocation in stochastic simulation optimization where the computational efficiency can be significantly enhanced, with the advantage of simulation modeling capability being preservedThis book covers both theoretic development and practical implementation guidelines.

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