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MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENSE MILITARY TECHNICAL ACADEMY NGUYEN LONG h A MULTI-OBJECTIVE EVOLUTIONARY ALGORITHM USING DIRECTIONS OF IMPROVEMENT AND APPLICATION THE THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS Hanoi – 2014 MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENSE MILITARY TECHNICAL ACADEMY A MULTI-OBJECTIVE EVOLUTIONARY ALGORITHM USING DIRECTIONS OF IMPROVEMENT AND APPLICATION h Specialized in: Fundamentals of Mathematics for Informatics Code: 62 46 01 10 THE THESIS IS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN MATHEMATICS SUPERVISORS: ASSOC PROF DR BUI THU LAM ASSOC PROF DR NGUYEN VAN HAI Hanoi - 2014 h Abstract A multi-objective optimization problem involves at least two conflicting objectives and it has a set of Pareto optimal solutions Multi-objective evolutionary algorithms (MOEAs) use a population of solutions to approximate the Pareto optimal set in a single run MOEAs have attracted a lot of research attention during the past decade They are still one of the hottest research areas in the field of Computational Intelligence and they are the main focus of this thesis Firstly, the main concepts for multi-objective optimization are presented, then the thesis con- h cerns about mentions the solving multi-objective optimization problems by multi-objective evolutionary algorithms This thesis also conducts a survey on the usage of directorial information in search’s guidance Through the survey, the thesis indicates that there is a need to have more investigation on how to have an e↵ective guidance from both aspects: Automatically guiding the evolutionary process to make the MOEA balanced between exploitation and exploration Combining decision maker’s preference with directions of improvement to guide the MOEAs during optimal process toward the most preferred region in the objective space To address this, the thesis builds up all its proposals based on a direction based multiobjective evolutionary algorithm (DMEA), the most recent one with a systematic way to maintain directions of improvement so some related issues on DMEA are raised and analysed, hypothesised as primary research problems in this thesis At the highlighted chapters, the thesis discusses all the issues on using directions of improvement in DMEA through thesis’s contributions: Design a new proposed direction based multi-objective evolutionary algorithm version ii II (DMEA-II) with following improvement techniques: • Using an adaptive ratio between convergence and spread directions • Using a Ray based density niching method for the main population • Using a new Ray based density selection scheme for dominated solutions selection • Using a new parents selection scheme for the o↵springs perturbation In order to validate the proposed algorithm, a series of experiments on a wide range of test problems was conducted It obtained quite good results on primary performance metrics, including the generation distance (GD), the inverse generation distance (IGD), the hypervolume (HYP) and the two set coverage (SC) The analysis on the results indicates the better performance of DMEA-II in comparison with the most popular MOEAs Proposes an interactive method for DMEA-II as the second aspect of having an e↵ective guidance An interactive method is introduced with three ray based approaches: Rays h Replacement, Rays Redistribution, Value Added Niching The experiments carried out a case study on several test problems and showed quite good results Introduces a SpamAssassin based Spam Email Detection System that uses DMEAII The proposed system helps users to have more good choices for the SpamAssassin system in configuration iii Acknowledgements The first of all, I would like to express my respectful thanks to my principal supervisor, Assoc.Prof Bui Thu Lam for his directly guidance to my PhD progress Assoc.Prof Bui has given me knowledge and passion as the motivation of this thesis His valued guidance has inspired much of the research in the thesis I also wish to thank my co-supportive Assoc.Prof Nguyen Van Hai for his suggestions and knowledge during my research, especially the relation between theories and real problems in work I also would like to thank Prof Hussein Abbass, Assoc.Prof Tran Quang Anh and Assoc.Prof Dao Thanh Tinh for their invaluable support throughout my PhD I feel lucky to work with such excellent people I also would like to thank all of my fellows in the Department of Software Technology and Evolutionary Computation research group for their assistance and support Last but not least, I also would like to acknowledge the support of my family, especially my parents Dr Nguyen Nghi, Truong Thi Hong, they worked hard and believed strongly in their h children I also would like to thanks my wife, sisters, brothers who always support me during my research iv Originality Statement I hereby declare that this thesis is my own work, with my knowledge and belief the thesis has no material previously published or written by others Any contributions made to the research by colleagues, with people in our research team at Le Quy Don Technical University or elsewhere, during my candidature is clearly acknowledged I also declare that the intellectual content in this submission is the research results of my own work, except to the extent that assistance from others in conception or in style, presentation and linguistic expression is acknowledged h v Contents Abstract ii List of Figures ix List of Tables xi Abbreviations xii Introduction Overview 1.2 Research Perspectives 1.3 Motivation 1.4 Questions and Hypothesises 1.5 Thesis organization 1.6 Original Contributions 10 h 1.1 Background concepts and Issues 2.1 2.2 13 Common concepts 13 2.1.1 Multi-objective problems 13 2.1.2 Notations 14 2.1.3 General Definitions 14 2.1.4 Pareto Optimality 2.1.5 Weak Pareto Optimality 17 2.1.6 Dominance 17 15 Conventional methods 18 vi 2.3 2.2.1 No-preference methods 19 2.2.2 A priori methods 19 2.2.3 A posteriori methods 20 2.2.4 Interactive methods 23 An overview of Multi-objective Evolutionary Algorithms 25 2.3.1 Non-elitist methods 25 2.3.2 Elitist methods 26 2.3.3 Performance measures 27 2.3.4 Test problems 29 2.4 Statistical testing 30 2.5 Search’s guidance in MOEAs 31 2.6 Technique of using guided directions 32 2.5.2 Advantages and disadvantages 45 Research Issues 48 2.6.1 Direction based multi-objective evolutionary algorithm (DMEA) 48 2.6.2 Issue 01: The disadvantages of the fixed ratio between types of directions 51 2.6.3 Issue 02: Lack of an efficient niching method for the main population 52 2.6.4 Issue 03: The disadvantages of using the weighted sum scheme 53 2.6.5 Issue 04: Using a ’hard’ niching method 53 2.6.6 Issue 05: Investigating on how the DM can interact with DMEA 53 h 2.7 2.5.1 Summary 54 A guided methodology using directions of improvement 55 3.1 Using an adaptive ratio between convergence and spread directions 55 3.2 Using a Ray based density niching for the main population 56 3.3 Using a ray based density selection schemes 59 3.4 Direction based Multi-objective Evolutionary Algorithm-II 60 3.4.1 General structure 60 3.4.2 Computational complexity 62 3.4.3 Experimental Studies 62 vii 3.4.4 Results and Discussion 68 3.5 Analyzing e↵ects of di↵erent selection schemes for the perturbation 81 3.6 Summary 86 A guided methodology using interaction with decision makers 87 4.1 Overview 87 4.2 A multi-point Interactive method for DMEA-II 92 4.3 4.2.1 Rays replacement 93 4.2.2 Rays Redistribution 94 4.2.3 Value Added Niching 96 4.2.4 Experimental Studies 97 4.2.5 Results and Discussion 98 Summary 102 An application of DMEA-II for a spam email detection system 104 Overview 104 5.2 Spam email detection 107 h 5.1 5.3 5.2.1 SpamAssassin 107 5.2.2 Methodology 108 5.2.3 An interactive method 113 5.2.4 Computational complexity 113 5.2.5 Experimental Studies 114 5.2.6 Results and Discussion 115 Summary 123 Conclusions and Future Work 124 6.1 Conclusions 124 6.2 Future directions 129 Publications 130 Appendix A Benchmark sets 132 viii