OneMax is not the Easiest Function for Fitness Improvements.

Abstract

We study the (1:s+1) success rule for controlling the population size of the (1,λ)- EA. It was shown by Hevia Fajardo and Sudholt that this parameter control mechanism can run into problems for large s if the fitness landscape is too easy. They conjectured that this problem is worst for the ONEMAX benchmark, since in some well-established sense ONEMAX is known to be the easiest fitness landscape. In this paper we disprove this conjecture. We show that there exist s and ɛ such that the self-adjusting (1,λ)-EA with the (1:s+1)-rule optimizes ONEMAX efficiently when started with ɛn zero-bits, but does not find the optimum in polynomial time on DYNAMIC BINVAL. Hence, we show that there are landscapes where the problem of the (1:s+1)-rule for controlling the population size of the (1,λ)-EA is more severe than for ONEMAX. The key insight is that, while ONEMAX is the easiest function for decreasing the distance to the optimum, it is not the easiest fitness landscape with respect to finding fitness-improving steps.