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

TL;DR

This paper investigates Wagner's modularity-inducing problem domain, revealing that modularity emergence under genetic algorithms is rare, condition-dependent, and influenced by fitness function fluctuations, contrasting with natural observations.

Contribution

It provides an empirical analysis of modularity evolution in a well-known problem domain, highlighting the conditional nature of modularity emergence and its dependence on search parameters.

Findings

Modularity is rare and condition-dependent in the domain.

Random fitness fluctuations significantly affect modularity emergence.

High-fitness modular solutions can be manually derived from non-modular ones.

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.