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General Schema Theory for Genetic Programming with Subtree-Swapping Crossover

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Genetic Programming (EuroGP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2038))

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Abstract

In this paper a new, general and exact schema theory for genetic programming is presented. The theory includes a microscopic schema theorem applicable to crossover operators which replace a subtree in one parent with a subtree from the other parent to produce the offspring. A more macroscopic schema theoremis also provided which is valid for crossover operators in which the probability of selecting any two crossover points in the parents depends only on their size and shape. The theory is based on the notions of Cartesian node reference systems and variable-arity hyperschemata both introduced here for the first time. In the paper we provide examples which show how the theory can be specialised to specific crossover operators and how it can be used to derive an exact definition of effective fitness and a size-evolution equation for GP.

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Author information

Authors and Affiliations

  1. School of Computer Science, The University of Birmingham, Birmingham, B15 2TT, UK

    Riccardo Poli

Authors
  1. Riccardo Poli
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Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham

    Julian Miller

  2. Computer Science Institute, University of Lausanne, Lausanne

    Marco Tomassini

  3. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy

    Pier Luca Lanzi

  4. Computer Science and Information Systems, University of Limerick, Limerick

    Conor Ryan

  5. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, Italy

    Andrea G. B. Tettamanzi

  6. Department of Computer Science, University College London, London

    William B. Langdon

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© 2001 Springer-Verlag Berlin Heidelberg

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Poli, R. (2001). General Schema Theory for Genetic Programming with Subtree-Swapping Crossover. In: Miller, J., Tomassini, M., Lanzi, P.L., Ryan, C., Tettamanzi, A.G.B., Langdon, W.B. (eds) Genetic Programming. EuroGP 2001. Lecture Notes in Computer Science, vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45355-5_12

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  • DOI: https://doi.org/10.1007/3-540-45355-5_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41899-3

  • Online ISBN: 978-3-540-45355-0

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