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Hash-Based Tree Similarity and Simplification in Genetic Programming for Symbolic Regression

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Abstract

We introduce in this paper a runtime-efficient tree hashing algorithm for the identification of isomorphic subtrees, with two important applications in genetic programming for symbolic regression: fast, online calculation of population diversity and algebraic simplification of symbolic expression trees. Based on this hashing approach, we propose a simple diversity-preservation mechanism with promising results on a collection of symbolic regression benchmark problems.

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Notes

  1. 1.

    Inexact due to the possibility of hash collisions causing the algorithm to return the wrong answer. With a reasonable hash function, collision probability is negligible.

  2. 2.

    The Sørensen-Dice coefficient (Eq. 1) returns a value in the interval [0, 1].

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Acknowledgement

The authors gratefully acknowledge support by the Christian Doppler Research Association and the Federal Ministry of Digital and Economic Affairs within the Josef Ressel Centre for Symbolic Regression.

Author information

Authors and Affiliations

  1. Josef Ressel Centre for Symbolic Regression, University of Applied Sciences Upper Austria, Softwarepark 11, 4232, Hagenberg, Austria

    Bogdan Burlacu, Lukas Kammerer & Gabriel Kronberger

  2. Heuristic and Evolutionary Algorithms Laboratory, University of Applied Sciences Upper Austria, Softwarepark 11, 4232, Hagenberg, Austria

    Bogdan Burlacu, Lukas Kammerer, Michael Affenzeller & Gabriel Kronberger

  3. Institute for Formal Models and Verification, Johannes Kepler University, Altenbergerstr. 69, 4040, Linz, Austria

    Michael Affenzeller

Authors
  1. Bogdan Burlacu
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  2. Lukas Kammerer
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  3. Michael Affenzeller
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  4. Gabriel Kronberger
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Corresponding author

Correspondence to Bogdan Burlacu .

Editor information

Editors and Affiliations

  1. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Burlacu, B., Kammerer, L., Affenzeller, M., Kronberger, G. (2020). Hash-Based Tree Similarity and Simplification in Genetic Programming for Symbolic Regression. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2019. EUROCAST 2019. Lecture Notes in Computer Science(), vol 12013. Springer, Cham. https://doi.org/10.1007/978-3-030-45093-9_44

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  • DOI: https://doi.org/10.1007/978-3-030-45093-9_44

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-45092-2

  • Online ISBN: 978-3-030-45093-9

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