I-Ching Divination Evolutionary Algorithm and its Convergence Analysis
提出一种基于易经占卜的模拟进化算法，定义三种新算子及两个空间，用马尔可夫链证明其收敛到全局最优，相比遗传算法等更快。
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.