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Strategies for Improving the Distribution of Random Function Outputs in GSGP

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Genetic Programming (EuroGP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10196))

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Abstract

In the last years, different approaches have been proposed to introduce semantic information to genetic programming. In particular, the geometric semantic genetic programming (GSGP) and the interesting properties of its evolutionary operators have gotten the attention of the community. This paper is interested in the use of GSGP to solve symbolic regression problems, where semantics is defined by the output set generated by a given individual when applied to the training cases. In this scenario, both mutation and crossover operators defined with fitness function based on Manhattan distance use randomly built functions to generate offspring. However, the outputs of these random functions are not guaranteed to be uniformly distributed in the semantic space, as the functions are generated considering the syntactic space. We hypothesize that the non-uniformity of the semantics of these functions may bias the search, and propose three different standard normalization techniques to improve the distribution of the outputs of these random functions over the semantic space. The results are compared with a popular strategy that uses a logistic function as a wrapper to the outputs, and show that the strategies tested can improve the results of the previous method. The experimental analysis also indicates that a more uniform distribution of the semantics of these functions does not necessarily imply in better results in terms of test error.

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Notes

  1. 1.

    The hyperrectangle in a semantic space under the Euclidean metric is the equivalent to a segment in a semantic space under the Manhattan distance.

  2. 2.

    The use of AQ instead of division—or protected division—makes the approach proposed by Dick [7] redundant. For this reason, we do not present the method in our experimental analysis.

  3. 3.

    Five training partitions of the 5-fold cross-validation, 5 samples generated for Keijzer-5 and Vladislavleva-1 and a single set generated for Keijzer-6 and Keijzer-7.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work was partially supported by the following Brazilian Research Support Agencies: CNPq, FAPEMIG, and CAPES.

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Authors and Affiliations

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

    Luiz Otavio V. B. Oliveira, Felipe Casadei & Gisele L. Pappa

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  1. Luiz Otavio V. B. Oliveira
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  2. Felipe Casadei
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  3. Gisele L. Pappa
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Corresponding author

Correspondence to Luiz Otavio V. B. Oliveira .

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Editors and Affiliations

  1. University College Dublin , Dublin, Ireland

    James McDermott

  2. Universidade Nova de Lisboa , Lisbon, Portugal

    Mauro Castelli

  3. Brno University of Technology , Brno, Czech Republic

    Lukas Sekanina

  4. Vrije Universiteit Amsterdam , Amsterdam, The Netherlands

    Evert Haasdijk

  5. University of Cádiz , Cádiz, Spain

    Pablo García-Sánchez

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Oliveira, L.O.V.B., Casadei, F., Pappa, G.L. (2017). Strategies for Improving the Distribution of Random Function Outputs in GSGP. In: McDermott, J., Castelli, M., Sekanina, L., Haasdijk, E., García-Sánchez, P. (eds) Genetic Programming. EuroGP 2017. Lecture Notes in Computer Science(), vol 10196. Springer, Cham. https://doi.org/10.1007/978-3-319-55696-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-55696-3_11

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