Search, Neutral Evolution, and Mapping in Evolutionary Computing: A Case Study of Grammatical Evolution

We present a new perspective of search in evolutionary computing (EC) by using a novel model for the analysis and visualization of genotype to phenotype maps. The model groups genes into quotient sets and shows their adjacencies. A unique quality of the quotient model is that it details geometric qualities of maps that are not otherwise easy to observe. The model shows how random mutations on genes make non-random phenotype preferences, based on the structure of a map. The interaction between such mutation-based preferences with fitness preferences is important for explaining population movements on neutral landscapes. We show the widespread applicability of our approach by applying it to different representations, encodings, and problems including grammatical evolution (GE), Cartesian genetic programming, parity and majority coding, OneMax, needle-in-haystack, deceptive trap and hierarchical if-and-only-if. We also use the approach to address conflicting results in the neutral evolution literature and to analyze concepts relevant to neutral evolution including robustness, evolvability, tunneling, and the relation between genetic form and function. We use the model to develop theoretical results on how mapping and neutral evolution affect search in GE. We study the two phases of mapping in GE, these being transcription (i.e., unique identification of genes with integers) and translation (i.e., many-to-one mapping of genotypes to phenotypes). It is shown that translation and transcription schemes belong to equivalence classes, and therefore the properties we derive for specific schemes are applicable to classes of schemes. We present a new perspective on population diversity. We specify conditions under which increasing degeneracy (by increasing codon size) or rearranging the rules of a grammar do not affect performance. It is shown that there is a barrier to nontrivial neutral evolution with the use of the natural transcription with modulo translation combination; a necessary but not sufficient condition for such evolution is that at least three bits should change on mutation within a single codon. This barrier can be avoided by using gray transcription. We empirically validate some findings.