Maximizing Drift is Not Optimal for Solving OneMax - Archive ouverte HAL Access content directly
Journal Articles Evolutionary Computation Year : 2021

Maximizing Drift is Not Optimal for Solving OneMax

Carola Doerr

Abstract

It seems very intuitive that for the maximization of the OneMax problem Om(x) := n i=1 x i the best that an elitist unary unbiased search algorithm can do is to store a best so far solution, and to modify it with the operator that yields the best possible expected progress in function value. This assumption has been implicitly used in several empirical works. In [Doerr, Doerr, Yang: Optimal parameter choices via precise black-box analysis, TCS, 2020] it was formally proven that this approach is indeed almost optimal. In this work we prove that drift maximization is not optimal. More precisely, we show that for most fitness levels between n/2 and 2n/3 the optimal mutation strengths are larger than the drift-maximizing ones. This implies that the optimal RLS is more risk-affine than the variant maximizing the step-wise expected progress. We show similar results for the mutation rates of the classic (1+1) Evolutionary Algorithm (EA) and its resampling variant, the (1+1) EA >0. As a result of independent interest we show that the optimal mutation strengths, unlike the drift-maximizing ones, can be even.
Fichier principal
Vignette du fichier
Buskulic.Doerr ECJ 2021 1904.07818.pdf (683.49 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03233719 , version 1 (25-05-2021)

Identifiers

Cite

Nathan Buskulic, Carola Doerr. Maximizing Drift is Not Optimal for Solving OneMax. Evolutionary Computation, 2021, pp.1-20. ⟨10.1162/evco_a_00290⟩. ⟨hal-03233719⟩
27 View
97 Download

Altmetric

Share

Gmail Facebook X LinkedIn More