University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations 2014 Unveiling Hidden Values of Optimization Models with Metaheuristic Approach Ann Kuo University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Library and Information Science Commons, and the Operational Research Commons Recommended Citation Kuo, Ann, "Unveiling Hidden Values of Optimization Models with Metaheuristic Approach" (2014). Publicly Accessible Penn Dissertations. 1334. https://repository.upenn.edu/edissertations/1334 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/1334 For more information, please contact [email protected]. Unveiling Hidden Values of Optimization Models with Metaheuristic Approach Abstract Considering that the decision making process for constrained optimization problem is based on modeling, there is always room for alternative solutions because there is usually a gap between the model and the real problem it depicts. This study looks into the problem of finding such alternative solutions, the non-optimal solutions of interest for constrained optimization models, the SoI problem. SoI problems subsume finding easiblef solutions of interest (FoIs) and infeasible solutions of interest (IoIs). In all cases, the interest addressed is post-solution analysis in one form or another. Post-solution analysis of a constrained optimization model occurs after the model has been solved and a good or optimal solution for it has been found. At this point, sensitivity analysis and other questions of import for decision making come into play and for this purpose the SoIs can be very valuable. An evolutionary computation approach (in particular, a population-based metaheuristic) is proposed for solving the SoI problem and a systematic approach with a feasible-infeasible- two-population genetic algorithm is demonstrated. In this study, the effectiveness of the proposed approach on finding SoIs is demonstrated with generalized assignment problems and generalized quadratic assignment problems. Also, the applications of the proposed approach on the multi-objective optimization and robust-optimization issues are examined and illustrated with two-sided matching problems and flowshop scheduling problems respectively. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Operations & Information Management First Advisor Steven O. Kimbrough Keywords Constrained Optimization, Deliberation Support, Genetic Algorithm, Metaheuristic, Post-Evaluation Analysis Subject Categories Library and Information Science | Operational Research This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/1334 UNVEILING HIDDEN VALUES OF OPTIMIZATION MODELS WITH METAHEURISTIC APPROACH Ann Kuo A DISSERTATION in Operations and Information Management For the Graduate Group in Managerial Science and Applied Economics Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2014 Supervisor of Dissertation Steven O. Kimbrough, Professor, OPIM Graduate Group Chairperson Eric T. Bradlow, K.P. Chao Professor, Marketing, Statistics and Education Dissertation Committee Steven O. Kimbrough, Professor, OPIM Monique Guignard-Spielberg, Professor, OPIM Kartik Hosanager, Professor, OPIM UNVEILING HIDDEN VALUES OF OPTIMIZATION MODELS WITH METAHEURISTIC APPROACH c COPYRIGHT 2014 Ann Jane-Ahn Kuo This work is licensed under the Creative Commons Attribution NonCommercial-ShareAlike 3.0 License To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/3.0/ ACKNOWLEDGEMENT I wish to express my deepest and sincere gratitude to my advisor Prof. Steven O. Kim- brough. Completing this dissertation could not have been possible without his perpetual encouragement, motivation, and support. His insights lead me to this intriguing study and all his contribution of time and ideas make my Ph.D. experience fruitful and stimulating. I am grateful to my dissertation committee members, Prof. Steven O. Kimbrough, Prof. Monique Guignard-Spielberg, and Prof. Kartik Hosanager for their time, suggestions, valu- able comments, and encouragement. I would also like to thank the University of Pennsylva- nia for the financial support which gave me the precious opportunity and made my Ph.D. work possible with the OPIM program. It gives me great pleasure in acknowledging the help of Prof. David Harlan Wood; he is always cheerful, enthusiastic, and willing to share his knowledge and experiences. Finally, I would like to express my heartfelt gratitude, love, and admiration to my parents Prof. T. S. Kuo and A. C. Kuo. I am immensely indebted to them for their upbringing, nurture, unconditional love and endless support in all my pursuits. iii ABSTRACT UNVEILING HIDDEN VALUES OF OPTIMIZATION MODELS WITH METAHEURISTIC APPROACH Ann Kuo Steven O. Kimbrough Considering that the decision making process for constrained optimization problem is based on modeling, there is always room for alternative solutions because there is usually a gap between the model and the real problem it depicts. This study looks into the problem of finding such alternative solutions, the non-optimal solutions of interest for constrained optimization models, the SoI problem. SoI problems subsume finding feasible solutions of interest (FoIs) and infeasible solutions of interest (IoIs). In all cases, the interest addressed is post-solution analysis in one form or another. Post-solution analysis of a constrained optimization model occurs after the model has been solved and a good or optimal solution for it has been found. At this point, sensitivity analysis and other questions of import for decision making come into play and for this purpose the SoIs can be very valuable. An evolutionary computation approach (in particular, a population-based metaheuristic) is proposed for solving the SoI problem and a systematic approach with a feasible-infeasible- two-population genetic algorithm is demonstrated. In this study, the effectiveness of the proposed approach on finding SoIs is demonstrated with generalized assignment problems and generalized quadratic assignment problems. Also, the applications of the proposed approach on the multi-objective optimization and robust-optimization issues are examined and illustrated with two-sided matching problems and flowshop scheduling problems respec- tively. iv TABLE OF CONTENTS ACKNOWLEDGEMENT . iii ABSTRACT . iv LIST OF TABLES . ix LIST OF ILLUSTRATIONS . xi CHAPTER 1 : Supporting Deliberation for Optimization Problems with the Meta- heuristic Approach . 1 1.1 Introduction . 1 1.2 Motivation and Related Work . 2 1.3 An Evolutionary Computation Based Approach - Genetic Algorithms (GAs) 12 1.4 Experiment Settings for Case Study on General Assignment Problems . 19 1.5 Comparison Between Penalty GA and FI-2Pop GA Results . 24 1.6 Two Different Infeasible Solution Fitness Measures . 28 1.7 Collecting the Solutions of Interest . 30 1.8 Using the Solutions of Interest . 35 1.9 Extended Experiments on the Generalized Quadratic Assignment Problem . 39 1.10 Summary and Discussion . 61 CHAPTER 2 : Considering Additional Objectives with the Metaheuristic Approach 64 2.1 Introduction . 64 2.2 Motivation and Related Work . 65 2.3 Evolutionary Matching for Stable Marriages Problem . 75 2.4 Extended Matching Problems - Hospitals Residents Problem with Couples (Couples Problem) . 78 v 2.5 Summary And Discussion . 88 CHAPTER 3 : Finding Robust Solutions with the Metaheuristic Approach . 93 3.1 Introduction . 93 3.2 Motivation and Related Work . 93 3.3 Robust-under-Risk . 96 3.4 Robust-under-Uncertainty . 107 3.5 Summary and Discussion . 139 CHAPTER 4 : Summary . 142 APPENDIX . 147 BIBLIOGRAPHY . 152 vi LIST OF TABLES TABLE 1 : Information on Benchmark Generalized Assignment Problem Sets . 19 TABLE 2 : Categories of GA Performance Assessment . 25 TABLE 3 : GAP11 & GAP12 FoIs: Count and quality of feasible solutions with objective function values near the best known solutions . 26 TABLE 4 : GAP11 & GAP12 IoIs: Count of infeasible solutions with objective function values ≥ or > the known optimal values . 27 TABLE 5 : Comparison for two infeasible solution fitness measures. GAP11 12 SoIs count and quality of feasible solutions with objective function values near the best known solutions . 30 TABLE 6 : Categories of SoI Heaps . 31 TABLE 7 : Two Optimal Solutions for GAP4-2 . 36 TABLE 8 : GAP4-2 Optimal & Near-Optimal Feasible Solutions; from FoI(Obj) 38 TABLE 9 : GAP4-2: Best found solution with job 25 assigned to machine 1 . 38 TABLE 10 : GAP4-2 FoIs with large sums of slacks from FoI(Slacks|MinObj) 39 TABLE 11 : GAP4-2 IoIs with min constraint violations from IoI(SumV) . 40 TABLE 12 : GAP4-2 IoIs Ranked by objective value . 41 TABLE 13 : GQAP: Elloumi Instance Configurations . 42 TABLE 14 : Elloumi c1003 Problem Set Solution of Interest (SoI) Findings . 48 TABLE 15 : Elloumi c1003 Problem Set IoI Information . 49 TABLE 16 : GQAP: Near-Optimal Feasible Solutions Information . 58 TABLE 17 : GQAP: Near/Optimal Feasible Solutions Truck Assignment . 58 TABLE 18 : GQAP: Near-Optimal Infeasible Solutions Information . 60 TABLE 19 : GQAP: Near Optimal Infeasible Solutions Truck Assignment . 60 TABLE 20 : 20x20 TPXOver Strongly Dominating Solution Counts, m04x06p50t100g2000 77 vii TABLE 21 : 20x20 TPXOver 0.8, Mutation 0.3, One-Away Strongly Dominating