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Fitness Landscape Analysis of Dimensionally-Aware Genetic Programming Featuring Feynman Equations

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

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12270))

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Abstract

Genetic programming is an often-used technique for symbolic regression: finding symbolic expressions that match data from an unknown function. To make the symbolic regression more efficient, one can also use dimensionally-aware genetic programming that constrains the physical units of the equation. Nevertheless, there is no formal analysis of how much dimensionality awareness helps in the regression process. In this paper, we conduct a fitness landscape analysis of dimensionally-aware genetic programming search spaces on a subset of equations from Richard Feynman’s well-known lectures. We define an initialisation procedure and an accompanying set of neighbourhood operators for conducting the local search within the physical unit constraints. Our experiments show that the added information about the variable dimensionality can efficiently guide the search algorithm. Still, further analysis of the differences between the dimensionally-aware and standard genetic programming landscapes is needed to help in the design of efficient evolutionary operators to be used in a dimensionally-aware regression.

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Notes

  1. 1.

    We have experimented with a range of more open-ended bloat-control mechanism, e.g., lexicographic optimisation for fitness and size. However, we observed that even in our rather discrete setting, optimising I.8.14 or I.27.6 would result in trees of a size of over 256 nodes.

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Acknowledgements

We’d like to thank Prof. Pablo Moscato for introducing us to  [17]. We’d also like to acknowledge support by the Australian Research Council, project DP200102364.

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Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

    Marko Durasevic & Domagoj Jakobovic

  2. Federal University of Technology Paraná (UTFPR), Curitiba, Brazil

    Marcella Scoczynski Ribeiro Martins

  3. Delft University of Technology, Delft, The Netherlands

    Stjepan Picek

  4. Optimisation and Logistics Group, The University of Adelaide, Adelaide, Australia

    Markus Wagner

Authors
  1. Marko Durasevic
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  2. Domagoj Jakobovic
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  4. Stjepan Picek
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  5. Markus Wagner
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Corresponding author

Correspondence to Domagoj Jakobovic .

Editor information

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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Durasevic, M., Jakobovic, D., Scoczynski Ribeiro Martins, M., Picek, S., Wagner, M. (2020). Fitness Landscape Analysis of Dimensionally-Aware Genetic Programming Featuring Feynman Equations. 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_8

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  • DOI: https://doi.org/10.1007/978-3-030-58115-2_8

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  • Online ISBN: 978-3-030-58115-2

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