, Volume 17, Issue 3-4, pp 395-399
Date: 16 Nov 2012

Stochastic analysis of OneMax problem using Markov chain

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Abstract

Experimental and analytical investigations are performed for OneMax problem using Wright–Fisher model. This study investigates the distribution of the first order schema frequency in the evolution process of Genetic Algorithm (GA). Effects of mutation in GA are analyzed for the standard mutation and asymmetric mutation models. If a population is in linkage equilibrium, it can be shown that OneMax problem is equivalent to the asymmetric mutation model. Thus, we can apply theoretical results obtained in the asymmetric mutation model to OneMax problem and investigate the convergence time of GA calculation within the framework of Wright–Fisher model.

This work was presented in part at the 17th International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–21, 2012.