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Complexity Measures for Multi-objective Symbolic Regression

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Computer Aided Systems Theory – EUROCAST 2015 (EUROCAST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

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Abstract

Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity.

In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi- objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.

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Acknowledgments

The work described in this paper was done within the COMET Project Heuristic Optimization in Production and Logistics (HOPL), #843532 funded by the Austrian Research Promotion Agency (FFG).

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Authors and Affiliations

  1. Heuristic and Evolutionary Algorithms Laboratory, School of Informatics, Communications and Media, University of Applied Sciences Upper Austria, Softwarepark 11, 4232, Hagenberg, Austria

    Michael Kommenda, Andreas Beham, Michael Affenzeller & Gabriel Kronberger

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

    Michael Kommenda, Andreas Beham & Michael Affenzeller

Authors
  1. Michael Kommenda
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  2. Andreas Beham
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  3. Michael Affenzeller
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  4. Gabriel Kronberger
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Corresponding author

Correspondence to Michael Kommenda .

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Editors and Affiliations

  1. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

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Kommenda, M., Beham, A., Affenzeller, M., Kronberger, G. (2015). Complexity Measures for Multi-objective Symbolic Regression. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_51

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  • DOI: https://doi.org/10.1007/978-3-319-27340-2_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

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