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

We extend the theory of non-elitist evolutionary algorithms (EAs) by considering the offspring population size in the (1, lambda) EA. We establish a sharp threshold at lambda = log(e/e-1) n approximate to 5log(10) n between exponential and polynomial running times on ONEMAX. For any smaller value, the (1, lambda) 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 lambda = 2 log(e/e-1) n approximate to 10log(10) n. Finally, we investigate the relationship between the offspring population size and arbitrary mutation rates on ONEMAX. We get sharp thresholds for lambda that decrease with the mutation rate. This illustrates the balance between selection and mutation. (C) 2013 Elsevier B.V. All rights reserved.