Convergence and convergence rate analysis of elitist genetic algorithm based on martingale approach
保留精英遗传算法收敛性和收敛速度的鞅方法分析

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.