The Limiting Distribution of Program Sizes in tree-based genetic programming

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 (1 − pa) n (a−1)n+1 p n a where n is the number of internal nodes in a tree and pa is a constant. This result generalises the result previously reported in [7, 10, 8, 9] for the case a = 1