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

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 12013)


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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  • DOI: 10.1007/978-3-030-45093-9_44
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Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.


  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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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.

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Correspondence to Bogdan Burlacu .

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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.

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