Evolvability is a measure of the ability of an Evolutionary Algorithm (EA) to improve the fitness of an individual when applying a genetic operator. Other than the specific problem, many aspects of the EA may impact on the evolvability most notably the genetic operators and, if present, the genotype-phenotype mapping function. Grammatical Evolution (GE) is an EA in which the mapping function plays a crucial role since it allows to map any binary genotype into a program expressed in any user-provided language, defined by a context-free grammar. While GE mapping favored a successful application of GE to many different problems, it has also been criticized for scarcely adhering to the variational inheritance principle, which itself may hamper GE evolvability. In this paper, we experimentally study GE evolvability in different conditions, that is, problems, mapping functions, genotype sizes, and genetic operators. Results suggest that there is not a single factor determining GE evolvability: in particular, the mapping function alone does not deliver better evolvability regardless of the problem. Instead, GE redundancy, which itself is the result of the combined effect of several factors, has a strong impact on the evolvability.
