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On the Limiting Distribution of Program Sizes in Tree-Based Genetic Programming

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Genetic Programming (EuroGP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4445))

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Abstract

We provide strong theoretical and experimental evidence that standard sub-tree crossover with uniform selection of crossover points pushes a population of a-ary GP trees towards a distribution of tree sizes of the form:

$$ \Pr\{n\}= (1-ap_a) {a n+1 \choose n} \, (1-p_a)^{(a-1)n+1}\, p_a^{n} $$

where n is the number of internal nodes in a tree and p a is a constant. This result generalises the result previously reported for the case a = 1.

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Author information

Authors and Affiliations

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

    Riccardo Poli, William B. Langdon & Stephen Dignum

Authors
  1. Riccardo Poli
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  2. William B. Langdon
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  3. Stephen Dignum
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Editor information

Marc Ebner Michael O’Neill Anikó Ekárt Leonardo Vanneschi Anna Isabel Esparcia-Alcázar

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© 2007 Springer Berlin Heidelberg

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Poli, R., Langdon, W.B., Dignum, S. (2007). On the Limiting Distribution of Program Sizes in Tree-Based Genetic Programming. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds) Genetic Programming. EuroGP 2007. Lecture Notes in Computer Science, vol 4445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71605-1_18

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  • DOI: https://doi.org/10.1007/978-3-540-71605-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71602-0

  • Online ISBN: 978-3-540-71605-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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