Why don't the modules dominate - Investigating the Structure of a Well-Known Modularity-Inducing Problem Domain

Abstract: Wagner's modularity inducing problem domain is a key contribution to the study of the evolution of modularity, including both evolutionary theory and evolutionary computation. We study its behavior under classical genetic algorithms. Unlike what we seem to observe in nature, the emergence of modularity is highly conditional and dependent, for example, on the eagerness of search. In nature, modular solutions generally dominate populations, whereas in this domain, modularity, when it emerges, is a relatively rare variant. Emergence of modularity depends heavily on random fluctuations in the fitness function, with a randomly varied but unchanging fitness function, modularity evolved far more rarely. Interestingly, high-fitness non-modular solutions could frequently be converted into even-higher-fitness modular solutions by manually removing all inter-module edges. Despite careful exploration, we do not yet have a full explanation of why the genetic algorithm was unable to find these better solutions.