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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.

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Authors and Affiliations

  1. Interdisciplinary Graduate School of Agriculture and Engineering, University of Miyazaki, Miyazaki, 889-2192, Japan

    QingLian Ma

  2. Department of Computer Science and Technology, Qinghai University, Xining, China

    Yu-an Zhang

  3. Graduate School of Engineering, University of Miyazaki, Miyazaki, 889-2192, Japan

    Kiminobu Koga

  4. Faculty of Engineering, University of Miyazaki, Miyazaki, 889-2192, Japan

    Kunihito Yamamori, Makoto Sakamoto & Hiroshi Furutani

Authors
  1. QingLian Ma
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  2. Yu-an Zhang
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  3. Kiminobu Koga
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  4. Kunihito Yamamori
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  5. Makoto Sakamoto
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  6. Hiroshi Furutani
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Corresponding author

Correspondence to Hiroshi Furutani.

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Ma, Q., Zhang, Ya., Koga, K. et al. Stochastic analysis of OneMax problem using Markov chain. Artif Life Robotics 17, 395–399 (2013). https://doi.org/10.1007/s10015-012-0075-8

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  • DOI: https://doi.org/10.1007/s10015-012-0075-8

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