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Sequential Symbolic Regression with Genetic Programming

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Book cover Genetic Programming Theory and Practice XII

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

Abstract

This chapter describes the Sequential Symbolic Regression (SSR) method, a new strategy for function approximation in symbolic regression. The SSR method is inspired by the sequential covering strategy from machine learning, but instead of sequentially reducing the size of the problem being solved, it sequentially transforms the original problem into potentially simpler problems. This transformation is performed according to the semantic distances between the desired and obtained outputs and a geometric semantic operator. The rationale behind SSR is that, after generating a suboptimal function f via symbolic regression, the output errors can be approximated by another function, in a subsequent iteration. The method was tested in eight polynomial functions, and compared with canonical genetic programming (GP) and geometric semantic genetic programming (SGP). Results showed that SSR significantly outperforms SGP and presents no statistical difference from GP. More importantly, they show the potential of the proposed approach: an effective way of applying geometric semantic operators to combine different (partial) solutions, and at the same time, avoiding the exponential growth problem arising from the use of semantic operators.

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Notes

  1. 1.

    The selection of building blocks based on fitness proposed by Rosca and Ballard (1994) is an exception to the syntax-oriented selection, although there is no guarantee that different modules are solving different parts of the problem.

  2. 2.

    It is unlikely that a solution will reach (near) zero error only for a subset of the points (training cases), unless it is the optimal solution, which in this case it will reach a (near) zero error for all points.

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Authors and Affiliations

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

    Luiz Otávio V.B. Oliveira, Gisele L. Pappa & Julio Albinati

  2. School of Computing, University of Kent, Chatham Maritime, UK

    Fernando E.B. Otero

Authors
  1. Luiz Otávio V.B. Oliveira
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  2. Fernando E.B. Otero
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  3. Gisele L. Pappa
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  4. Julio Albinati
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Corresponding author

Correspondence to Luiz Otávio V.B. Oliveira .

Editor information

Editors and Affiliations

  1. Center for the Study of Complex Systems (CSCS), University of Michigan, Ann Arbor, Michigan, USA

    Rick Riolo

  2. Evolution Enterprises, Milan, Michigan, USA

    William P. Worzel

  3. Evolved Analytics, Midland, Michigan, USA

    Mark Kotanchek

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Oliveira, L., Otero, F., Pappa, G., Albinati, J. (2015). Sequential Symbolic Regression with Genetic Programming. In: Riolo, R., Worzel, W., Kotanchek, M. (eds) Genetic Programming Theory and Practice XII. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-16030-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-16030-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16029-0

  • Online ISBN: 978-3-319-16030-6

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