A MULTI-OBJECTIVE EVOLUTIONARY ALGORITHM USING DIRECTIONS OF IMPROVEMENT AND APPLICATION

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF NATIONAL DEFENSE MILITARY TECHNICAL ACADEMY NGUYEN LONG 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 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: 1. ASSOC. PROF. DR BUI THU LAM 2. ASSOC. PROF. DR NGUYEN VAN HAI Hanoi - 2014 Abstract Amulti-objectiveoptimizationprobleminvolvesatleasttwoconflictingobjectivesandithas 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 Computation al Intelligence and they are the main focus of th i s thesis. Firstly, the main concepts for multi-objective optimization are presented, then the thesis con- cerns about mentions the solving multi-objective optimization problems by multi-objective evolutionary algorithms. This thesis also conducts a sur vey on the usage of directorial infor- mation 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 asp ects: 1. Automati ca l l y guiding the evolutionary process to make the MOEA balanced between exploitation and exploration. 2. Combining decisi on 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 multi- objective evolutionary algorithm (DMEA), the most recent one with a systematic way to maintain directions of impr ovement so some related issues on DMEA are raised and anal- ysed, hypothesised as primary research problems in this thesis. At the highlighted chapters, the thesis discusses all the is su es on using directions of improve- ment in DMEA through thesis’s contributions: 1. Design a new proposed direction based multi-objective evolutionary alg ori t h m version ii II (DMEA-II) with following improvement techniques: • Using an ada p t i ve ratio between convergence and spread directions. • Using a Ray based density niching method for the main populatio n . • Using a new Ray based density selection scheme for dominated solutions selection. • Using a new pare nts 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 perfor m a n ce of DMEA-II in comparison with the most popul a r MOEAs. 2. Propo ses 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 Replacement, Rays Red i st r i b u t i on , Value Added Niching. The experiments carried out acasestudyonseveraltestproblemsandshowedquitegoodresults. 3. Introdu ces a SpamAssassin based Spam Email Detection System that uses DMEA- II. The pr o posed system helps use rs to have m or e good choices for the Sp a m Assa ssi n system in configuration. iii Acknowledgeme nts The first of all, I would like to express my r espectful thanks to my principal sup er vi sor , Assoc.Prof. Bui Thu Lam for his directly guid a n ce 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 b etween theories and real problems in work. I a l so 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. IalsowouldliketothankallofmyfellowsintheDepartmentofSoftwareTechnologyand Evolutionary Computation research group for their assistance and support. Last but not least, I also would like to acknowledge the supp ort of my family, especially my parents Dr. Nguyen Nghi, Truong Thi Hong, they worked hard an d believed strongly in their children. I also would like to thanks my wife, sisters, brothers who always support me during my research. iv Originality Statement Iherebydeclarethatthisthesisismyownwork,withmyknowledgeandbeliefthethesis has no material previously publish ed or written by others. Any contributions made to the research by colleagues, with people in our research team at Le Qu y Don Technical University or elsewhere, during my candidature is clearly acknowledged. Ialsodeclarethattheintellectualcontentinthissubmissionistheresearchresultsofmyown work, except to the extent that assistance from others in conception or in style, presentation and linguistic expression is acknowledged. v Contents Abstract ii List of Figures ix List of Tables xi Abbreviations xii 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Research Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Questions and Hypothesises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.5 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.6 Original Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Background concepts and Issues 13 2.1 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.1.5 Weak Pareto Optimality . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.1.6 Dominance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.2 Conventional methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 vi 2.2.1 No-preference metho ds . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 A priori metho ds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.2.3 A p osteriori methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2.4 Interactive methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3 An overview of Multi-objective Evolutionary Algorithms . . . . . . . . . . . . 25 2.3.1 Non-elitist metho ds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 2.5.1 Technique of using guided directions . . . . . . . . . . . . . . . . . . . 32 2.5.2 Advantages and disadvantages . . . . . . . . . . . . . . . . . . . . . . . 45 2.6 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 metho d 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 2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3 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 po p u l a ti o n . . . . . . . . . . . 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 4 A guided methodology using interaction with decision makers 87 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 4.2 A multi-point Interactive method for DMEA- II . . . . . . . . . . . . . . . . . 92 4.2.1 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 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 5 An application of DMEA-II for a spam email detection system 104 5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.2 Spam email detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 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 5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6 Conclusions and Future Work 124 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 6.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Publications 130 Appendix A Benchmark sets 132 viii [...]... exploitation and exploration for a good optimal algorithm 1.2 Research Perspectives The majority of theoretical work has been derived from issues analysing, algorithm designing and experimentation The approach taken in this thesis is also based on the careful designed experiments and the analysis of experimental results 1.3 Motivation In optimization area, using evolution algorithms (EAs) brings a lot of. .. important characteristics make MOEAs to be e cient when solving MOPs Chapter 3 describes and analyses these important characteristics of DMEA All issues of using directions of improvement related to these characteristics in DMEA which are indicated in Chapter 2 are solved This leads to a new version of DMEA, namely DMEA-II In order to vali9 1.6 ORIGINAL CONTRIBUTIONS date the proposed algorithm, a series... of the problem) using a mapping function This array is usually considered as a phenotype – Real-valued : For this type of representation, the solution is represented by an array of real values This array is considered as a chromosome and each element of this array is a gene Here the genotype and phenotype are identical Each element of the array is considered a gene – Graph: In some cases, the problem... is hard to maintain the balance between convergence and diversity properties during the search This thesis will discuss the determination and the e↵ective usage of the guided information in MOEAs 1 1.1 OVERVIEW Evolutionary Algorithms Evolution via natural selection of a randomly chosen population of individuals as a search through the space of possible chromosome values In that sense, an evolutionary. .. Strength Pareto Evolutionary Algorithm 2 Multi-objective Evolutionary Algorithm Based on Decomposition Multi-objective Genetic Algorithm Niched Pareto Genetic Algorithm Pareto-Archived Evolution Strategy Multi-objective Particle Swarm Optimization Pareto Di↵erential Evolution Decision Maker Generational Distance Inverse Generational Distance Hypervolume Two Set Converge Spam Detection Rate False Alarm Rate... of feasible trade-o↵ solutions for an anti-spam email system (using Apache SpamAssassin) The experiments on Vietnamese language databases and rules are implemented The results indicated that, when solving the problem using DMEA-II, it achieved more e cient results but also created a set of ready-to-use rule scores • Chapter 6 Conclusions and future works are given 1.6 Original Contributions Using evolutionary. .. DC DS Meaning Evolutionary Algorithm Genetic Algorithm Evolution Strategies Evolution Programming Genetic Programming Multi-objective Optimization Problem Multi-objective Evolutionary Algorithm Pareto Optimal Front Pareto Optimal Set Ray based Density Direction based Multi-objective Evolutionary Algorithm Direction based Multi-objective Evolutionary Algorithm- II Non-Dominated Sorting Genetic Algorithm. .. problems, EAs are adaptively and e↵ectively used to obtain a set of approximated Pareto optimal solutions However, EAs also have some di culties such as: the obtained solutions are approximated Pareto optimal solutions so they are not really desired optimal solutions for the problems It also requires a high number of generations to get a good set of solutions To avoid these disadvantages, a hybridization... for MOEAs are presented Up to date, a significant number of MOEAs are reported in depth At the end of the chapter, the recent general developments and research issues on search’s guidance are addressed At the highlighted part of the chapter, using directional information for search’s guidance in MOEAs is discussed For more details, the chapter also indicates several issues in using directions of improvement. .. Evolutionary algorithms allow to find an entire set of Pareto optimal solutions in a single run of the algorithm, instead of having to perform a series of separate runs as in the case of the traditional mathematical programming techniques Recently, the guided techniques have been discussed, conceptualized and used to guide multiobjective evolutionary algorithms (MOEAs) during the search process towards the . Spread xii ! ! xiii! BẢNG THUẬT NGỮ SỬ DỤNG TRONG LUẬN ÁN Tiếng Anh Tiếng Việt Evolutionary Algorithm Giải thuật tiến hóa Multi-objective Optimization Problem Bài toán tối ưu đa mục tiêu Multi-objective. Algorithm Giải thuật tiến hóa Pareto Optimal Front Lớp tối ưu Pareto Pareto Optimal Set Tập tối ưu Pareto Directions of Improvement Hướng cải thiện Convergence Direction Hướng hội tụ. thiện Convergence Direction Hướng hội tụ Spread Direction Hướng tản mát Differential Direction Hướng vi phân Gradient Direction Hướng Gradient Generational Distance Khoảng cách thế hệ