Iowa State University Capstones, Theses and Graduate Theses and Dissertations Dissertations 2009 Continuous optimization via simulation using Golden Region search Alireza Kabirian Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/etd Part of the Industrial Engineering Commons Recommended Citation Kabirian, Alireza, "Continuous optimization via simulation using Golden Region search" (2009). Graduate Theses and Dissertations. 10572. https://lib.dr.iastate.edu/etd/10572 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Graduate Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Continuous optimization via simulation using Golden Region search by Alireza Kabirian A dissertation submitted to the graduate faculty in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Major: Industrial Engineering Program of Study Committee: Sigurdur Olafsson, Major Professor Douglas D Gemmill John K Jackman Max D Morris Jennifer Jane Blackhurst David M Frankel Iowa State University Ames, Iowa 2009 Copyright © Alireza Kabirian, 2009. All rights reserved. ii To: Cyrus, the Great and My Parents: Jamileh and Fathollah iii Table of Contents Acknowledgement ........................................................................................................................................ v Abstract ........................................................................................................................................................ vi Chapter 1: Introduction ................................................................................................................................. 1 1. What is Optimization? ........................................................................................................................... 1 1.1. Components of Optimization Problems ........................................................................................ 1 1.2. Classification of Optimization Problems ...................................................................................... 2 1.2.1 Objective Function .................................................................................................................... 2 1.2.2 Decision Variables .................................................................................................................... 3 1.2.3 Constraints ................................................................................................................................ 3 1.2.4 Functions ................................................................................................................................... 4 1.2.5 Feasible region .......................................................................................................................... 5 1.3. Optimization Methods .................................................................................................................. 5 2. Numerical Optimization of Expensive and Noisy Functions ................................................................ 6 2.1. Examples- Objective Functions .................................................................................................... 6 2.2. Examples- Functions in Constraints ............................................................................................. 8 2.3. Properties of the problem .............................................................................................................. 9 3. What is Discrete-Event Simulation? .................................................................................................... 10 3.1. Principles and Definitions ........................................................................................................... 10 3.2. Advantages and Disadvantages ................................................................................................... 13 4. Simulation based Optimization ............................................................................................................ 14 5. Hypothesis of This Research ............................................................................................................... 18 6. Organization of This Thesis ................................................................................................................. 19 Chapter 2: Problem Background ................................................................................................................. 20 1. Simulation Optimization Problems ...................................................................................................... 20 2. Methods of Simulation Optimization .................................................................................................. 21 2.1. Survey Articles in the Literature ................................................................................................. 21 2.2. Available Methods ...................................................................................................................... 24 2.2.1 Single-Objective Quantitative-Variable Methods ................................................................... 25 2.2.2 Single-Objective Qualitative-Variable Methods ..................................................................... 37 2.2.3 Multiobjective Methods .......................................................................................................... 38 3. Commercial Softwares of Simulation Optimization ............................................................................ 39 Chapter 3: Hybrid Probabilistic Search ...................................................................................................... 40 1. Introduction ......................................................................................................................................... 40 2. Probabilistic Search Methods .............................................................................................................. 41 3. Analysis of Hybrid Probabilistic Search Methods ............................................................................... 43 3.1. Algorithm of Hybrid Probabilistic Search .................................................................................. 44 3.2. Convergence of Hybrid Probabilistic Search .............................................................................. 46 4. Example Procedure .............................................................................................................................. 46 Chapter 4: Golden Region Search Method ................................................................................................. 49 1. Introduction ......................................................................................................................................... 49 2. Notation ............................................................................................................................................... 49 3. Overview of the Golden Region Algorithm ........................................................................................ 51 4. Detailed Golden Region Algorithm ..................................................................................................... 53 4.1. Promising Region Selection ........................................................................................................ 53 4.1.1 Space Score ............................................................................................................................. 54 iv 4.1.2 Quality Score .......................................................................................................................... 55 4.1.3 Metamodel Score .................................................................................................................... 56 4.2. New Point Generation ................................................................................................................. 57 4.3. Adaptive Criteria Coefficients .................................................................................................... 58 4.4. Stopping Conditions .................................................................................................................... 59 5. Implementation Issues ......................................................................................................................... 60 5.1. How to partition .......................................................................................................................... 60 5.2. Metamodeling ............................................................................................................................. 61 5.3. Parameter Selection .................................................................................................................... 62 6. GR Convergence Analysis and Hybrid GR ......................................................................................... 63 Chapter 5: Efficiency of Golden Region Search ......................................................................................... 67 1. What is a good Simulation Optimization method? .............................................................................. 67 2.