Mutation Rate Control in the $$(1+\lambda )$$ Evolutionary Algorithm with a Self-adjusting Lower Bound

Abstract

We consider the 2-rate (1 + λ) Evolutionary Algorithm, a heuristic that evaluates λ search points per each iteration and keeps in the memory only a best-so-far solution. The algorithm uses a dynamic probability distribution from which the radius at which the λ "offspring" are sampled. It has previously been observed that the performance of the 2-rate (1 + λ) Evolutionary Algorithm crucially depends on the threshold at which the mutation rate is capped to prevent it from converging to zero. This effect is an issue already when focusing on the simplestructured OneMax problem, the problem of minimizing the Hamming distance to an unknown bit string. Here, a small lower bound is preferable when λ is small, whereas a larger lower bound is better for large λ. We introduce a secondary parameter control scheme, which adjusts the lower bound during the run. We demonstrate, by extensive experimental means, that our algorithm performs decently on all OneMax problems, independently of the offspring population size. It therefore appropriately removes the dependency on the lower bound. We also evaluate our algorithm on several other benchmark problems, and show that it works fine provided the number of offspring, λ, is not too large.