保留精英遗传算法收敛性和收敛速度的鞅方法分析

论文引入鞅方法取代传统的马尔科夫链理论,研究保留精英遗传算法(EGA)的收敛条件和收敛速度.通过把EGA的最大适应值函数过程描述为下鞅,基于下鞅收敛定理构造使算法满足几乎处处收敛的充分条件,分析了概率1收敛充分条件与算法操作参数的关系,并计算了EGA获得全局最优解所需的最大进化代数.使用鞅方法分析遗传算法收敛性具有独特的优势,成为分析遗传算法收敛性及其性能的新方法.

Convergence and convergence rate analysis of elitist genetic algorithm based on martingale approach

The martingale approach is introduced in this paper to study the convergence conditions and convergence rate of elitist genetic algorithm(EGA) instead of the traditional Markov chain theory. The maximal fitness function process is described as a submartingale. Based on the submartingale convergence theorem, we develop the almost everywhere convergence sufficient conditions of the EGA. The relations between the probability 1 convergence sufficient conditions and the algorithm operating parameters are analyzed; and the maximal evolutional generations needed to obtain the global optimal solution are estimated. The martingale approach has its unique advantage and is a new method to analyze the convergence and performance of the genetic algorithm.