Offspring population size matters when comparing evolutionary algorithms with self-adjusting mutation rates

We analyze the performance of the 2-rate (1 + λ) Evolutionary Algorithm (EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a (1 + λ) EA variant using multiplicative update rules on the OneMax problem. We compare their efficiency for offspring population sizes ranging up to λ = 3, 200 and problem sizes up to n = 100,000. Our empirical results show that the ranking of the algorithms is very consistent across all tested dimensions, but strongly depends on the population size. While for small values of λ the 2-rate EA performs best, the multiplicative updates become superior for starting for some threshold value of λ between 50 and 100. Interestingly, for population sizes around 50, the (1 + λ) EA with static mutation rates performs on par with the best of the self-adjusting algorithms. We also consider how the lower bound pmin for the mutation rate influences the efficiency of the algorithms. We observe that for the 2-rate EA and the EA with multiplicative update rules the more generous bound pmin = 1/n2 gives better results than pmin = 1/n when λ is small. For both algorithms the situation reverses for large λ.

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