Empirical Analysis of GP Tree-Fragments

Researchers have attempted to explain the power of Genetic Programming (GP) search using various notions of schema. However empirical studies of schemas have been limited due to their vast numbers in typical populations. This paper addresses the problem of analyzing schemas represented by tree-fragments. It describes a new efficient way of representing the huge sets of fragments in a population of GP programs and presents an algorithm to find all fragments using this efficient representation. Using this algorithm, the paper presents an initial analysis of fragments in populations of up to 300 programs, each up to seven nodes deep. The analysis demonstrates a surprisingly large variation in the numbers of fragments through evolution and a non-monotonic rise in the most useful fragments. With his method, empirical investigation of the GP building block hypothesis and schema theory in realistic sized GP systems becomes possible.

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