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思维进化算法已有的收敛性分析均是在依概率收敛意义下考虑的,而几乎处处收敛强于依概率收敛.在详细分析思维进化算法趋同算子和异化算子转移概率的基础上,利用种群最大适应度值函数描述思维进化算法的演化过程,将最大适应度值函数的进化过程转化为下鞅数列,并根据数学期望的性质和最大适应度值函数的特点,利用下鞅收敛定理严格证明了思维进化算法的几乎处处收敛性.
The existing convergence analysis of thought evolutionary algorithm is considered in the sense of probability convergence, while the convergence almost everywhere is stronger than the probability convergence.On the basis of analyzing the transition probability of the convergence operator and alienation operator in thought evolutionary algorithm, The maximum fitness value function of population describes the evolutionary process of thought evolutionary algorithm and transforms the evolution process of maximum fitness value function into lower martingale series. According to the properties of mathematical expectation and the maximum fitness value function, It proves that the evolutionary algorithm of thought almost everywhere convergence.