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Small Solutions for Real-World Symbolic Regression Using Denoising Autoencoder Genetic Programming

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Genetic Programming (EuroGP 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13986))

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Abstract

Denoising Autoencoder Genetic Programming (DAE-GP) is a model-based evolutionary algorithm that uses denoising autoencoder long short-term memory networks as probabilistic model to replace the standard recombination and mutation operators of genetic programming (GP). In this paper, we use the DAE-GP to solve a set of nine standard real-world symbolic regression tasks. We compare the prediction quality of the DAE-GP to standard GP, geometric semantic GP (GSGP), and the gene-pool optimal mixing evolutionary algorithm for GP (GOMEA-GP), and find that the DAE-GP shows similar prediction quality using a much lower number of fitness evaluations than GSGP or GOMEA-GP. In addition, the DAE-GP consistently finds small solutions. The best candidate solutions of the DAE-GP are 69% smaller (median number of nodes) than the best candidate solutions found by standard GP. An analysis of the bias of the selection and variation step for both the DAE-GP and standard GP gives insight into why differences in solution size exist: the strong increase in solution size for standard GP is a result of both selection and variation bias. The results highlight that learning and sampling from a probabilistic model is a promising alternative to classic GP variation operators where the DAE-GP is able to generate small solutions for real-world symbolic regression tasks.

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Notes

  1. 1.

    For a detailed description on DAE-LSTM, refer to Wittenberg [31].

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Acknowledgements

We thank our group in Mainz for previous work and insightful discussions on this topic. Parts of this research were conducted using the supercomputer Mogon offered by Johannes Gutenberg University Mainz (hpc.uni-mainz.de), which is a member of the AHRP (Alliance for High Performance Computing in Rhineland Palatinate, www.ahrp.info) and the Gauss Alliance e.V. The authors gratefully acknowledge the computing time granted on the supercomputer Mogon at Johannes Gutenberg University Mainz (hpc.uni-mainz.de).

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Authors and Affiliations

  1. Johannes Gutenberg University, Mainz, Germany

    David Wittenberg & Franz Rothlauf

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  1. David Wittenberg
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  2. Franz Rothlauf
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Correspondence to David Wittenberg .

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Editors and Affiliations

  1. Universidade Federal de Minas Gerais, Belo Horizonte, Minas Gerais, Brazil

    Gisele Pappa

  2. Università degli studi di Torino, Turin, Italy

    Mario Giacobini

  3. Brno University of Technology, Brno, Czech Republic

    Zdenek Vasicek

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Wittenberg, D., Rothlauf, F. (2023). Small Solutions for Real-World Symbolic Regression Using Denoising Autoencoder Genetic Programming. In: Pappa, G., Giacobini, M., Vasicek, Z. (eds) Genetic Programming. EuroGP 2023. Lecture Notes in Computer Science, vol 13986. Springer, Cham. https://doi.org/10.1007/978-3-031-29573-7_7

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  • DOI: https://doi.org/10.1007/978-3-031-29573-7_7

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