On the non-uniform redundancy in grammatical evolution

Abstract

This paper investigates the redundancy of representation in grammatical evolution (GE) for binary trees. We analyze the entire GE solution space by creating all binary genotypes of predefined length and map them to phenotype trees, which are then characterized by their size, depth and shape. We find that the GE representation is strongly non-uniformly redundant. There are huge differences in the number of genotypes that encode one particular phenotype. Thus, it is difficult for GE to solve problems where the optimal tree solutions are underrepresented. In general, the GE mapping process is biased towards short tree structures, which implies high GE performance if the optimal solution requires small programs.