父代种群参与竞争遗传算法几乎必然收敛

熟知,标准遗传算法如不采用“杰出者记录策略”则必不收敛。本文发现：允许父代种群参与竞争是标准遗传算法几乎必然收敛的条件。特别地,我们运用鞅收敛定理证明：允许父代种群参与竞争型遗传算法能以概率1确保在限步内达到全局最优解,且收敛与种群规模无关。所获结果对该类遗传算法的应用奠定了可靠基础。

ALMOST SURE STRONG CONVERGENCE OF A CLASS OF GENETIC ALGORITHMS WITH PARENT-OFFSPRINGS COMPETITION

It is well known that if the cononical genetic algorithm(CGA) does not adopt the "elitist record strategy" , it can not guarantee its convergence. In this paper, we consider a class of genetic algorithms(GAs) with the strategy that parents are always put into com- petition with their offsprings. It is shown that such strategy is the necessary and sufficient condition for CGA to converge. Especially by applying submartingale theory and measure theory, we prove that after a finite number of iterations, the parents population will be settled in the set of global optimal solutions with probility one. Different from other GA convergence results, no restriction is imposed on the population size of the proposed model. The obtained results lie a reliable foundation for application of the con-sidered GAs.