Watson, Richard A. “A simple two-module problem to exemplify building-block assembly under crossover.” In International Conference on Parallel Problem Solving from Nature , pp. 161-171. Springer, Berlin, Heidelberg, 2004.
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Theoretically and empirically it is clear that a genetic algorithm with crossover will outperform a genetic algorithm without crossover in some fitness landscapes, and vice versa in other landscapes. Despite an extensive literature on the subject, and recent proofs of a principled distinction in the abilities of crossover and non-crossover algorithms for a particular theoretical landscape, building general intuitions about when and why crossover performs well when it does is a different matter. In particular, the proposal that crossover might enable the assembly of good building-blocks has been difficult to verify despite many attempts at idealized building-block landscapes. Here we show the first example of a two-module problem that shows a principled advantage for crossover. This allows us to understand building-block assembly under crossover quite straightforwardly and build intuition about more general landscape classes favoring crossover or disfavoring it.