The Impact Of Increased Optimization Problem Dimensionality On Cu

Wayne State University Wayne State University Theses 1-1-2015 The Impact Of Increased Optimization Problem Dimensionality On Cultural Algorithm Performance Yang Yang Wayne State University, Follow this and additional works at: https://digitalcommons.wayne.edu/oa_theses Part of the Artificial Intelligence and Robotics Commons Recommended Citation Yang, Yang, "The Impact Of Increased Optimization Problem Dimensionality On Cultural Algorithm Performance" (2015) Wayne State University Theses 482 https://digitalcommons.wayne.edu/oa_theses/482 This Open Access Thesis is brought to you for free and open access by DigitalCommons@WayneState It has been accepted for inclusion in Wayne State University Theses by an authorized administrator of DigitalCommons@WayneState THE IMPACT OF INCREASED OPTIMIZATION PROBLEM DIMENSIONALITY ON CULTURAL ALGORITHM PERFORMANCE by YANG YANG THESIS Submitted to the Graduate School of Wayne State University, Detroit, Michigan in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE 2015 MAJOR: COMPUTER SCIENCE Approved By: _ Advisor Date © COPYRIGHT BY YANG YANG 2015 All Rights Reserved ACKNOWLEDGMENTS I would like to acknowledge the contributions of my advisor Dr Robert G Reynolds and my committee members Dr Jing Hua, Dr Loren Schwiebert I also would like to acknowledge the others in my research team without which this work would not have been possible: Thomas Palazzolo, Dustin Stanley, Areej Salaymeh and David Warnke ii TABLE OF CONTENTS ACKNOWLEDGMENTS ii LIST OF TABLES vi LIST OF FIGURES vii CHAPTER 1: INTRODUCTION CHAPTER 2: THE CONE’S WORLD: A COMPLEX SYSTEMS TEST BED 2.1 Introduction to Complex Systems 2.2 The Cone’s World Generator CHAPTER 3: THE LEARNING COMPONENT OF THE SIMULATION: CULTURAL ALGORITHMS 10 3.1 Introduction to the Cultural Algorithm 10 3.2 Belief Space and Knowledge Sources 12 3.2.1 Normative Knowledge 13 3.2.2 Situational Knowledge 14 3.2.3 Domain Knowledge 15 3.2.4 Historical Knowledge 15 3.2.5 Topographical Knowledge 16 3.3 Communication Protocol 18 3.3.1 Acceptance Function 19 3.3.2 Influence Function 19 3.3.3 Update Function 21 iii CHAPTER 4: SOCIAL FABRIC AND SOCIAL METRICS 23 4.1 Social Fabric 23 4.2 Neighborhood Topology 25 4.3 Agent Decision Making 25 4.4 Social Metrics 29 4.4.1 The Social Tension 31 4.4.2 Minority / Majority Win Scores and Innovation Cost 33 CHAPTER 5: INTRODUCTION OF THE CULTURAL ALGORITHMS TOOLKIT 2.0 SYSTEM 35 5.1 Repast as Development Environment 35 5.2 Cone’s World Generation 36 5.3 Main Simulation Loop 38 5.4 Instructions of GUI 40 CHAPTER 6: EXPERIMENTAL FRAMEWORK AND RESULTS 45 6.1 Data and Results Format 45 6.2 Experiment Framework 46 6.3 Experiment Results 48 6.3.1 Performance in Different Dimensions 48 6.3.2 Knowledge Source Performance 50 6.3.3 Social Metrics Summary Tables 52 CHAPTER 7: SUMMARY RESULTS AND ANALYSIS 55 7.1 Introduction 55 iv 7.2 Overall Performance Comparison 55 7.3 Knowledge Source Performance Comparison 58 7.4 Social Metrics Summary 62 CHAPTER 8: CONCLUSIONS AND FUTURE WORK 68 8.1 Conclusion 68 8.2 Future Work 69 REFERENCES 70 ABSTRACT 72 AUTOBIOGRAPHICAL STATEMENT 74 v LIST OF TABLES Table 6.1 The Raw Data Example Part 46 Table 6.2 The Raw Data Example Part 46 Table 6.3 The Test Run Array for the Dimension / Complexity 47 Table 6.4 The Performance Comparison in Dimensions 48 Table 6.5 The Performance Comparison in Dimensions 48 Table 6.6 The Performance Comparison in Dimensions 49 Table 6.7 The Performance Comparison in Dimensions 49 Table 6.8 The KS Performance Comparison in Dimension 51 Table 6.9 The KS Performance Comparison in Dimension 51 Table 6.10 The KS Performance Comparison in Dimension 52 Table 6.11 The KS Performance Comparison in Dimension 52 Table 6.12 The Social Metrics Summary in Dimension 53 Table 6.13 The Social Metrics Summary in Dimension 53 Table 6.14 The Social Metrics Summary in Dimension 54 Table 6.15 The Social Metrics Summary in Dimension 54 Table 7.1 The Summary of Performance Comparisons Part 55 Table 7.2 The Summary of Performance Comparisons Part 57 Table 7.3 The Summary of Knowledge Source Comparisons 59 Table 7.4 The T-test Results Table 61 Table 7.5 The Summary of Social Metrics Comparisons 63 Table 7.6 The Statistical Expression of Social Tension Cool Down 66 vi LIST OF FIGURES Figure 2.1 An Example Landscape In Two-Dimensional Space Figure 2.2 The Logistic Function Figure 2.3 The Logistic Function with Specific A Values Figure 3.1 The Basic Pseudo-code for Cultural Algorithms 11 Figure 3.2 The Schematic of Cultural Algorithms 12 Figure 3.3 The Structure of Normative Knowledge 13 Figure 3.4 The Structure of Situational Knowledge 14 Figure 3.5 The Structure of Topographical Knowledge 16 Figure 3.6 The Pseudo-code for the Topographical Knowledge Influence Function 18 Figure 3.7 The Knowledge Update in the Belief Space 21 Figure 4.1 The Social Fabric Schema 24 Figure 4.2 Some Example Neighborhood Topologies 25 Figure 4.3 Knowledge Source Interaction at the Population Level 26 Figure 4.4 Majority Win Conflict Resolution in the Social Network 27 Figure 4.5 Weighted Majority Win Conflict Resolution in the Social Network 29 Figure 4.6 An Embedded Social Fabric Component in CAT 31 Figure 4.7 The Pseudo-code for Calculating the Social Tension 32 Figure 4.8 The Pseudo-Code for Calculating the Minority Win Score, Majority Win Score, and Innovation Cost Index 34 vii Figure 5.1 Choosing of A Value in the Logistic Function 36 Figure 5.2 A 2D Landscape Example A = 1.01 37 Figure 5.3 A 2D Landscape Example A = 3.35 38 Figure 5.4 A 2D Landscape Example A = 3.99 38 Figure 5.5 The Repast Control Bar 40 Figure 5.6 Parameter Setting in the GUI 41 Figure 5.7 The Cone's World 2D Landscape Display 42 Figure 5.8 The Best Individual Fitness Graph 43 Figure 5.9 The Overall Social Tension Graph 44 Figure 5.10 The Weighted Majority Win Metrics Graph 44 Figure 7.1 The Social Tension Graph of Run #55 64 Figure 7.2 The Fitness Graph of Run #55 64 Figure 7.3 The Social Tension Graph of Run #28 65 Figure 7.4 The Social Tension Graph of Run #60 65 viii 60 called the significance level of the test, usually 0.05 or 0.01 If the p-value is below the threshold chosen for statistical significance, then the null hypothesis is rejected We conducted the t-test to test the influence of dimensionality on each Knowledge Source performance We suggested the following null hypothesis: “Dimensionality doesn’t affect the performance of the certain Knowledge Source.” For each Knowledge Source, we have 15 samples in data set of each dimensionality Each data set from a dimensionality will be compared with other data sets from different dimensionalities So we have six tests (2D-3D, 2D-4D, 2D-5D, 3D-4D, 3D-5D and 4D-5D) for observing the influence of dimensionality in a Knowledge Source We tried two threshold values, 0.05 and 0.01, in our t-tests If the p-value is less than 0.05, it implies that two data sets are different If p-value is less than 0.01, it means these two data sets are definitely different and have no possibility of correlation The t-test results table 7.4 is shown below: 61 Table 7.4 The T-test Results Table Knowledge Source Normative KS Situational KS Domain KS History KS Topographical KS Test object 2D and 3D 2D and 4D 2D and 5D 3D and 4D 3D and 5D 4D and 5D 2D and 3D 2D and 4D 2D and 5D 3D and 4D 3D and 5D 4D and 5D 2D and 3D 2D and 4D 2D and 5D 3D and 4D 3D and 5D 4D and 5D 2D and 3D 2D and 4D 2D and 5D 3D and 4D 3D and 5D 4D and 5D 2D and 3D 2D and 4D 2D and 5D 3D and 4D 3D and 5D 4D and 5D p-value 7.87E-08 6.25E-13 4.83E-18 1.16E-07 9.47E-14 0.000238 0.687146 0.185944 0.711615 0.139779 0.510345 0.336123 0.579693 0.194917 0.056194 0.080452 0.016224 0.708904 0.74002 0.025523 0.121365 0.013395 0.06521 0.376752 5.1E-05 7.11E-06 5.57E-13 0.020176 0.000334 0.921916 Result(p