A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations

In this paper we use the schema theory presented in [Poli and McPhee, 2000] to better understand the changes in size distribution when using GP with standard crossover and linear structures. Applications of the theory to problems both with and without fitness suggest that standard crossover induces specific biases in the distributions of sizes, with a strong tendency to over sample small structures, and indicate the existence of strong redistribution effects that may be a major force in the early stages of a GP run. We also present two important theoretical results: An exact theory of bloat, and a general theory of how average size changes on flat landscapes with glitches. The latter implies the surprising result that a single program glitch in an otherwise flat fitness landscape is sufficient to drive the average program size of an infinite population, which may have important implications for the control of code growth.