思维进化算法的转移概率分析及几乎处处收敛性证明

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。

Migration probabilities analysis and almost sure convergence proof of mind evolutionary algorithm

The convergence in probability of mind evolutionary algorithm (MEA) is proved by using the Markovian chain. The almost sure convergence is stronger than the convergence in probability. The migration probabilities of the similar-taxis and the dissimilation are analyzed in detail, and the evolution process of the maximal fitness function is described as a submartingale series. Based on the characteristic of the conditional expectation and the maximal fitness function, the almost sureconvergence of MEA is proved rigorously by using the sub-martingale convergence theorem.