最小騙し問題を用いた世代交代モデルの解析

抄録

GAs(Genetic Algorithms) evolve populatiions to search solutions for optimization problems by using the crossover, that is the unique operator in similar stochastic direct optimization techniques like SAs(Simulated Annealings). Generation alternation models are important to give controls on search processes. Analytic works should show how to design an encoding/crossover and a generation alternation model for given problems. Existing works have often used SGA(simple or standard GA) for a fixed generation alternation model, although it was often pointed out to be problematic for real applications because of its high selection pressure. This paper shows an analysis focused upon how generation alternation models influence crossover's effect in solving the minimal deceptive problems. We prepared two generation alternation models; SGA as one extreme and the rMGG(routellete minimal generation gap model) for the other extreme from Satoh's experimental analysis. We have made a Markov analysis for the MDPs(minimal deceptive problems) with relatively small populations. We show SGA-based GAs are easily deceived than rMGG-based ones, and stepping stones help crossover's effect in deceptive problems. We have planed three experiments on three bits and four bits FDPs(fully deceptive problems), and demonstrate these conjectures are not violated in these cases.