The choice of the offspring population size in the (1,λ1,λ) evolutionary algorithm

We extend the theory of non-elitist evolutionary algorithms (EAs) by considering the offspring population size in the (1,λ1,λ) EA. We establish a sharp threshold at λ=logee−1n≈5log10n between exponential and polynomial running times on OneMax. For any smaller value, the (1,λ1,λ) EA needs exponential time on every function that has only one global optimum. We also consider arbitrary unimodal functions and show that the threshold can shift towards larger offspring population sizes. In particular, for the function LeadingOnes there is a sharp threshold at λ=2logee−1n≈10log10n. Finally, we investigate the relationship between the offspring population size and arbitrary mutation rates on OneMax. We get sharp thresholds for λ that decrease with the mutation rate. This illustrates the balance between selection and mutation.