Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space. Part II: Analysis of the diversification role of crossover

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Abstract
In this part of the paper we concentrate on the unique diversification role of the crossover operator in genetic algorithms. The explorative behavior of a generic crossover operator is revealed through a detailed large-sample analysis. Recursive equations for the population distributions are derived for a uniform crossover operator in multi-dimensional continuous space, showing how the crossover operator probes new regions of the solution space while keeping the population within the feasible region. The results of this analysis can be extended to the setting of a discrete space in a straightforward manner, shedding much light on the understanding of the essential role of crossover in genetic algorithms. This paper is the second part of another paper [1] that concentrated on the role of selection and mutation in the large-population scenario.