Hidden-Markov-Based Self-adaptive Differential Evolution Marwa Mohamed ElSaied Hassan Keshk B.Sc. (Information Systems), Helwan University, Egypt. A thesis submitted in fulfilment of the requirements for the degree of Master of Computer Science School of Engineering and Information Technology The University of New South Wales Australia August 2017 ii PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet Surname or Family name: Mohamed ElSaied Hassan Keshk First name: Marwa Other name/s: Abbreviation for degree as given in the University calendar:Master School: SEIT Faculty: UNSW Canberra Title: Hidden-Markov-Based Self-adaptive Differential Evolution Abstract 350 words maximum: (PLEASE TYPE) Heuristic search is an efficient way to solve complex optimization problems, and sometimes it is the only way to do so. Differential Evolution (DE) is a population-based heuristic search suitable mostly for continuous optimization problems. The efficiency of DE to optimize a problem can largely degrade if the right values for its parameters are not chosen. Finding the right values for DE’s parameters is a non-trivial task. Many researchers resort to parameter tuning and self-adaptation mechanisms. Existing methods vary in their performance and design philosophies. In this thesis, I start by introducing a semantic evolutionary visualization framework to investigate evolutionary dynamics. The different visualizations track the ongoing changes within an evolutionary run by exploring pedigree trees and the fitness landscapes. The visualization alone was not sufficient to shed light on a very high dimensional space. Consequently, I resorted to introducing a new self-adaptive algorithm using Hidden Markov Models (HMMs). Markov models have been used extensively in the past to analyze convergence of evolutionary optimization methods. I have leveraged this opportunity to introduce a new algorithm that we call DE-HMM, where HMMs is used for real-time learning of evolutionary dynamics to allow for dynamic adjustment of the two intrinsic DE parameters: F and CR. DE-HMM categorizes each evolutionary transition into two discrete states; low and high, representing the rate of change in a population over time. The HMM posterior and likelihood ratios are estimated to assign the values for F and CR during the evolutionary process. Two unconstrained benchmark set are used to assess DE-HMM performance, demonstrating its overall superiority in terms of solution quality and computational resources, when compared to other state-of-the art algorithms. The self-adaptive DE-HMM is then augmented with local search to solve constrained optimization problems. A two-stage method is introduced; with the two states being either global or local based on the degree of feasibility and rate of diversity. The methodology demonstrated competitive results when tested on the constrained CEC2010 benchmark dataset. Declaration relating to disposition of project thesis/dissertation I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstracts International (this is applicable to doctoral theses only). …………………………………………………………… ……………………………………..……………… ……….……………………...…….… Signature Witness Date The University recognises that there may be exceptional circumstances requiring restrictions on copying or conditions on use. Requests for restriction for a period of up to 2 years must be made in writing. Requests for a longer period of restriction may be considered in exceptional circumstances and require the approval of the Dean of Graduate Research. FOR OFFICE USE ONLY Date of completion of requirements for Award: THIS SHEET IS TO BE GLUED TO THE INSIDE FRONT COVER OF THE THESIS iii Copyright Statement ‘I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted. I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.’ Signed Data: ...................... iv Authenticity Statement ‘I certify that the Library deposit digital copy is a direct equivalent of the final officially approved version of my thesis. No emendation of content has occurred and if there are any minor variations in formatting, they are the result of the conversion to digital format.’ Signed Data: .................... v Originality Statement I hereby declare that this submission is my own work and to the best of my knowl- edge and belief, it contains no material previously published or written by another person, nor material which to a substantial extent has been accepted for the award of any other degree or diploma at UNSW or any other educational institution, ex- cept where due acknowledgment is made in the thesis. Any contribution made to the research by colleagues, with whom I have worked at UNSW or elsewhere, during my candidature, is fully acknowledged. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that as- sistance from others in the project’s design and conception or in style, presentation and linguistic expression is acknowledged. Signed Data: ......................... vi Acknowledgment In the name of Allah, all the faithful gratitude, praises are due to Allah, the Almighty God, the Ubiquitous God, the most Gracious and Merciful. Thanks to ALLAH for his support and blessing to complete this work and I hope that this study would be beneficial and valuable as a scientific research in the Evolutionary Computation field. I would like to express my genuine thanks and deepest gratitude to everyone who have supported and assisted me to successfully achieve this work. First of all, I would like to express my sincere appreciation to my supervisor, Professor Hussein Abbass, and my Co-supervisor, Dr. Hemant Singh for their outstanding supervision, continuous and precious guidance, insightful discussions and their effort for reviewing and providing me genuine feedback of my publications and thesis. I would like to express my great thanks to Mrs. Denise Russell for her helpful suggestions by proofreading my publications and thesis. I would like to thank the University of New South Wales, Canberra at the Australian Defense Force Academy for providing me with a scholarship to study at that institution. I thank my mother, father, brother and sister for supporting and encouraging me to complete my master degree. I wish to express my gratitude and sincere appreciation to my husband, Nour, who always helps me a lot in my work and my life. Also, I wish to thank my little daughter, Nardeen, who has always been the flower of my life. I would like to thank everyone at the Trusted Autonomy group for the good time we spent, sharing ideas and learning from each others. Moreover, I offer my appreciation to the school administration and IT support staffs who provided me with all the necessary facilities. Finally, many thanks for my friends in canberra vii and in my home country who support and assist me all the time to finish my master study. viii Abstract Heuristic search is an efficient way to solve complex optimization problems, and sometimes it is the only way to do so. Differential Evolution (DE) is a population- based heuristic search suitable mostly for continuous optimization problems. The efficiency of DE to optimize a problem can largely degrade if the right values for its parameters are not chosen. Finding the right values for DE’s parameters is a non-trivial task. Many researchers resort to parameter tuning and self-adaptation mechanisms. Existing methods vary in their performance and design philosophies. In this thesis, I start by introducing a semantic evolutionary visualization framework to investigate evolutionary dynamics. The different visualizations track the ongoing changes within an evolutionary run by exploring pedigree trees and the fitness landscapes. The visualization alone was not sufficient to shed light on a very high dimensional space. Consequently, I resorted to introducing a new self-adaptive algorithm using Hidden Markov Models (HMMs). Markov models have been used extensively in the past to analyze convergence of evolutionary optimization methods. I have leveraged this opportunity to intro- duce a new algorithm that we call DE-HMM, where HMMs is used for real-time learning of evolutionary dynamics to allow for dynamic adjustment of the two intrinsic DE parameters: F and CR. DE-HMM categorizes each evolutionary transition into two discrete states; low and high, representing the rate of change in a population over time. The HMM posterior and likelihood ratios are estimated to assign the values for F and CR during the evolutionary process. Two unconstrained benchmark set are used to assess DE-HMM performance, demonstrating its overall superiority in terms of solution quality and computational resources, when compared to other state-of-the art algorithms. ix The self-adaptive DE-HMM is then augmented with local search to solve con- strained optimization problems. A two-stage method is introduced; with the two states being either global or local based on the degree of feasibility and rate of diversity.