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European Conference on Genetic Programming

EuroGP 2016: Genetic Programming pp 246–260Cite as

Geometric Semantic Genetic Programming Is Overkill

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9594))

Abstract

Recently, a new notion of Geometric Semantic Genetic Programming emerged in the field of automatic program induction from examples. Given that the induction problem is stated by means of function learning and a fitness function is a metric, GSGP uses geometry of solution space to search for the optimal program. We demonstrate that a program constructed by GSGP is indeed a linear combination of random parts. We also show that this type of program can be constructed in a predetermined time by much simpler algorithm and with guarantee of solving the induction problem optimally. We experimentally compare the proposed algorithm to GSGP on a set of symbolic regression, Boolean function synthesis and classifier induction problems. The proposed algorithm is superior to GSGP in terms of training-set fitness, size of produced programs and computational cost, and generalizes on test-set similarly to GSGP.

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Notes

  1. 1.

    for two Booleans is equivalent to \(\vee \), for two classes outputs the one with lower id, for a class and outputs this class, otherwise . for two Booleans is equivalent to \(\wedge \), for two classes outputs the one with greater id, for 1 and a class outputs this class, otherwise . We omitted full tables of these functions for brevity.

  2. 2.

    The distinction between linear combination and interpolation is made to emphasize that linear combination is any weighted sum of programs, while interpolation is a weighted sum that goes through the certain points.

  3. 3.

    Points given by \(x_{k}=\frac{1}{2}(a+b)+\frac{1}{2}(b-a)\cos (\frac{2k-1}{2n}\pi ),k=1..n\), where [a, b] is the range of training set, and n is number of data points. Using Chebyshev nodes minimizes the likelihood of Runge’s phenomenon [29].

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Acknowledgements

This work is funded by National Science Centre Poland grant number DEC-2012/07/N/ST6/03066.

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Authors and Affiliations

  1. Institute of Computing Science, Poznan University of Technology, Poznań, Poland

    Tomasz P. Pawlak

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  1. Tomasz P. Pawlak
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Correspondence to Tomasz P. Pawlak .

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Editors and Affiliations

  1. Dalhousie University, Halifax, Nova Scotia, Canada

    Malcolm I. Heywood

  2. University College Dublin, Dublin, Ireland

    James McDermott

  3. Universidade Nova de Lisboa, Lisboa, Portugal

    Mauro Castelli

  4. CIUSC Dept Informatics Engg, University of Coimbra, Coimbra, Portugal

    Ernesto Costa

  5. Edinburgh Napier University, Edinburgh, United Kingdom

    Kevin Sim

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Pawlak, T.P. (2016). Geometric Semantic Genetic Programming Is Overkill. In: Heywood, M., McDermott, J., Castelli, M., Costa, E., Sim, K. (eds) Genetic Programming. EuroGP 2016. Lecture Notes in Computer Science(), vol 9594. Springer, Cham. https://doi.org/10.1007/978-3-319-30668-1_16

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  • DOI: https://doi.org/10.1007/978-3-319-30668-1_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30667-4

  • Online ISBN: 978-3-319-30668-1

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