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I-Ching divination evolutionary algorithm : convergence analysis and its applications

English Abstract

Analytical methods, enumerative methods, and random methods are three types of techniques in searching optimum solutions. In practice, many applications have discontinued functions in the complicated space of solutions or have a huge search space. It is impossible to use either analytical methods or enumerative methods to solve these problems. However, random methods have more advantages in addressing these questions than the other two methods. Derived from the concept of random search, evolutionary algorithm (EA) has been successfully applied to optimize various objective functions. In the search procedures, EA aims to improve the ability of an organism (or system) to survive in dynamically changing and competitive environments. EA has been applied in numerous optimization problems as reported in previous literatures. In general, genetic algorithm (GA), genetic programming (GP), differential evolution (DE), evolution strategies (ES), and particle swarm optimization (PSO) are best-known simulated evolutionary algorithms(EAs). Nevertheless, suffering from time consumption and premature convergence problems, EAs perform badly in many search and optimization problems. Consequently, many researchers are focusing on designing more efficient EAs by defining parallel models, hybrid algorithms, new operators, and so on. By studying of Chinese history philosophy, I found many similarities between IChing divination process and genetic algorithms, which brings me an in-depth examination of I-Ching divination process. Then, I started to explore the possibilities of applying I-Ching divination process into optimization problems. Firstly, an innovative simulated evolutionary algorithm, called I-Ching Divination Evolutionary Algorithm (IDEA), is developed as one part of my PhD studies. There are three operators evolved from I-Ching transformations in this new optimization algorithm, intrication operator, turnover operator, and mutual operator. These new operators are very flexible in the evolution procedure. Additionally, two new spaces are defined, which are denoted as Hexagram space and State space. Secondly, I investigate the convergence analysis of the proposed IDEA. In this ii part, Markov model is adopted to analyze the characters of the operators. Then, the proposed algorithm is proved to be a homogeneous Markov Chain with the transition matrix. After giving some basic concepts of necessary theorems, I present a precise proof of the states converging to the global optimum. Thirdly, I compare the proposed approach, I-Ching divination evolutionary algorithm with other well-known algorithms, such as genetic algorithm, particle swarm optimization, and differential evolution algorithm. Based on the performance on the 22 common used benchmark functions, the proposed I-Ching divination evolutionary algorithm is much faster in reaching the global optimum. Furthermore, IDEA has also been applied to solve two different practical problems. One is for data clustering, and the other is for substitution box (S-Box) designing. Overall, my PhD thesis focuses on the above three parts aiming to develop a new evolutionary algorithm for machine learning and recognition. All of the studies are assessed by real-world applications, and published in international conferences and journals.

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Zhang, Tong


Faculty of Science and Technology


Department of Computer and Information Science




Evolutionary computation


Chen, C. L.

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