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Genetic Programming Theory and Practice XIV pp 149–164Cite as

Discovering Relational Structure in Program Synthesis Problems with Analogical Reasoning

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

Abstract

Much recent progress in Genetic Programming (GP) can be ascribed to work in semantic GP, which facilitates program induction by considering program behavior on individual fitness cases. It is therefore interesting to consider whether alternative decompositions of fitness cases might also provide useful information. The one we present here is motivated by work in analogical reasoning. So-called proportional analogies (‘gills are to fish as lungs are to mammals’) have a hierarchical relational structure that can be captured using the formalism of Structural Information Theory. We show how proportional analogy problems can be solved with GP and, conversely, how analogical reasoning can be engaged in GP to provide for problem decomposition. The idea is to treat pairs of fitness cases as if they formed a proportional analogy problem, identify relational consistency between them, and use it to inform the search process.

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Notes

  1. 1.

    https://github.com/kkrawiec/fuel.

  2. 2.

    Strictly, Iter here is slightly more complex than that previously mentioned, in that it expresses an inductive construction known as a catamorphism [26].

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Acknowledgements

Thanks are due to Dave Bender and the CRCC in Bloomington for providing us with the original list of letter-string analogy examples. K. Krawiec acknowledges support from grant 2014/15/B/ST6/05205 funded by the National Science Centre, Poland. Both authors thank the reviewers for valuable and insightful suggestions and comments.

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Authors and Affiliations

  1. Department of Computer Science, University of York, York, UK

    Jerry Swan

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

    Krzysztof Krawiec

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  1. Center for the Study of Complex Sys, University of Michigan, Ann Arbor, MI, USA

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    Bill Worzel

  3. Colorado State University, Fort Collins, CO, USA

    Brian Goldman

  4. Ann Arbor, MI, USA

    Bill Tozier

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Swan, J., Krawiec, K. (2018). Discovering Relational Structure in Program Synthesis Problems with Analogical Reasoning. In: Riolo, R., Worzel, B., Goldman, B., Tozier, B. (eds) Genetic Programming Theory and Practice XIV. Genetic and Evolutionary Computation. Springer, Cham. https://doi.org/10.1007/978-3-319-97088-2_10

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