Defining locality in genetic programming to predict performance

A key indicator of problem difficulty in evolutionary computation problems is the landscape´s locality, that is whether the genotype-phenotype mapping preserves neighbourhood. In genetic programming the genotype and phenotype are not distinct, but the locality of the genotype-fitness mapping is of interest. In this paper we extend the original standard quantitative definition of locality to cover the genotype-fitness case, considering three possible definitions. By relating the values given by these definitions with the results of evolutionary runs, we investigate which definition is the most useful as a predictor of performance.