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A network perspective on genotype–phenotype mapping in genetic programming

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Abstract

Genotype–phenotype mapping plays an essential role in the design of an evolutionary algorithm. Variation occurs at the genotypic level but fitness is evaluated at the phenotypic level, therefore, this mapping determines if and how variations are effectively translated into quality improvements. In evolutionary algorithms, this mapping has often been observed as highly redundant, i.e., multiple genotypes can map to the same phenotype, as well as heterogeneous, i.e., some phenotypes are represented by a large number of genotypes while some phenotypes only have few. We numerically study the redundant genotype–phenotype mapping of a simple Boolean linear genetic programming system and quantify the mutational connections among phenotypes using tools of complex network analysis. The analysis yields several interesting statistics of the phenotype network. We show the evidence and provide explanations for the observation that some phenotypes are much more difficult to find as the _target of a search than others. Our study provides a quantitative analysis framework to better understand the genotype–phenotype map, and the results may be utilized to inspire algorithm design that allows the search of a difficult _target to be more effective.

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Acknowledgements

This research was supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada Discovery Grant RGPIN-2016-04699 to T.H., and the Koza Endowment fund provided to W.B. by Michigan State University and supported by its BEACON Center for the Study of Evolution in Action.

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Authors and Affiliations

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

    Ting Hu

  2. Department of Computer Science, Memorial University, St. John’s, NL, Canada

    Ting Hu

  3. Faculty of Business and Economics, Information Systems Department, University of Lausanne, Lausanne, Switzerland

    Marco Tomassini

  4. Department of Computer Science and Engineering, and BEACON Center, Michigan State University, East Lansing, MI, USA

    Wolfgang Banzhaf

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  1. Ting Hu
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Correspondence to Ting Hu.

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Hu, T., Tomassini, M. & Banzhaf, W. A network perspective on genotype–phenotype mapping in genetic programming. Genet Program Evolvable Mach 21, 375–397 (2020). https://doi.org/10.1007/s10710-020-09379-0

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