The DU map: a visualization to gain insights into genotype-phenotype mapping and diversity

The relation between diversity and genotype to phenotype mapping has been the focus of several studies. In those Evolutionary Algorithms (EAs) where the genotype is a sequence of symbols, the contribution of each of those symbols in determining the phenotype may vary greatly possibly being null. In the latter case, the unused portions of the genotype may host a large amount of the population diversity. However, reasoning on coarse-grained measures makes it hard to validate such a claim and, more in general, to gain insights into the interactions between genotype-phenotype mapping and diversity. In this paper, we propose a novel visualization which summarizes in a single, compact heat map (the DU map), three kinds of information: (a) how diverse are the genotypes in the population at the level of single symbols; (b) if and to what degree each individual symbol in the genotype contributes to the phenotype; (c) how the two previous measures vary during the evolution. We experimentally verify the usefulness of the DU map w.r.t. its primary goal and, more broadly, when used to analyze different EA design options. We apply it to Grammatical Evolution (GE) as it constitutes an ideal testbed for the DU map, due to the availability of different mapping functions.