Effects of module encapsulation in repetitively modular genotypes on the search space

We introduce the concept of modularity-preserving representations. If a representation is modularity-preserving, the existence of modularity in the problem space is translated into a corresponding modularity in the search space. This kind of representation allows us to analyze the impact of modularity at the genomic level. We investigate the question of what constitutes a module at the genomic level of evolutionary search and provide a static analysis of how to identify good and bad modules based on their ability to reduce the search space, thus, biasing the search space towards a solution. We also prove, under a set of assumptions, that the systematic encapsulation of lower order modules into higher order modules does not change the size or bias of a search space and that this process produces a hierarchy of equivalent search spaces.