Escaping local optima using crossover with emergent diversity

Population diversity is essential for avoiding premature convergence in Genetic Algorithms (GAs) and for the effective use of crossover. Yet the dynamics of how diversity emerges in populations are not well understood. We use rigorous run time analysis to gain insight into population dynamics and GA performance for the (μ+1) GA and the Jump_k test function. We show that the interplay of crossover followed by mutation may serve as a catalyst leading to a sudden burst of diversity. This leads to improvements of the expected optimisation time of order Ω (n/log n) compared to mutation-only algorithms like the (1+1) EA. Moreover, increasing the mutation rate by an arbitrarily small constant factor can facilitate the generation of diversity, leading to speedups of order Ω(n). Experiments complement our theoretical ndings and further highlight the benets of crossover on Jump_k.