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Markov chain analysis of evolutionary algorithms for monotonic functions

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Abstract

The theoretical investigation of evolutionary algorithms (EAs) has increased our knowledge of the computational mechanism of algorithms. In this paper, we report the convergence properties of an algorithm that is a variant of (1+1) EA, partially ordered evolutionary algorithm (PO-EA), which was initially designed for representing the evolutionary behaviors of all linear functions. Recently, PO-EA has been expected to give a model for deriving an upper bound on the expected hitting time of EA for monotonic functions. A monotonic function is a pseudo-boolean function whose value increases by flipping positive number of zeros to one. This study makes use of Markov chain model to analyze the movement of PO-EA. We divide PO-EA into two parts, PO-mutation and ZeroMax models, and study their mutation rate dependences of the expected hitting times.

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Acknowledgements

This work is supported by Science and Technology Project in Qinghai Province (No. 2017-ZJ-717); Natural Science Foundation of China (No.61640206)D

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Authors and Affiliations

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

    QinLian Ma

  2. Department of Computer Technology and Applications, Qinghai University, Qinghai, China

    Yu-an Zhang

  3. Faculty of Engineering, University of Miyazaki, Miyazaki, Japan

    Kunihito Yamamori

  4. Innovative Computing Research Center, Doshisha University, Kyoto, Japan

    Hiroshi Furutani

  5. Faculty of Life and Medical Sciences, Doshisha University, Kyoto, Japan

    Satoru Hiwa & Tomoyuki Hiroyasu

Authors
  1. QinLian Ma
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  2. Yu-an Zhang
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  3. Kunihito Yamamori
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  4. Hiroshi Furutani
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  5. Satoru Hiwa
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  6. Tomoyuki Hiroyasu
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Corresponding author

Correspondence to Hiroshi Furutani.

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Ma, Q., Zhang, Ya., Yamamori, K. et al. Markov chain analysis of evolutionary algorithms for monotonic functions. Artif Life Robotics 24, 82–87 (2019). https://doi.org/10.1007/s10015-018-0463-9

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  • DOI: https://doi.org/10.1007/s10015-018-0463-9

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