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Hybrid Single Node Genetic Programming for Symbolic Regression

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Transactions on Computational Collective Intelligence XXIV

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 9770))

Abstract

This paper presents a first step of our research on designing an effective and efficient GP-based method for symbolic regression. First, we propose three extensions of the standard Single Node GP, namely (1) a selection strategy for choosing nodes to be mutated based on depth and performance of the nodes, (2) operators for placing a compact version of the best-performing graph to the beginning and to the end of the population, respectively, and (3) a local search strategy with multiple mutations applied in each iteration. All the proposed modifications have been experimentally evaluated on five symbolic regression benchmarks and compared with standard GP and SNGP. The achieved results are promising showing the potential of the proposed modifications to improve the performance of the SNGP algorithm. We then propose two variants of hybrid SNGP utilizing a linear regression technique, LASSO, to improve its performance. The proposed algorithms have been compared to the state-of-the-art symbolic regression methods that also make use of the linear regression techniques on four real-world benchmarks. The results show the hybrid SNGP algorithms are at least competitive with or better than the compared methods.

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Notes

  1. 1.

    https://en.wikipedia.org/wiki/Symbolic_regression.

  2. 2.

    https://cs.gmu.edu/~eclab/projects/ecj/.

  3. 3.

    Checked using the t-test calculated with the significance level \(\alpha =0.05\).

  4. 4.

    The only exception is EFS: we changed the round variable to false (which was originally hard-coded to true) according to the issue on the algorithm’s GitHub repository, see https://github.com/exgp/efs/issues/1.

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Acknowledgment

This research was supported by the Grant Agency of the Czech Republic (GAČR) with the grant no. 15-22731S entitled “Symbolic Regression for Reinforcement Learning in Continuous Spaces”.

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Authors and Affiliations

  1. Czech Institute of Informatics, Robotics, and Cybernetics, CTU in Prague, Prague, Czech Republic

    Jiří Kubalík, Eduard Alibekov, Jan Žegklitz & Robert Babuška

  2. Department of Cybernetics, Faculty of Electrical Engineering, CTU in Prague, Prague, Czech Republic

    Eduard Alibekov & Jan Žegklitz

  3. Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands

    Robert Babuška

Authors
  1. Jiří Kubalík
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  2. Eduard Alibekov
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  3. Jan Žegklitz
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  4. Robert Babuška
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Corresponding author

Correspondence to Jiří Kubalík .

Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Manageme, Wrocław University of Technology, Wrocław, Poland

    Ngoc Thanh Nguyen

  2. Swinburne University of Technology, Hawthorn, Australia

    Ryszard Kowalczyk

  3. Escola Superior de Tecnologiy de Setébual, Setúbal, Portugal

    Joaquim Filipe

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Kubalík, J., Alibekov, E., Žegklitz, J., Babuška, R. (2016). Hybrid Single Node Genetic Programming for Symbolic Regression. In: Nguyen, N., Kowalczyk, R., Filipe, J. (eds) Transactions on Computational Collective Intelligence XXIV. Lecture Notes in Computer Science(), vol 9770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53525-7_4

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  • DOI: https://doi.org/10.1007/978-3-662-53525-7_4

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  • Print ISBN: 978-3-662-53524-0

  • Online ISBN: 978-3-662-53525-7

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