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MODIFIED AND ENSEMBLE INTELLIGENT WATER DROP ALGORITHMS AND THEIR APPLICATIONS BASEM O. F. ALIJLA UNIVERSITI SAINS MALAYSIA 2015 MODIFIED AND ENSEMBLE INTELLIGENT WATER DROP ALGORITHMS AND THEIR APPLICATIONS by BASEM O. F. ALIJLA Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosphy October 2015 ACKNOWLEDGEMENTS With the name of Allah, Most Gracious, Most Merciful. First and foremost, my sincere glorifications and adorations go to almighty Allah for his guidance, protection and strength over me to complete my research study. I would like to express sincere gratitude to my supervisors, Professor Lim Chee Peng, Professor Ahamad Tajudin Khader, and Dr. Wong Li Pei for their insightful guidance throughout the entire period of my research. I will forever remain grateful for the continued help, and wise counseling. Special thanks and appreciations to Professor Lim Chee Peng for his endless help, especially in publishing my research work. I am also grateful to my friend Dr. Mohammad Azmi Al-Betar for his help and useful discussion during the course of this research. Indeed, without Allah then my parents’ prayers, I could not have completed this research. My special thanks to my beloved parents for their continued supports, encouragements, and prayers. Thank you mum, dad, my brothers, and sisters, you are always in my mind and heart. In the same context, love and support my deepest and special thanks go to my wife for her patience, understanding, fervent prayers and for taking care of our kids. Your great support, efforts, and endurance is highly appreciated. My sincere appreciations are extended to the Islamic Development Bank (IDB) for its financial support under the IDB merit scholarship program. I am also grateful to the School of Computer Sciences, Universiti Sains Malaysia, which has provided all the facilities and equipments needed throughout my research. Last but not least; thank you to all my friends in Malaysia, and those who support me in any respect during my research. ii TABLE OF CONTENTS Page Acknowledgements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv Abstrak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx CHAPTER 1 – INTRODUCTION 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Motivation and Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Research Contributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Research Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.7 Thesis Structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 CHAPTER 2 – BACKGROUND AND LITERATURE REVIEW 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2 Background to the Intelligent Water Drops Algorithm . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1 Problem formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Initialization phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2(a) Static parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2(b) Dynamic parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Solution construction phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.3 iii 2.3 2.4 2.2.3(a) Edge selection mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.3(b) Velocity and local soil Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.2.4 Reinforcement phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2.5 Termination phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3.1 Foundation of optimization methods for COPs . . . . . . . . . . . . . . . . . . . . . . 25 2.3.2 Taxonomy of optimization methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.3 Trajectory-based meta-heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.3(a) Hill Climbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3.3(b) Simulated Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.3.3(c) Iterated Local Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.4 Population-based meta-heuristic methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3.5 Critical analysis of existing methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Case studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4.1 Feature subset selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4.1(a) Rough set for subset feature selection (RSFS) . . . . . . . . . . . 45 2.4.1(b) Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Travelling salesman problem (TSP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.2(a) Overview to TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.4.2(b) Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Multiple knapsack problem (MKP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4.3(a) Overview to MKP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.4.3(b) Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4.2 2.4.3 2.5 CHAPTER 3 – A MODIFIED INTELLIGENT WATER DROPS ALGORITHM iv 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.2 The original selection method in IWD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.3 Ranking-based selection methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.1 Linear ranking selection.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.3.2 Exponential ranking selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 The modified IWD algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.4.1 Experimental study for rough set feature subset selection. . . . . . . . . . 60 3.4.1(a) Setting the value of SP parameter.. . . . . . . . . . . . . . . . . . . . . . . . . 60 3.4.1(b) Results and discussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Experimental study for travelling salesman problem. . . . . . . . . . . . . . . . 68 3.4.2(a) Setting the value of SP parameter.. . . . . . . . . . . . . . . . . . . . . . . . . 69 3.4.2(b) Results and discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Experimental study for multiple knapsack problem. . . . . . . . . . . . . . . . . 74 3.4.3(a) Setting the value of SP parameter.. . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.3(b) Results and discussions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.5 Comparing modified IWD with other state-of-the-art methods . . . . . . . . . . . . . 79 3.6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4 3.4.2 3.4.3 CHAPTER 4 – AN ENSEMBLE OF INTELLIGENT WATER DROPS ALGORITHMS 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2 The proposed models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2.1 The Master-River, Multiple-Creek IWD model . . . . . . . . . . . . . . . . . . . . . 82 4.2.1(a) Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.2.1(b) Master river construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.1(c) Creek construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 A hybrid MRMC-IWD model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 4.2.2 v 4.3 Experimental study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.3.1 Experiments and results for TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3.2 Experiments and results for RSFS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.4 Comparing MRMC-IWD with other state-of-the-art methods. . . . . . . . . . . . . . 100 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 CHAPTER 5 – APPLYING THE HYBRID MRMC-IWD TO REAL-WORLD CLASSIFICATION APPLICATIONS 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5.2 The FS-MRMC-IWD for FS using benchmark data sets . . . . . . . . . . . . . . . . . . . . 102 5.2.1 Experiments setting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.2.2 Experimental results and comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.2.2(a) Comparing the performance of FS-MRMC-IWD against other methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 5.2.2(b) Comparison of classification accuracies.. . . . . . . . . . . . . . . . . . 116 5.3 Real-world applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.3.1 Detection and recognition system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.3.1(a) Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.3.1(b) Features extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.3.1(c) Features subset selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.3.1(d) Data Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.3.2 Human motion detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.3.2(a) Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 5.3.2(b) Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.3.2(c) Features selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.3.2(d) Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 5.3.3 Fault detection and diagnosis of induction motors . . . . . . . . . . . . . . . . . . 129 5.3.3(a) Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 vi 5.3.3(b) Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.3.3(c) Features selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.3.3(d) Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 CHAPTER 6 – CONCLUSION AND FUTUREWORK 6.1 Summary of the research and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 6.2 Achievement of research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 6.3 Direction of future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 APPENDICES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 APPENDIX A – FEATURE SELECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 A.1 Feature selection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 A.1.1 Filter-based selection methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 A.1.2 A.2 Wrappers-based FS methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Rough set and fuzzy rough for feature selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.2.1 Fundamentals of Rough set theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 A.2.2 Rough set feature selection (RSFS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 A.2.3 Fundamentals of fuzzy rough set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 A.2.4 Fuzzy rough set for feature selection (FRFS). . . . . . . . . . . . . . . . . . . . . . . . 166 vii LIST OF TABLES Page Table 2.1 Applications of the IWD algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Table 2.2 The main properties of the data sets used for RSFS experiments . 47 Table 2.3 Characteristics of the data sets used for TSP . . . . . . . . . . . . . . . . . . . . . . 49 Table 2.4 The main Characteristics of ten mknapcb1 instances obtained from the OR-Library.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Table 3.1 Parameters settings of the IWD algorithm for RSFS. . . . . . . . . . . . . . 60 Table 3.2 Comparison of the results of the ERS-IWD algorithm with various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Comparison of the results of the LRS-IWD algorithm with various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Performance comparison of the proposed methods with other algorithms on rough set feature subset selection benchmark problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Significance tests of the LRS-IWD and ERS-IWD algorithms using t-test with α < 0.05. "None" denotes that both results are the same (i.e., no valid p-values). Highlight (bold) denote that result is significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Significance tests of the FPS-IWD and ERS-IWD algorithms using t-test with α < 0.05. Highlight (bold) denote that result is significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Table 3.7 Parameters setting of the IWD algorithm for TSP. . . . . . . . . . . . . . . . . 68 Table 3.8 The average tour lengths from 10 runs of the ERS-IWD algorithm with different SP values. The highlighted (bold) values denote the best result for each data set. . . . . . . . . . . . . . . . . . . . . 69 The average tour lengths from 10 runs of the LRS-IWD algorithm with different SP values. The highlighted (bold) values denote the best result for each data set. . . . . . . . . . . . . . . . . . . . . . 70 Compare the Performance of the ERS-IWD, LRS-IWD, and FPS-IWD algorithms in solving eight TSPLIB data sets. The highlighted (bold) values denote the best result for each data set. 72 Table 3.3 Table 3.4 Table 3.5 Table 3.6 Table 3.9 Table 3.10 viii Table 3.11 Significance tests of the ERS-IWD and LRS-IWD algorithms using t-test with α < 0.05. Highlight (bold) denote that result is significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Significance tests of the FPS-IWD and LRS-IWD algorithms using t-test with α < 0.05. Highlight (bold) denote that result is significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Significance tests of the ERS-IWD and FPS-IWD algorithms using t-test with α < 0.05. Highlight (bold) denote that result is significantly different. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Table 3.14 Parameters settings of the IWD algorithm for MKP. . . . . . . . . . . . . . . 74 Table 3.15 Average profits from10 runs of the ERS-IWD method with different SP values. The highlighted (bold) values denote the best result of each data set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Average profits from10 runs of the LRS-IWD method with different SP values. The highlighted (bold) values denote the best result of each data set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 Performance comparison of ERS-IWD, LRS-IWD, and FPS-IWD in solving 10 instances of mknapcb1 data set obtained from the OR-Library. The highlighted (bold) values denote the best result for each instance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 The results of MRMC-IWD for three TSPLIB data sets with various C settings. Avg. indicates the average tour length of 10 runs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 The results of MRMC-IWD as compared with those of the modified IWD algorithm, and GCGA without local search (Yang et al., 2008). The Error (%) denotes the percentage deviation of the average tour length from the best known results. Avg. indicates the average tour length. . . . . . . . . . . . . . . . . . . . . 94 The results of hybrid MRMC-IWD as compared with those of MRMC-IWD, GCGA with local search (Yang et al., 2008), improved ABC with local search (Kocer and Akca, 2014)and PSO (Kocer and Akca, 2014). The error (%) denotes the percentage of deviation of the average from the best known result, Avg. indicates the average tour length, "-" indicates that result is not available in publications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 The results of MRMC-IWD for three RSFS data sets with various C settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Table 3.12 Table 3.13 Table 3.16 Table 3.17 Table 4.1 Table 4.2 Table 4.3 Table 4.4 ix Table 4.5 The results of MRMC-IWD as compared with those from the modified IWD algorithm and other models published by Jensen and Shen (2003). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Table 4.6 Comparison between hybrid MRMC-IWD and MRMC-IWD. Note that column "Iterations" indicates the average number of iterations required to achieve the optimal solution. . . . . . . . . . . . . . . . . 100 Table 5.1 The main properties of the real UCI data sets. . . . . . . . . . . . . . . . . . . . . . 104 Table 5.2 Parameters setting for the hybrid MRMC-IWD for feature selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Table 5.3 Comparison between FS-MRMC-IWD and four state-of-the-art methods (i.e., HS,GA,PSO, and HC) published in (Diao and Shen, 2012), using the consistency-based evaluation technique in terms of the average subset size and evaluation score. Symbols v, -, and * respectively, denote that the result is significantly better, no statistical difference, and worse than those provided by HS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 Table 5.4 Comparison between FS-MRMC-IWD and four state-of-the-art methods (i.e., HS,GA,PSO, and HC published in Diao and Shen (2012), (2012), using CFS in terms of the average subset size and evaluation score. Symbols v, -, and *, respectively, denote that the result is significantly better, no statistical difference, and worse than those provided by HS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 Table 5.5 Comparison between FS-MRMC-IWD and four state-of-the-art methods (i.e., HS,GA,PSO, and HC published in Diao and Shen (2012), using the FRFS evaluation technique in terms of the average subset size and evaluation score. Symbols v, -, and *, respectively denote that the result is significantly better, no statistical difference, and worse than those provided by HS. . . . . . 115 Table 5.6 Classification accuracy rates (measured in %) of C4.5 using features selected by the consistency-based evaluation technique and from different optimization methods published in Diao and Shen (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Table 5.7 C4.5 classification accuracy rates (measured in %) using the feature subsets selected by CFS and different optimization methods published in Diao and Shen (2012). . . . . . . . . . . . . . . . . . . . . . . 118 Table 5.8 C4.5 classification accuracy (measured in %) using feature subsets selected by FRFS and different optimization methods published in Diao and Shen (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 x Table 5.9 Comparing the classification accuracies between full and reduced features using different evaluation techniques. Highlight (bold) denote that result is significantly better. . . . . . . . . . 120 Table 5.10 Time-domain features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Table 5.11 Frequency-domain features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 Table 5.12 Number of samples collected for human motion data set. . . . . . . . . 125 Table 5.13 The results of feature selection for human motion detection using FS-MRMC-IWD. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Table 5.14 Comparing the classification performance accuracies (measured in %) between full and selected features for human motion detection. Highlight (bold) denote that result is significantly better. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 Table 5.15 Data samples for fault detection of induction motors. . . . . . . . . . . . . . 130 Table 5.16 The results of feature subset selected using FS-MRMC-IWD for motor fault detection.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Table 5.17 Comparing the classification accuracies performance (measured in %) between full and reduced feature sets for motor fault detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 Table A.1 real values Information system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 Table A.2 Similarity relation for three features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Table A.3 Positive Regions and Degree of dependency. . . . . . . . . . . . . . . . . . . . . . . 169 xi LIST OF FIGURES Page Figure 1.1 A 3D-fitness landscape of an optimization problem (Coppin, 2004). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Figure 1.2 The main stages of the research methodology.. . . . . . . . . . . . . . . . . . . . . 10 Figure 2.1 A flowchart shows the fundamental of the IWD algorithm (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 2.2 General taxonomy of optimization methods. . . . . . . . . . . . . . . . . . . . . . . 27 Figure 3.1 An example showing the selection probabilities of five candidate location according to the FPS method (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Sensitivity of FPS method to the scaling function with a indistinguishable fitness value (Alijla et al., 2014) . . . . . . . . . . . . . . . . 55 Inability of the FPS method to handle the selection dominated by an outstanding location (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . 55 Linear probability distribution of 10 individuals with different values of SP (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Exponential probability distribution of 10 individuals with different values of SP (Alijla et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . 58 Average length of reducts from 20 runs of the ERS-IWD algorithm with various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Average length of reducts from 20 runs of the LRS-IWD algorithm with various SP values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Decrement of the SP value results in improvement of the ERS-IWD performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Increment of the SP value results in improvement of the performance of the LRS-IWD algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . 70 Figure 4.1 The structure of MRMC-IWD and its communication model. . . . 83 Figure 4.2 The main phases of the MRMC-IWD model. . . . . . . . . . . . . . . . . . . . . . 86 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6 Figure 3.7 Figure 3.8 Figure 3.9 xii Figure 4.3 The convergence trends of MRMC-IWD and hybrid MRMC-IWD for the first 300 iterations of seven selected TSPLIB data sets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(a) eil51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(b) eil76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(c) eil101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(d) kroA100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(e) kroA200 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(f) lin105 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 4.3(g) lin318 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Figure 5.1 Comparing the bootstrapped means and 95% confidence intervals of the subset size from FS-MRMC-IWD and average subset sizes from HS (as published in Diao and Shen (2012) using the consistency-based evaluation technique. . . . . . . . . . . . . . . . . 107 Figure 5.1(a) Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.1(b) Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.1(c) Waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.1(d) Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.1(e) Ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.1(f) Libras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.1(g) Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Figure 5.2 Comparing the average subset sizes of HS (published in Diao and Shen (2012) with the bootstrap results (i.e., means and 95% confidence intervals ) of MRMC-IWD using the CFS evaluation technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.2(a) Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.2(b) Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.2(c) Waveform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.2(d) Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.2(e) Ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 xiii Figure 5.2(f) Libras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.2(g) Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 Figure 5.3 Comparing the average subset size of HS published in Diao and Shen (2012) with the bootstrap results (i.e., mean and 95% confidence interval) of FS-MRMC-IWD using the FRFS evaluation technique.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.3(a) Ionosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.3(b) Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.3(c) Sonar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.3(d) Libras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.3(e) Arrhythmia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.4 The main components of a pattern recognition system. . . . . . . . . . . 121 Figure A.1 A flowchart shows the fundamental of the IWD algorithm. . . . . . . . 156 Figure A.2 Filter-based approach for feature selection. . . . . . . . . . . . . . . . . . . . . . . . . 157 Figure A.3 Wrapper-based approach feature selection. . . . . . . . . . . . . . . . . . . . . . . . . 158 Figure A.4 Fuzzy Rough Quick Reduct Algorithm.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 xiv LIST OF ABBREVIATIONS ABC Artificial Bee Colony ACO Ant Colony Optimization ACS Ant Colony System AIWD Adaptive Intelligent Water Drops CFS Correlation-based Feature Selection CLB Creek Local Best EC Evolutionary Computation EIWD Enhanced Intelligent Water Drops ERS-IWD Exponential Ranking selection Intelligent Water Drops FCV Fold Cross Validation FFT Fast Fourier Transform FPS Fitness Proportionate Selection FPS-IWD Fitness Proportionate Selection Intelligent Water Drops FRFS Fuzzy Rough Feature subset Selection FS Feature Selection FS-MRMC-IWD Feature Selection Master River Multiple Creeks Intelligent Water Drops GA Genetic Algorithm GD Great Deluge HC Hill Climbing HMC Harmony Memory Consideration HS Harmony Search IILS Iterative Improvement Local Search xv IWD Intelligent Water Drops IWD-CO IWD-Continuous Optimization LAHC Late Acceptance Hill Climbing LRS-IWD Linear Ranking Selection Intelligent Water Drops MACO Mutated Ant Colony Optimization MHC Multiple Hill Climbing MKP Multiple Knapsack Problem MLB Master Local Best MRMC-IWD Master River Multiple Creeks Intelligent Water Drops NB Naive Bayes NP-hard Non-deterministic Polynomial-time hard PA Pitch Adjustment PSO Particle Swarm Optimization QoS Quality of Service RC Random Consideration RMHC Random Mutation Hill Climbing RMS Root Mean Square RS Rough Set RSFS Rough Set Feature Subset Selection RST Rough Set Theory SA Simulated Annealing SI Swarm Intelligence SP Selection Pressure std Standard Deviation xvi SVM Support Vector Machine TSP Travelling Salesman Problem UCI University of California Irvine machine learning repository USM Universiti Sains Malaysia VQNN Vaguely Quantified Nearest Neighbor WEKA Waikato Environment for Knowledge Analysis xvii ALGORITMA TITISAN AIR CERDAS TERUBAH SUAI DAN GABUNGAN SERTA APLIKASINYA ABSTRAK Algoritma Titisan Air Cerdas (TAC) ialah model berasaskan kawanan yang sememangnya berguna untuk mengatasi masalah-masalah pengoptimuman. Tujuan utama kajian ini adalah untuk meningkatkan keupayaan algoritma TAC dan mengatasi keterbatasan algoritma tersebut, yang berkaitan dengan kepelbagaian populasi serta mengimbangangi penerokaan dan pengeksploitasian dalam menangani masalah-masalah pengoptimuman. Pertama, algoritma TAC yang diubahsuai, diperkenalkan. Dua kaedah pemilihan berdasarkan kedudukan, iaitu kedudukan linear dan kedudukan eksponen, dicadangkan untuk menggantikan kaedah pemilihan kelekapan yang seimbang. Kedua, algoritma Titisan Air Cerdas yang berdasarkan Sungai Induk Pelbagai Caruk Alir Sungai (SICAS-TAC) dicadangkan untuk mengeksploitasikan keupayaan penerokaan algoritma TAC yang diubahsuai. Di samping itu, model hibrid SICAS-TAC juga dibentangkan. Model hibrid ini menggabungkan algoritma SICAS-TAC dengan peningkatan lelaran carian setempat, untuk meningkatkan keupayaan penjelajahan kepada algoritma SICAS-TAC. Keberkesanan model-model yang dicadangkan dinilai secara sistematik dan menyeluruh dengan menggunakan tiga masalah pengoptimuman kombinatorik iaitu, masalah pemilihan ciri subset berdasarkan set kasar, masalah beg galas berbilang, dan masalah jurujual kembara. Kesesuaian dan keberkesanan model hibrid SICAS-TAC disiasat dengan menyelesaikan masalah pengoptimuman dunia sebenar xviii yang berkaitan dengan pemilihan ciri dan klasifikasi. Beberapa set data tanda aras umum dan dua masalah dunia sebenar, iaitu masalah pengesanan pergerakan manusia dan masalah pengesanan kerosakan motor, telah dikaji. Keputusan kajian telah menunjukkan keberkesanan model-model yang dicadangkan dalam meningkatkan prestasi algoritma TAC yang asal dan juga menyelesaikan masalah-masalah pengoptimuman dunia sebenar. xix MODIFIED AND ENSEMBLE INTELLIGENT WATER DROP ALGORITHMS AND THEIR APPLICATIONS ABSTRACT The Intelligent Water Drop (IWD) algorithm is a swarm-based model that is useful for undertaking optimization problems. The main aim of this research is to enhance the IWD algorithm and overcome its limitations pertaining to population diversity, as well as balanced exploration and exploitation in handling optimization problems. Firstly, a modified IWD algorithm is introduced. Two ranking-based selection methods, i.e. linear ranking and exponential ranking, are proposed to replace the fitness proportionate selection method. Secondly, the Master River Multiple Creeks Intelligent Water Drops (MRMC-IWD) algorithm is proposed in an attempt to exploit the exploration capability of the modified IWD algorithm. In addition, the hybrid MRMC-IWD model is proposed. It combines MRMC-IWD with the iterated improvement local search method, to empower MRMC-IWD with the exploitation capability. The usefulness of the proposed models is evaluated systematically and comprehensively using three combinatorial optimization problems, i.e., rough set feature subset selection, multiple knapsack problem, and travelling salesman problem. The applicability of the hybrid MRMC-IWD model is investigated to solving real-world optimization problems related to feature selection and classification tasks. A number of publicly available benchmark data sets and two real-world problems, namely human motion detection and motor fault detection, are studied. The results ascertain the effectiveness of the xx proposed models in improving the performance of the original IWD algorithm as well as undertaking real-world optimization problems. xxi CHAPTER 1 INTRODUCTION 1.1 Introduction Optimization is a process that concerns with finding the best solution of a given problem from among the possible solutions within an affordable time and cost (Weise et al., 2009). The first step in the optimization process is formulating the optimization problem through an objective function and a set of constrains that encompass the problem search space (i.e., regions of feasible solutions). Every alternative (i.e., solution) is represented by a set of decision variables. Each decision variable has a domain, which is a representation of the set of all possible values that the decision variable can take. The second step in optimization starts by utilizing an optimization method (i.e., search method) to find the best candidate solutions. Candidate solution has a configuration of decision variables that satisfies the set of problem constrains, and that maximizes or minimizes the objective function (Boussaid et al., 2013). It converges to the optimal solution (i.e., local or global optimal solution) by reaching the optimal values of the decision variables. Figure 1.1 depicts a 3D-fitness landscape of an optimization problem. It shows the concept of the local and global optima, where the local optimal solution is not necessarily the same as the global one (Weise et al., 2009). Optimization can be applied to many real-world problems in various domains. As an example, mathematicians apply optimization methods to identify the best outcome pertaining to some mathematical functions within a range of variables (Vesterstrom and Thomsen, 2004). In the presence of conflicting criteria, engineers use optimization methods to 1 Figure 1.1: A 3D-fitness landscape of an optimization problem (Coppin, 2004). find the best performance of a model subject to certain criteria, e.g. cost, profit, and quality (Machado et al., 2001; Marler and Arora, 2004; Yildiz, 2009). In general, optimization problems can be categorized into several categories, depending on whether they are discrete or continuous, single objective or multi-objectives, and constrained or unconstrained (Boussaid et al., 2013). They can be classified into discrete or continuous based on the domain of encoding the solution. Solutions of continuous problems are encoded with real-valued variables, while solutions of discrete problems are encoded with discrete variables. In this light, discrete optimization problems, which are known as combinatorial optimization problems (COPs), include problems that have a finite set of solutions (Blum and Roli, 2003). Optimization problems can be categorized into constrained and unconstrained based on whether the decision variables are restricted to some limitations (i.e., constrains) or otherwise. The number of objective function is the distinctive property that differentiates between singleobjective and multi-objectives optimization problems (Marler and Arora, 2004). 2 Numerous optimization methods have been devised and successfully applied to solving optimization problems. Generally, they can be classified into two main categories: deterministic (exact) and non-deterministic (stochastic) methods (Lin et al., 2012). Deterministic methods such as linear programming and dynamic programming exhaustively employ the analytical properties of a problem to search for the optimal solution. However, no method can be guaranteed to find the optimal solution especially for NP-hard problems (i.e. problems that have no known solution in polynomial time) (Lin et al., 2012). Non-deterministic methods search with some randomness to solve NP-hard problems to achieve good (near-optimal) solutions in polynomial time. In this regards, meta-heuristic methods play a major role in tackling optimization problems. They utilize heuristic information within a high-level problem-agonistic framework to solve optimization problems. In this context, a branch of meta-heuristic optimization methods that has attracted much attention of researchers is emulating the natural behaviors of real systems in solving optimization problems. These methods are known as nature-inspired meta-heuristics (Yang, 2010). As an example, the genetic algorithm (GA) (Holland, 1975; Goldberg and Holland, 1988) is inspired by biological evolution of organisms, such as inheritance, mutation, crossover, and selection, to solve optimization problems. An innovative family of nature-inspired models known as swarm intelligence (SI) has emerged (Blum and Li, 2008). SI methods are based on the phenomena of different natural swarms, e.g. ant colony optimization (ACO) inspired by the foraging behavior of real ants (Dorigo and Di Caro, 1999; Dorigo and Blum, 2005), particle swarm optimization (PSO) inspired by the social behavior of bird flocking or fish schooling (Shi, 2001; Kennedy, 2010), artificial bee colony (ABC) inspired by the foraging behavior of honey bees in their colony (Karaboga, 2005). A variety of SI- 3 based methods have been successfully used in solving different optimization problems. They are characterized by collaborative learning, i.e., a population of agents collaborates and cooperates among themselves within their environment to solve a problem (Blum and Li, 2008). Furthermore, the interactions among agents enable the model to explore several regions of the search space simultaneously, in order to converge to the global optimum solution in an effective manner (Blum and Li, 2008). The Intelligent Water Drop (IWD) algorithm (Shah-Hosseini, 2007) is a relatively recent SI model. It is inspired by the natural phenomenon of water drops flowing with soil and velocity along a river. It imitates a number of natural phenomena pertaining to the water drops flowing through an easier path in a river, i.e., a path with less barriers and obstacles. Technically, the IWD algorithm is a constructive-based meta-heuristic algorithm (Shah-Hosseini, 2007) that comprises a set of cooperative computational agents (water drops) iteratively constructing the solution of a problem. The water drop constructs a solution by traversing a path with a finite set of discrete movements. It begins the process with an initial state. Thereafter, it iteratively moves step-by-step passing through several intermediate states (partial solutions) until a final sate (complete solution) is reached. A probabilistic approach is used to control the movements of the water drops. At every iteration of the IWD algorithm, a new complete population (i.e., a set of solutions) is generated. The new generation of solutions benefits from the previous generation through the environment attributes, i.e., soil and velocity. They are used to control the probability distribution of selecting the candidate movements, and to extend the partial solution. The soil level indicates the cumulative proficiency of a particular movement. It represents the communication mechanism that enables the water drops to cooperate among themselves. The velocity is an attribute that influences 4 the dynamics updating process of the soil level based on heuristic information, which is related to the problem under scrutiny. Although the IWD algorithm has been successfully employed to solve numerous optimization problems (i.e., combinatorial, continuous, and multi-objectives) from different application fields (Siddique and Adeli, 2014), little efforts have been made by researchers in investigating the fundamental algorithmic aspects of IWD. Many researchers focus on the application field of IWD as an optimization method. This research is focused on investigating the algorithmic aspects of the IWD algorithm to tackle optimization problems, i.e., how to preserve population diversity and balance exploration and exploitation of the search process. The rest of this chapter is organized as follows. Section 1.2 provides the research motivation and problem statement. Sections 1.3 and 1.4, respectively, present the research objectives and contributions. An overview of the research methodology is presented in Section 1.5. Section 1.6 introduces the research scope. Section 1.7 explains thesis structure with indication to the contents of each chapter. 1.2 Motivation and Problem Statement The IWD algorithm was proposed by Shah-Hosseini (2007), adding a new SI-based nature-inspired optimization method to the literature. It has been shown to be effective in solving COPs, such as travelling salesman problem (TSP), multiple knapsack problem (MKP), and n-queen puzzle problem (Shah-Hosseini, 2007, 2008, 2012a,b). As a new meta-heuristic optimization method, IWD has also been successfully applied to solving numerous optimization problems in different fields (Siddique and Adeli, 2014). 5 However, research to enhance the performance of IWD in solving COPs is still active. In Niu et al. (2012), five modified schemes that explore three IWD operators (i.e., soil and velocity values, transition rule, and soil update mechanism) were proposed to enhance the IWD performance. These schemes could overcome the early convergence and population diversity problems in IWD. Therefore, the key motivation of this research is to investigate the fundamental algorithmic aspects (i.e., population diversity as well as balance in exploration and exploitation) to enhance the performance of IWD for undertaking optimization problems. IWD is a constructive-based meta-heuristic algorithm that iteratively constructs new solutions at every iteration. The process of solution construction is influenced by a probabilistic procedure, i.e., fitness proportionate selection (FPS), which is based on two parameters i.e., soil and velocity. They are updated throughout the solution construction process at every iteration, in order to guide the search process toward the optimal solution The published results by Shah-Hosseini (2007) indicated that good results could be achieved at the early stage of the IWD optimization process ( i.e., the first few iterations ). However, all the water drops could stuck at a local solution, and unable to achieve further improvements. This problem is known as search stagnation (Stützle and Dorigo, 1999). It is a common problem in constructive, swarm-based optimization methods, which include IWD (Niu et al., 2012). Swarm-based optimization methods depend on global optimal solutions found thus far to generate new solutions. While this technique could lead to good solutions, other 6 sub-optimal solutions could also contribute towards generating better solutions. As the swarm-based methods inject a strong selection pressure to the global-optimal solutions found thus far, the search process could converge prematurely at a rapid pace. Conversely, a weak selection pressure could diverse the search to unfavorable regions, resulting in a slow convergence. Therefore, the Darwinian’s survival of the fittest principle should be observed to control the balance between diversification and intensification during the search process. The soil update mechanism and FPS are the main factors affecting the selection pressure in IWD (Niu et al., 2012). After certain number of IWD iterations, it is possible for lower soil levels to be assigned to the components of the local optimal solutions. As such, in successive iterations, the water drops are likely to combine these components in the solution, causing the water drops to be stuck in local optima, therefore unable to escape and explore another region of the search space. Furthermore, IWD works with single large population of water drops. Many findings in the literature indicate that re-running IWD with different random initialization and using the best solution found among all runs could allow IWD to escape from stagnation (Ahmed and Glasgow, 2012). Splitting the large population into several small sub-populations and running IWD in an asynchronous way could also maintain diversity in a good way (Reimann et al., 2004). In addition, the divide-and-conquer technique can be considered to maintain interaction among the sub-populations. 7 1.3 Research Objectives The aim of this research is to develop enhanced IWD algorithms, which can be used to tackle combinatorial optimization problems effectively. The ultimate goal is to show that enhanced IWD algorithms perform better than the original IWD algorithm and other state-of-the-art methods in solving COPs. The primary objectives of this research are as follows: • to utilize a suitable selection mechanism in the solution construction phase of the IWD algorithm to enhance its population diversity; • to modify the IWD algorithm by utilizing the divide-and-conquer and multipopulation strategies to empowering its exploration capability; • to hybridize the modified IWD algorithm with a local based search method to enhance its exploitation capability; • to assess the usefulness of the enhanced IWD algorithms using benchmark COPs and demonstrating its applicability to real-world problems. 1.4 Research Contributions In this research, the objectives mentioned in Section 1.3 lead to the following tangible contributions. • The original IWD algorithm is modified by replacing the fitness proportionate selection method (FPS) in the solution construction phase with two ranking-based selection methods i.e. the exponential and linear ranking selection methods. This 8 proposed modification results in a model called Modified IWD. It is proposed to avoid the search stagnation problem by enhancing population diversity. • An ensemble model of the Modified IWD algorithm is proposed to improve the exploration capability of the Modified IWD algorithm. The resulting model is known as the Master River Multiple Creeks IWD model, and is denoted as MRMC-IWD. • The MRMC-IWD model is hybridized with a local search algorithm, which enhances local exploitation of the search space; therefore achieving a balance between exploration and exploitation in the resulting model, which known as hybrid MRMC-IWD. • The applicability of the hybrid MRMC-IWD model is comprehensively assessed using benchmark and real-world optimization problems. The problems include UCI (University of California Irvine machine learning repository) benchmark data sets (Bache and Lichman, 2013) and two real-world problems, namely human motion detection and motor fault detection. 1.5 Research Methodology Figure 1.2 depicts a three-stage methodology, which has been employed to achieve the research objectives mentioned in Section 1.3. The first stage modifies the original IWD algorithm to improve its performance for solving COPs. It includes two subsequent steps: (i) modifies the original IWD algorithm by replacing the original selection (i.e., FPS) method in the solution construction phase by two ranking-based selection methods ( i.e., linear and exponential ranking); (ii) modifies the fundamental 9 algorithmic aspect (i.e., exploration) of the IWD by proposing an ensemble model of the modified IWD algorithms called MRMC-IWD. In each step, benchmark data sets are used in the experimental study to evaluate the usefulness of the proposed modification. The second stage combines the MRMC-IWD model with a local based method. Again, evaluation is conducted to assess the effectiveness of the proposed models. The last stage assess the applicability of the proposed model (i.e., Hybrid MRMC-IWD) to real-world problems. Figure 1.2: The main stages of the research methodology. 10 To evaluate the proposed models (i.e. MRMC-IWD and hybrid MRMC-IWD) and to facilitate performance comparison with other state-of-the-art methods, three case studies are carried out, namely TSP, MKP, and rough set features subset selection (RSFS) that are widely used in the literature (Chu and Beasley, 1998; Yu and Liu, 2004; Matthias et al., 2007; Shah-Hosseini, 2008; Xie and Liu, 2009; Smith-Miles and Lopes, 2012; Azad et al., 2014). These problems are selected because they are NPhard, and have different level of difficulties. The problem complexity (i.e., the number of alternatives) grows exponentially with respect to the size of the problem (Helsgaun, 2000). Since TSP and MKP have known bounds, they are useful to ascertain the effectiveness of the solutions produced by the proposed models. On the other hand, RSFS is crucial in pattern recognition applications. Contrary to TSP, RSFS presents strong inter-dependency among the decision variables (i.e., features). The feature sequences within the subset are not important, and the optimal solutions are normally unknown (Yu and Liu, 2004). Contrarily to both TSP and RSFS, the MKP is a constrain based optimization problem (Shah-Hosseini, 2008; Azad et al., 2014). Therefore, TSP, MKP, and RSFS problems are selected as case studies to evaluate the usefulness of the proposed models and to benchmark the results against those published in the literature. As a result, the effectiveness of the proposed models for undertaking general optimization problems can be validated. 11 1.6 Research Scope This research focuses on enhancing the performance of the IWD algorithm to tackle COPs. Three main approaches, namely the selection mechanism in the solution construction phase of the IWD algorithm, the ensemble model of the IWD algorithm with a novel problem decomposition technique, and the hybrid IWD model have been investigated to overcome the search stagnation problem; therefore improving original IWD performance. In this context, this research is limited to the use ranking-based selection methods (i.e., linear and exponential), as well as it is limited to k-means clustering algorithm to decompose the entire problem into few simple sub-problems. To assess the effectiveness of the proposed models, a series of experiments pertaining to three COPs (i.e., TSP, RSFS, and MKP) with performance comparison against other state-of-theart methods is conducted. In this regards, this research is limited to the combinatorial single-objective optimization problems. The applicability of the proposed models to two real-world problems related to feature selection and classification task, namely human motion detection and motor fault detection, is investigated. 12 1.7 Thesis Structure The rest of this thesis is organized as follows: Chapter 2 (Background and Literature Review): In this chapter, a detailed descriptions of the IWD algorithm, including learning mechanisms, fundamental steps and mathematical formulation. A review pertaining to optimization and the associated approaches (i.e., selection methods, multi-populations, and hybridization), which are used to enhance the performance of the IWD algorithm in solving COPs is presented. An overview of the evaluation problems (i.e., RSFS, TSP, and MKP) and the associated data sets used in the experiments are also presented. Chapter 3 (Modified Intelligent Water Drops Algorithm): This chapter introduces the first contribution, i.e., the modified IWD algorithm. The effectiveness of the selection mechanism in the solution construction phase of the IWD algorithm is investigated. Two ranking-based methods are proposed to replace the FPS method in the solutions construction phase of the original IWD algorithm. The experimental results pertaining to benchmark COPs and evaluation of the proposed ranking-based selection methods are presented. Chapter 4 (An Ensemble of Intelligent Water Drops Algorithms): In this chapter two new contributions are presented. Firstly, the Master-River Multiple-Creek IWD (MRMC-IWD) model is introduced. The proposed model is motivated by a multipopulation scheme with the divide-and-conquer strategy to simplify the search process, and to exploit the exploration capability of the modified IWD algorithm. Secondly, the hybrid MRMC-IWD model is proposed by hybridizing MRMC-IWD with 13 a local search method, i.e., Iterative Improvement Local search (IILS). The aim is to empower MRMC-IWD with local exploitation capabilities, therefore achieving a balance between exploration and exploitation. The effectiveness of the proposed models is investigated using a series of experiments pertaining to the benchmark COPs. Chapter 5 (Applications of the hybrid MRMC-IWD model): The hybrid MRMCIWD model devised in Chapter 5 is applied to UCI benchmark feature selection and classification problems. Comparative studies against other state-of-the-art methods are presented. In addition, two real-world problems, namely human motion detection as well as motor fault detection are examined, to assess and demonstrate the applicability of the hybrid MRMC-IWD model. Chapter 6 (Conclusion): Concluding remarks and a summary of the key findings are presented in this chapter. A discussion of future researches that can be carried out to further investigate the enhanced IWD models to handle different optimization problems is presented. Appendices (Appendix A): A detail description to feature selection methods is presented. It is mainly organized into two part, First part provides a succinct review of categories of feature selection methods. In the second part, a detailed description of rough set and fuzzy rough set for subset feature selection and illustrative example are provided. 14 CHAPTER 2 BACKGROUND AND LITERATURE REVIEW 2.1 Introduction The main focus of this research is to enhance the performance of the IWD algorithm to tackle COPs. This chapter is mainly organized into three sections. In section 2.2 a detailed description on the IWD algorithm is presented. Section 2.3 reviews optimization methods and literatures related to the IWD method to solve COPs. Section 2.4 presents an overview of the three COPs (i.e., RSFS, TSP, MKP) as well as the characteristics of the data sets, which are employed in the experimental studies to evaluate and validate the usefulness of the proposed model and to benchmark the results against those published in the literature. 2.2 Background to the Intelligent Water Drops Algorithm In nature, water in a river follows an easier path with fewer barriers and obstacles. Water flows with a particular speed. Water stream changes the environmental properties of the river, and subsequently changes the direction of water flow to create an optimal path between the upstream and downstream of a river. The IWD algorithm is a constructive-based SI optimization method introduced by Shah-Hosseini (2007). It is inspired by the natural phenomena of water drops moving along the river bed. The IWD algorithm computationally realizes some of the natural phenomena and uses them as a computational mechanism to solve COPs. It comprises a number of computational 15 agents (i.e., water drops). At each iteration, water drops construct a solution based on a finite set of discrete movements. Two key properties of natural water drops are imitated by the IWD algorithm, i.e. velocity and soil, which are changed during a series of transitions pertaining to the movement of water drops. Each water drop iteratively moves step-by-step from one location to the next until a complete solution is produced. It begins with an initial state, i.e. an initial velocity, and carries zero amount of soil. Water drops cooperate with each other to update the environmental properties, i.e. soil and velocity. Changes in the soil and velocity parameters have an influential role on the selection probability of the flow direction. When a water drop moves from one location to the next, its velocity and soil level are updated. The velocity is changed nonlinearly, and is proportional to the inverse of the amount of soil between two locations. Therefore, water drops in a path with less soil move faster. The water drop carries an amount of soil in each movement, which is non-linearly proportional to the inverse of the time needed by the water drop to move from the current location to the next. On the other hand, the time taken by a water drop to move from one location to another is proportional to its velocity and inversely proportional to the distance between two locations. Figure 2.1 depicts a flowchart of the fundamental of the IWD algorithm, as presented in Algorithm 2.1. In the following sub-sections, a detailed description of the problem formulation as well as the main phases of the IWD algorithm i.e. initialization, solution construction, reinforcement, and termination are presented. 16 Figure 2.1: A flowchart shows the fundamental of the IWD algorithm (Alijla et al., 2014). 17 Algorithm 2.1 : The main steps of the IWD algorithm (Alijla et al., 2014). 1: Input: Data instances. 2: Output: Subset of features. 3: Formulate the optimization problem as fully connected graph. 4: Initialize the static parameters i.e. parameters are not changed during the search process. 5: while algorithm termination condition is not met do 6: Initialize the dynamic parameters i.e. parameters changed during the search process. 7: Spread iwd number of water drops randomly on a construction graph. 8: Update the list of visited vertex (Vvisited ), to include the source vertex. 9: while construction termination condition is not met do 10: for k = 1 to iwd do 11: i = the current vertex for drop k. 12: j = selected next vertex, which does not violate problem constrains. 13: move drop k from vertex i to vertex j. 14: update the following parameters. (a). Velocity of the drop k. (b). Soil value within the drop k. (c). Soil value within the edge e(i,j). 15: end for 16: end while 17: Select the best solution in the iteration population (T IB ) 18: Update the soil value of all edges included in the (T IB ) 19: Update the global best solution (T T B ) 20: if quality of T T B < quality of T IB then 21: T T B = T IB 22: end if 23: end while 24: return T T B 18 2.2.1 Problem formulation As shown in Algorithm 2.1 (line 3), formulating an appropriate problem is a preliminary step for solving any optimization problem using the IWD algorithm. The IWD algorithm uses a fully connected weighted graph called the construction graph i.e. G(V, E), to represent an optimization problem, where V = {vi |i = 1...N} denotes the set of vertices in the graph, E = {(i, j)|(i, j) ∈ V × V, i 6= j, i, j = 1...N}. denotes a set of edges, and N is the total number of decision variables. Consider a solution, πk = {ak j |k = 1...iwd, j = 1...|Dk |}, where k denotes the index of a solution within the population, iwd is the total number of solutions in the population (i.e., the number of water drops), and ak j ∈ A is a set of all possible components of the solution. As an example, solution πk = {ak1 , ak2 , ..., ak|Dk | }, where |Dk | ≤ N is the dimension of the solution k, which is one of the possible permutations constructed from the possible components of A. 2.2.2 Initialization phase As show in Algorithm 2.1 (line 4), the initialization phase is used to initialize a set of static and dynamic parameters of the IWD algorithm. Thereafter, the water drops are spread randomly. 2.2.2(a) Static parameters The static parameters are initialized with static values, and they remain unchanged during the search process. They are: 19 • iwd: is the number of water drops, which denotes a set of agents that forms the solution population. • Velocity updating parameters (av , bv , cv ): a set of parameters used to control the velocity update function, as defined in Eq. (2.4) • Soil updating parameters (as , bs , cs ): a set of parameters used to control the soil update function, as defined in Eq. (2.7) • Max_iter: the maximum number of iterations before terminating the IWD algorithm. • initSoil: the initial value of the local soil. 2.2.2(b) Dynamic parameters The dynamic parameters are initialized before search begins, and are updated during the search process. They are reverted to their initial values at the beginning of each iteration. The dynamic parameters are: • Vkvisited : a list of vertices visited by water drop k. • intiVelk : the initial velocity of water drop k. • Soilk : the initial soil loaded on water drop k. At the beginning, water drops are spread randomly at the vertices of the construction graph, and Vkvisited is updated to include the initial state (i.e., vertex). 20 2.2.3 Solution construction phase The main aim of this phase is to construct a population of iwd solutions. A solution comprises a finite set of components, πk = {ak j |k = 1...iwd, j = 1...|Dk |}, Dk is the dimension of solution k. Water drop k starts with an empty set of solution components, πk = {}. The first vertex of the tour is added to πk whenever the water drop is spread. Then, at each step of the construction phase, the water drop extends the partial solution by traversing a new vertex, i.e., a feasible component that does not violate any constraints of the problem. The construction phase is completed by the transition of all water drops through the graph until the stopping criteria for constructing a complete population is met (see Algorithm 2.1, lines 9-16). The construction phase is composed of the following steps: 2.2.3(a) Edge selection mechanism Consider water drop k residing at the current vertex i intends to move to the next vertex j through an edge, e(i, j), where e ∈ E. The probability of selecting e(i, j) is determined by pki (j), as defined in Eqs. (2.1) and (2.2). Then, the water drop visits k vertex j by adding it to Vvisited . f (soil(i, j)) pki (j) = ∑ f (soil(i, l)) (2.1) k ∀l ∈V / visited f (soil(i, j)) = 1 ε + g(soil(i, j)) (2.2) where ε is a small positive number used to prevent division by zero in function f (.) 21 g(soil(i, j)) = soil(i, j) if soil(i, l) soil(i, j) − min k min soil(i, l) > 0, k ∀l ∈V / visited (2.3) Otherwise. ∀l ∈V / visited where soil(i, l) refers to the amount of soil within the local path between vertices i, and j. 2.2.3(b) Velocity and local soil Update The velocity of water drop k at time t + 1 is denoted by vel k (t + 1). It is updated every time it moves from vertex i to vertex j using Eq. (2.4). vel k (t + 1) = vel k (t) + av bv + cv ∗ soil2 (i, j) (2.4) where av , bv , and cv are the static parameters used to represent the non-linear relationship between the velocity of water drop k (i.e., vel k ) and the inverse of the amount of soil in the local path (i.e., soil(i, j)). When water drop k moves from vertex i to vertex j, both soil k (i.e., the soil within water drop k)and soil(i, j) are updated using Eqs. (2.6) and (2.5) respectively. soilk = soilk + ∆soil(i, j) (2.5) soil(i, j) = (1 − ρn ) ∗ soil(i,j) − ρn ∗ ∆soil(i, j) (2.6) 22 where ρn is a small positive constant between zero and one, (i.e., 0 < ρn < 1 ); ∆soil(i, j) is the amount of soil removed from the local path and carried by the water drop. Note that ∆soil(i, j) is non-linearly proportional to the inverse of the time needed for a water drop to travel from the current vertex to the next, as defined in Eq. (2.7). ∆soil(i, j) = bs + cs as 2 ∗ time (i, j : velk (t + 1)) (2.7) where as , bs , and cs are the static parameters used to represent the non-linear relationship between ∆soil(i, j) and the inverse of the time. Note that time(i, j : vel k (t +1)) refers to the time needed for water drop k to transit from vertex i to vertex j at time t + 1. It is proportional to the distance between the two vertices as well as is proportional to the inverse of the vel k (t + 1) as is defined as shown in Eq. (2.8). time(i, j : velk (t + 1)) = HUD(i, j) vel k (t + 1) (2.8) where HUD(i, j) refers to a heuristic desirability degree between vertices i and j. The processes of selecting a vertex to visit as well as updating the velocity and local soil are iterated subject to the stopping criteria for obtaining a complete solution. 23 2.2.4 Reinforcement phase As shown in Algorithm 2.1 (lines 17-21), the fittest solution of each population is known as the iteration-best solution, and is denoted as T IB . It is determined using Eq. (2.9). TTB = arg min q(x) (2.9) ∀l∈T IWB where q(.) is the fitness function which is used to evaluate the quality of the solutions, and T IW B is the population of the solutions. To reinforce the water drops in the subsequent iterations to follow T IB and achieve the fittest solution over the iterations, the soil of all edges in T IB is updated using Eq. (2.10). This update process is known as global soil update. soil(i, j) = (1 + ρiwd ) ∗ soil(i,j) − ρiwd ∗ 1 q(TIB ) (2.10) where ρiwd is a small positive constant between zero and one, (i.e., 0 < ρiwd < 1 ). In each iteration, the best solution (global best), (i.e.,T T B ), is either replaced by T IB or maintained, as defined in Eq. (2.11). T TB = T IB i f q(T IB ) < q(T TB ) T TB Otherwise. (2.11) 24