A structure preserving crossover in grammatical evolution

Grammatical evolution is an algorithm for evolving complete programs in an arbitrary language. By utilising a Backus Naur Form grammar the advantages of typing are achieved. A separation of genotype and phenotype allows the implementation of operators that manipulate (for instance by crossover and mutation) the genotype (in grammatical evolution - a sequence of bits) irrespective of the genotype to phenotype mapping (in grammatical evolution $an arbitrary grammar). This paper introduces a new type of crossover operator for grammatical evolution. The crossover operator uses information automatically extracted from the grammar to minimise any destructive impact from the crossover. The information, which is extracted at the same time as the genome is initially decoded, allows the swapping between entities of complete expansions of non-terminals in the grammar without disrupting useful blocks of code on either side of the two point crossover. In the domains tested, results confirm that the crossover is (i) more productive than hill-climbing; (ii) enables populations to continue to evolve over considerable numbers of generations without intron bloat; and (iii) allows populations (in the domains tested) to reach higher fitness levels, quicker.