Theoretical and empirical study of the (1 + (λ, λ)) EA on the leadingones problem

Abstract

In this work we provide a theoretical and empirical study of the (1 + (λ,λ)) EA on the LeadingOnes problem. We prove an upper bound of O(n2) fitness evaluations on the expected runtime for all population sizes λ < n. This asymptotic bound does not depend on the parameter λ. We show via experiments that the value of λ has a small influence on the runtime (less than a factor of two). The value of λ that optimizes the runtime is small relative to n. We propose an extension of the existing (1 + (λ, λ)) EA by using different population sizes in the mutation and in the crossover phase of the algorithm and show via experiments that this modification can outperform the original algorithm by a small constant factor.