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Publication Detail
On the Limiting Distribution of Program Sizes in Tree-based Genetic Programming
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  • Authors:
    Poli R, Langdon WB, Dignum S
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  • Notes:
    keywords: genetic algorithms, genetic programming notes: see \citepoli:2007:eurogp size: 12 pages
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: Prn = (1 - ap)C(an + 1,n) (1-p)**(a-1)n+1 p**n where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported in \citepoli:2001:EuroGP_exact, \citemcphee:2001:astamsbgplr, \citeRowe01, \citepoli03:ECJ_gener_schem_part_I \citepoli03:ECJ_gener_schem_part_II for the case a=1.
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