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How the Combinatorics of Neutral Spaces Leads Genetic Programming to Discover Simple Solutions

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Genetic Programming Theory and Practice XX

Part of the book series: Genetic and Evolutionary Computation ((GEVO))

Abstract

For various evolutionary systems it was found that the abundance of phenotypes in a search space, defined as the size of their respective neutral networks, is key to understanding the trajectory an evolutionary process takes from an initial to a target solution. In this chapter we use a Linear Genetic Programming system to demonstrate that the abundance of phenotypes is determined by the combinatorics offered in its neutral components. This translates into the size of the neutral space available to a phenotype and also can explain the beautiful and rather curious observation that the abundance of phenotypes is dependent on their complexity in a negative exponential fashion.

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Notes

  1. 1.

    An alternative is to divide phenotypes into a static (structural) and a dynamic (behavioral) part.

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Acknowledgements

The authors gratefully acknowledge the reviewers’ insightful comments which helped to improve the manuscript.

Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA

    Wolfgang Banzhaf

  2. School of Computing, Queen’s University, Kingston, ON, Canada

    Ting Hu

  3. Department of Computer Science, University of Stirling, Stirling, UK

    Gabriela Ochoa

Authors
  1. Wolfgang Banzhaf
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  2. Ting Hu
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  3. Gabriela Ochoa
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Corresponding author

Correspondence to Wolfgang Banzhaf .

Editor information

Editors and Affiliations

  1. School of Information, Communications and Media, University of Applied Sciences Upper Austria, Hagenberg, Austria

    Stephan Winkler

  2. Engineering Sciences Graduate Program, Tecnológico Nacional de México, IT de Tijuana, Tijuana, Baja California, Mexico

    Leonardo Trujillo

  3. Department of Computer Science and Engineering, Michigan State University, East Lansing, MI, USA

    Charles Ofria

  4. School of Computing, Queen's University, Kingston, ON, Canada

    Ting Hu

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Banzhaf, W., Hu, T., Ochoa, G. (2024). How the Combinatorics of Neutral Spaces Leads Genetic Programming to Discover Simple Solutions. In: Winkler, S., Trujillo, L., Ofria, C., Hu, T. (eds) Genetic Programming Theory and Practice XX. Genetic and Evolutionary Computation. Springer, Singapore. https://doi.org/10.1007/978-981-99-8413-8_4

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  • DOI: https://doi.org/10.1007/978-981-99-8413-8_4

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  • Print ISBN: 978-981-99-8412-1

  • Online ISBN: 978-981-99-8413-8

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