The Univariate Marginal Distribution Algorithm Copes Well with Deception and Epistasis

In their recent work, Lehre and Nguyen (2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with decepti...

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Bibliographic Details
Published in:Evolutionary computation Vol. 29; no. 4; p. 543
Main Authors: Doerr, Benjamin, Krejca, Martin S
Format: Journal Article
Language:English
Published: United States 01.12.2021
Subjects:
Algorithms
Biological Evolution
Epistasis, Genetic
Models, Genetic
Population Density
Estimation-of-distribution algorithm
runtime analysis
univariate marginal distribution algorithm
epistasis
theory
ISSN:1530-9304, 1530-9304
Online Access:Get more information
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Summary:In their recent work, Lehre and Nguyen (2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by the choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most λ(n2+2elnn) fitness evaluations. Since an offspring population size λ of order nlogn can prevent genetic drift, the UMDA can solve the DLB problem with O(n2logn) fitness evaluations. In contrast, for classic evolutionary algorithms no better runtime guarantee than O(n3) is known (which we prove to be tight for the (1+1) EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than many classic evolutionary algorithms; such a result was previously known only for the compact genetic algorithm. Together with the lower bound of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.
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ISSN:1530-9304
1530-9304
DOI:10.1162/evco_a_00293