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RESEARCH PRODUCT

On the Bias of Syntactic Geometric Recombination in Genetic Programming and Grammatical Evolution

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For fixed-length binary representations as used in genetic algorithms, standard recombination operators (e.g.,~one-point crossover) are unbiased. Thus, the application of recombination only reshuffles the alleles and does not change the statistical properties in the population. Using a geometric view on recombination operators, most search operators for fixed-length strings are geometric, which means that the distances between offspring and their parents are less than, or equal to, the distance between their parents. In genetic programming (GP) and grammatical evolution (GE), the situation is different since the recombination operators are applied to variable-length structures. Thus, most recombination operators for GE and GP are not geometric.This paper focuses on the bias of recombination in GE and GP and studies whether the application of recombination alone produces specific types of solutions with a higher probability. We consider two different types of recombination operators: standard recombination and syntactic geometric recombination. In our experiments, we performed random walks through the binary tree search space and found that syntactic geometric recombination operators are biased and strongly reduce population diversity. In a performance comparison, we found that syntactic geometric recombination leads to large fitness improvements in the first generations, but that fitness converges after several generations and no further search is possible.