Genotype representations in grammatical evolution

Grammatical evolution (GE) is a form of grammar-based genetic programming. A particular feature of GE is that it adopts a distinction between the genotype and phenotype similar to that which exists in nature by using a grammar to map between the genotype and phenotype. Two variants of genotype representation are found in the literature, namely, binary and integer forms. For the first time we anal- yse and compare these two representations to determine if one has a performance advantage over the other. As such this study seeks to extend our understanding of GE by examining the impact of different genotypic representations in order to determine whether certain representations, and associated diversity-generation op- erators, improve GE’s efficiency and effectiveness. Four mutation operators using two different representations, binary and gray code representation respectively, are investigated. The differing combinations of representation and mutation operator are tested on three benchmark problems. The results provide support for the use of an integer-based genotypic representation as the alternative representations do not exhibit better performance, and the integer reprensentation provides a statistically significant advantage on one of the three benchmarks. In addition, a novel wrapping operator for the binary and gray code representations is examined, and it is found that across the three problems examined there is no general trend to recommend the adoption of an alternative wrapping operator. The results also back up earlier findings which support the adoption of wrapping.