Optimal Parameter Settings for the (1 + λ, λ) Genetic Algorithm

The (1+(λ,λ)) genetic algorithm is one of the few algorithms for which a super-constant speed-up through the use of crossover could be proven. So far, this algorithm has been used with parameters based also on intuitive considerations. In this work, we rigorously regard the whole parameter space and show that the asymptotic time complexity on the OneMax test function class proven by Doerr and Doerr (GECCO 2015) for the intuitive choice is best possible among all settings for population size, mutation probability, and crossover bias. Our proofs also give some advice on how to choose the parameters for other optimization problems.