Weighted Hierarchical Grammatical Evolution
Alberto Bartoli, Mauro Castelli,
IEEE Transactions on Cybernetics (TCyb)
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Grammatical Evolution (GE) is one of the most widespread techniques in evolutionary computation. Genotypes in GE are bit strings while phenotypes are strings of a language defined by a user-provided context-free grammar (CFG). In this work, we propose a novel procedure for mapping genotypes to phenotypes that we call Weighted Hierarchical GE (WHGE). WHGE imposes a form of hierarchy on the genotype and encodes grammar symbols with a varying number of bits based on the relative expressive power of those symbols. WHGE does not impose any constraint on the overall GE framework, in particular, WHGE may handle recursive grammars, uses the classical genetic operators, and does not need to define any bound in advance on the size of phenotypes.We assessed experimentally our proposal in depth on a set of challenging and carefully selected benchmarks, comparing the results to the standard GE framework as well as to two of the most significant enhancements proposed in the literature: Position-independent GE and Structured GE. Our results show that WHGE delivers very good results in terms of fitness as well as in terms of the properties of the genotype-phenotype mapping procedure.