4.6 Article

I-Ching Divination Evolutionary Algorithm and its Convergence Analysis

Journal

IEEE TRANSACTIONS ON CYBERNETICS
Volume 47, Issue 1, Pages 2-13

Publisher

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2015.2512286

Keywords

Convergence analysis; evolutionary algorithm (EA); I-Ching divination EA (IDEA); I-Ching operators (ICOs); Markov chain

Funding

  1. National Natural Science Foundation of China [61572540]
  2. Macau Science and Technology Development Fund [008/2010/A1, 017/2012/A1]
  3. Multiyear Research Grants

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An innovative simulated evolutionary algorithm (EA), called I-Ching divination EA (IDEA), and its convergence analysis are proposed and investigated in this paper. Inherited from ancient Chinese culture, I-Ching divination has always been used as a divination system in traditional and modern China. 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 in this paper, which are denoted as hexagram space and state space. In order to analyze the convergence property of I-Ching divination algorithm, Markov model was adopted to analyze the characters of the operators. Meanwhile, the proposed algorithm is proved to be a homogeneous Markov chain with the positive transition matrix. After giving some basic concepts of necessary theorems, definition of admissible functions and I-Ching map, a precise proof of the states converge to the global optimum is presented. Compared with the genetic algorithm, particle swarm optimization, and differential evolution algorithm, our proposed IDEA is much faster in reaching the global optimum.

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