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Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication

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Genetic Programming Theory and Practice XVII

Part of the book series: Genetic and Evolutionary Computation ((GEVO))

Abstract

Symbolic regression is a powerful system identification technique in industrial scenarios where no prior knowledge on model structure is available. Such scenarios often require specific model properties such as interpretability, robustness, trustworthiness and plausibility, that are not easily achievable using standard approaches like genetic programming for symbolic regression. In this chapter we introduce a deterministic symbolic regression algorithm specifically designed to address these issues. The algorithm uses a context-free grammar to produce models that are parameterized by a non-linear least squares local optimization procedure. A finite enumeration of all possible models is guaranteed by structural restrictions as well as a caching mechanism for detecting semantically equivalent solutions. Enumeration order is established via heuristics designed to improve search efficiency. Empirical tests on a comprehensive benchmark suite show that our approach is competitive with genetic programming in many noiseless problems while maintaining desirable properties such as simple, reliable models and reproducibility.

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Notes

  1. 1.

    http://www.evolved-analytics.com/.

  2. 2.

    https://www.nutonian.com/products/eureqa/.

  3. 3.

    https://dev.heuristiclab.com.

  4. 4.

    https://dev.heuristiclab.com.

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Acknowledgements

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

Author information

Authors and Affiliations

  1. Heuristic and Evolutionary Algorithms Laboratory (HEAL), University of Applied Sciences Upper Austria, Hagenberg, Austria

    Lukas Kammerer, Gabriel Kronberger, Bogdan Burlacu, Stephan M. Winkler, Michael Kommenda & Michael Affenzeller

  2. Department of Computer Science, Johannes Kepler University, Linz, Austria

    Lukas Kammerer, Stephan M. Winkler & Michael Affenzeller

  3. Josef Ressel Center for Symbolic Regression, University of Applied Sciences Upper Austria, Hagenberg, Austria

    Lukas Kammerer, Gabriel Kronberger, Bogdan Burlacu & Michael Kommenda

Authors
  1. Lukas Kammerer
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  2. Gabriel Kronberger
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  3. Bogdan Burlacu
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  4. Stephan M. Winkler
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  5. Michael Kommenda
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  6. Michael Affenzeller
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Corresponding author

Correspondence to Lukas Kammerer .

Editor information

Editors and Affiliations

  1. Computer Science and Engineering, John R. Koza Chair, Michigan State University, East Lansing, MI, USA

    Wolfgang Banzhaf

  2. BEACON Center, Michigan State University, East Lansing, MI, USA

    Erik Goodman

  3. Department of Computer Science and Engineering, Michigan State University, Okemos, MI, USA

    Leigh Sheneman

  4. Depto Ingenieria en Electronic Electrica Tecnológico Nacional de México/ IT, Tijuana, Baja California, Mexico

    Leonardo Trujillo

  5. Evolution Enterprises, Ann Arbor, MI, USA

    Bill Worzel

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Kammerer, L., Kronberger, G., Burlacu, B., Winkler, S.M., Kommenda, M., Affenzeller, M. (2020). Symbolic Regression by Exhaustive Search: Reducing the Search Space Using Syntactical Constraints and Efficient Semantic Structure Deduplication. In: Banzhaf, W., Goodman, E., Sheneman, L., Trujillo, L., Worzel, B. (eds) Genetic Programming Theory and Practice XVII. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-030-39958-0_5

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  • DOI: https://doi.org/10.1007/978-3-030-39958-0_5

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