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Benchmarking a \((\mu +\lambda )\) Genetic Algorithm with Configurable Crossover Probability

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Parallel Problem Solving from Nature – PPSN XVI (PPSN 2020)

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Abstract

We investigate a family of \((\mu +\lambda )\) Genetic Algorithms (GAs) which creates offspring either from mutation or by recombining two randomly chosen parents. By scaling the crossover probability, we can thus interpolate from a fully mutation-only algorithm towards a fully crossover-based GA. We analyze, by empirical means, how the performance depends on the interplay of population size and the crossover probability.

Our comparison on 25 pseudo-Boolean optimization problems reveals an advantage of crossover-based configurations on several easy optimization tasks, whereas the picture for more complex optimization problems is rather mixed. Moreover, we observe that the “fast” mutation scheme with its are power-law distributed mutation strengths outperforms standard bit mutation on complex optimization tasks when it is combined with crossover, but performs worse in the absence of crossover.

We then take a closer look at the surprisingly good performance of the crossover-based \((\mu +\lambda )\) GAs on the well-known LeadingOnes benchmark problem. We observe that the optimal crossover probability increases with increasing population size \(\mu \). At the same time, it decreases with increasing problem dimension, indicating that the advantages of the crossover are not visible in the asymptotic view classically applied in runtime analysis. We therefore argue that a mathematical investigation for fixed dimensions might help us observe effects which are not visible when focusing exclusively on asymptotic performance bounds.

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Acknowledgments

Our work was supported by the Chinese scholarship council (CSC No. 201706310143), by the Paris Ile-de-France Region, by ANR-11-LABX-0056-LMH (LabEx LMH), and by COST Action CA15140.

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Authors and Affiliations

  1. LIACS, Leiden University, Leiden, The Netherlands

    Furong Ye & Thomas Bäck

  2. Sorbonne Université, CNRS, LIP6, Paris, France

    Hao Wang & Carola Doerr

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  1. Furong Ye
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  2. Hao Wang
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  3. Carola Doerr
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  4. Thomas Bäck
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Corresponding author

Correspondence to Furong Ye .

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Editors and Affiliations

  1. Leiden University, Leiden, The Netherlands

    Thomas Bäck

  2. Leiden University, Leiden, The Netherlands

    Mike Preuss

  3. Leiden University, Leiden, The Netherlands

    André Deutz

  4. Sorbonne University, Paris, France

    Hao Wang

  5. Sorbonne University, Paris, France

    Carola Doerr

  6. Leiden University, Leiden, The Netherlands

    Michael Emmerich

  7. University of Münster, Münster, Germany

    Heike Trautmann

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Ye, F., Wang, H., Doerr, C., Bäck, T. (2020). Benchmarking a \((\mu +\lambda )\) Genetic Algorithm with Configurable Crossover Probability. In: Bäck, T., et al. Parallel Problem Solving from Nature – PPSN XVI. PPSN 2020. Lecture Notes in Computer Science(), vol 12270. Springer, Cham. https://doi.org/10.1007/978-3-030-58115-2_49

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  • DOI: https://doi.org/10.1007/978-3-030-58115-2_49

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