On the limiting distribution of program sizes in tree-based genetic programming

Authors:
Riccardo Poli;William B. Langdon;Stephen Dignum
Affiliations:
Department of Computer Science, University of Essex, UK;Department of Computer Science, University of Essex, UK;Department of Computer Science, University of Essex, UK
Venue:
EuroGP'07 Proceedings of the 10th European conference on Genetic programming
Year:
2007

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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 - apa) (an+1 n) (1-pa)(a-1)n+1 pan where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported for the case a = 1.