OneMax is not the Easiest Function for Fitness Improvements

TL;DR

This paper challenges the idea that OneMax is the easiest fitness landscape for evolutionary algorithms, showing that it is not the easiest for finding improving steps and highlighting limitations of population control mechanisms.

Contribution

It disproves the conjecture that OneMax is the easiest landscape for the success rule in population control, revealing more complex landscape behaviors.

Findings

OneMax is not the easiest landscape for finding improving steps.

The success rule can perform efficiently on OneMax but fail on other landscapes like Dynamic BinVal.

Landscape complexity affects the effectiveness of population control mechanisms.

Abstract

We study the $(1:s+1)$ success rule for controlling the population size of the $(1,\lambda)$-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 and show that OneMax is not the easiest fitness landscape with respect to finding improving steps. As a consequence, we show that there exists $s$ and $\varepsilon$ such that the self-adjusting $(1,\lambda)$-EA with $(1:s+1)$-rule optimizes OneMax efficiently when started with $\varepsilon n$ 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 $(1, \lambda)$-EA is more severe than for OneMax.