Stochastic analysis of OneMax problem using Markov chain

  • Authors:

  • Qinglian Ma;Yu-An Zhang;Kiminobu Koga;Kunihito Yamamori;Makoto Sakamoto;Hiroshi Furutani

  • Affiliations:

  • Interdisciplinary Graduate School of Agriculture and Engineering, University of Miyazaki, Miyazaki, Japan 889-2192;Department of Computer Science and Technology, Qinghai University, Xining, China;Graduate School of Engineering, University of Miyazaki, Miyazaki, Japan 889-2192;Faculty of Engineering, University of Miyazaki, Miyazaki, Japan 889-2192;Faculty of Engineering, University of Miyazaki, Miyazaki, Japan 889-2192;Faculty of Engineering, University of Miyazaki, Miyazaki, Japan 889-2192

  • Venue:
  • Artificial Life and Robotics
  • Year:
  • 2013

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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.