Recent work has provided functions that can be used to prove a principled distinction between the capabilities of mutation-based and crossover-based algorithms. However, prior functions are isolated problem instances that do not provide much intuition about the space of possible functions that is relevant to this distinction or the characteristics of the problem class that affect the relative success of these operators. Modularity is a ubiquitous and intuitive concept in design, engineering and optimisation, and can be used to produce functions that discriminate the ability of crossover from mutation. In this paper, we present a new approach to representing modular problems, which parameterizes the amount of modular structure that is present in the epistatic dependencies of the problem. This adjustable level of modularity can be used to give rise to tuneable discrimination of the ability of genetic algorithms with crossover versus mutation-only algorithms.
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