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Recent research [9,2] has enabled the accurate prediction of the limiting distribution of tree sizes for Genetic Programming with standard sub-tree swapping crossover when GP is applied to a flat fitness landscape. In that work, however, tree sizes are measured in terms of number of internal nodes. While the relationship between internal nodes and length is one-to-one for the case of a-ary trees,...
Recent theoretical work has characterised the search bias of GP sub-tree swapping crossover in terms of program length distributions, providing an exact fixed point for trees with internal nodes of identical arity. However, only an approximate model (based on the notion of average arity) for the mixed-arity case has been proposed. This leaves a particularly important gap in our knowledge because multi-arity...
Research has shown that beyond a certain minimum program length the distributions of program functionality and fitness converge to a limit. Before that limit, however, there may be program-length classes with a higher or lower average fitness than that achieved beyond the limit. Ideally, therefore, GP search should be limited to program lengths that are within the limit and that can achieve optimum...
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