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On the Influence of Grammars on Crossover in Grammatical Evolution

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Genetic Programming (EuroGP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12691))

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Abstract

Standard grammatical evolution (GE) uses a one-point crossover (“ripple crossover”) that exchanges codons between two genotypes. The two resulting genotypes are then mapped to their respective phenotypes using a Backus-Naur form grammar. This article studies how different types of grammars affect the resulting individuals of a ripple crossover. We distinguish different grammars based on the expected number of non-terminals chosen when mapping genotype codons to phenotypes, \(B_{avg}\). The grammars only differ in \(B_{avg}\) but can express the same phenotypes. We perform crossover operations on the genotypes and find that grammars with \(B_{avg} > 1\) lead to high numbers of either very small trees or invalid individuals. Due to the re-sampling of the invalid individuals, the algorithmic runtime is higher compared to grammars with a small \(B_{avg}\), despite being able to express the same phenotypes. In grammars with \(B_{avg} \le 1\), the bias towards small trees is reduced and instead, the frequency of valid large trees is increased. Our results give insights on favorable grammar designs and underline the central role of grammar design in GE.

Parts of this research were conducted using the supercomputer Mogon offered by Johannes Gutenberg University Mainz (hpc.uni-mainz.de). The authors gratefully acknowledge the computing time granted on Mogon.

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Notes

  1. 1.

    Unlike genetic programming [10], in GE no function set exists, but functions are defined by sequences of terminals and non-terminals.

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Authors and Affiliations

  1. Johannes Gutenberg University, Mainz, Germany

    Dirk Schweim

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  1. Dirk Schweim
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Correspondence to Dirk Schweim .

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Editors and Affiliations

  1. Queen’s University, Kingston, ON, Canada

    Ting Hu

  2. University of Coimbra, Coimbra, Portugal

    Nuno Lourenço

  3. University of Trieste, Trieste, Italy

    Eric Medvet

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Schweim, D. (2021). On the Influence of Grammars on Crossover in Grammatical Evolution. In: Hu, T., Lourenço, N., Medvet, E. (eds) Genetic Programming. EuroGP 2021. Lecture Notes in Computer Science(), vol 12691. Springer, Cham. https://doi.org/10.1007/978-3-030-72812-0_8

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  • DOI: https://doi.org/10.1007/978-3-030-72812-0_8

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