A Schema-Based Version of Geiringer's Theorem for Nonlinear Genetic Programming with Homologous Crossover

摘要

Geiringer's theorem is a statement which tells us something about the limiting frequency of occurrence of a certain individual when a classical genetic algorithm is executed in the absence of selection and mutation. Recently Poli, Stephens, Wright and Rowe extended the original theorem of Geiringer to include the case of variable length genetic algorithms and linear genetic programming. In the current paper a rather powerful version of Geiringer's theorem which has been established recently by Mitavskiy is used to derive a schema-based version of the theorem for nonlinear genetic programming with homologous crossover.