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A Reduced Markov Model of GAs Without the Exact Transition Matrix

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Parallel Problem Solving from Nature - PPSN VIII (PPSN 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3242))

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Abstract

Modelling a finite population genetic algorithm (GA) as a Markov chain can quickly become unmanageable since the number of population states increases rapidly with the population size and search space size. One approach to resolving this issue is to “lump” similar states together, so that a tractable Markov chain can be produced. A paper by Spears and De Jong in [1] presents an algorithm that can be used to lump states together, thus compressing the probability transition matrix. However, to obtain a lumped model, one needs to calculate the exact transition matrix before the algorithm can be applied to it. In this paper, we explore the possibility of producing a reduced Markov model without the need to first produce the exact model. We illustrate this approach using the Vose model and Spears lumping algorithm on the Onemax problem with a selection-mutation GA.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham, B15 2TT, Great Britain

    Cheah C. J. Moey & Jonathan E. Rowe

Authors
  1. Cheah C. J. Moey
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  2. Jonathan E. Rowe
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Editor information

Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Xin Yao

  2. Automated Scheduling, Optimisation and Planning Group, School of Computer Science & IT, University of Nottingham, NG8 1BB, Nottingham, UK

    Edmund K. Burke

  3. Intelligent Systems Group Department of Computer Science and Artificial Intelligence, University of the Basque Country, Paseo Manuel de Lardizábal 1, 20018, San Sebastian, Donostia, Spain

    José A. Lozano

  4. University of the West of England, Bristol, United Kingdom

    Jim Smith

  5. GeNeura Team, Depto. Arquitectura y Tecnología de Computadores, Universidad de Granada, Spain

    Juan Julián Merelo-Guervós

  6. School of Computer Science, The University of Birmingham, B15 1TT, Edgbaston, Birmingham, UK

    John A. Bullinaria

  7. School of Computer Science, University of Birmingham, B15 2TT, Birmingham, Great Britain

    Jonathan E. Rowe

  8. School of Computer Science, University of Birmingham, United Kingdom

    Peter Tiňo

  9. School of Computer Science, The University of Birmingham, B15 2TT, Birmingham, UK

    Ata Kabán

  10. Faculty of Computer Science, Dortmund University of Technology, 44221, Dortmund, Germany

    Hans-Paul Schwefel

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© 2004 Springer-Verlag Berlin Heidelberg

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Moey, C.C.J., Rowe, J.E. (2004). A Reduced Markov Model of GAs Without the Exact Transition Matrix. In: Yao, X., et al. Parallel Problem Solving from Nature - PPSN VIII. PPSN 2004. Lecture Notes in Computer Science, vol 3242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30217-9_8

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  • DOI: https://doi.org/10.1007/978-3-540-30217-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23092-2

  • Online ISBN: 978-3-540-30217-9

  • eBook Packages: Springer Book Archive

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