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Semantic Geometric Initialization

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Book cover Genetic Programming (EuroGP 2016)

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

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Abstract

A common approach in Geometric Semantic Genetic Programming (GSGP) is to seed initial populations using conventional, semantic-unaware methods like Ramped Half-and-Half. We formally demonstrate that this may limit GSGP’s ability to find a program with the sought semantics. To overcome this issue, we determine the desired properties of geometric-aware semantic initialization and implement them in Semantic Geometric Initialization (Sgi) algorithm, which we instantiate for symbolic regression and Boolean function synthesis problems. Properties of Sgi and its impact on GSGP search are verified experimentally on nine symbolic regression and nine Boolean function synthesis benchmarks. When assessed experimentally, Sgi leads to superior performance of GSGP search: better best-of-run fitness and higher probability of finding the optimal program.

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Notes

  1. 1.

    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 [25].

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Acknowledgements

T. Pawlak acknowledges support from grant no. DEC-2012/07/N/ST6/03066, K. Krawiec from grant no 2014/15/B/ST6/05205, both funded by the National Science Centre, Poland.

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Authors and Affiliations

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

    Tomasz P. Pawlak & Krzysztof Krawiec

Authors
  1. Tomasz P. Pawlak
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  2. Krzysztof Krawiec
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Corresponding author

Correspondence to Tomasz P. Pawlak .

Editor information

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., Krawiec, K. (2016). Semantic Geometric Initialization. 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_17

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  • DOI: https://doi.org/10.1007/978-3-319-30668-1_17

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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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