The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis

TL;DR

This paper demonstrates that with proper parameter choices, the univariate marginal distribution algorithm (UMDA) effectively handles deceptive and epistatic problems, outperforming traditional evolutionary algorithms in certain scenarios.

Contribution

It shows that the negative results on UMDA's performance were due to parameter choices, and with appropriate parameters, UMDA can efficiently solve complex problems involving deception and epistasis.

Findings

UMDA optimizes the DLB problem with high probability using $O(n^2 \, \log n)$ evaluations.

Proper parameter selection prevents genetic drift, enabling UMDA to outperform classic evolutionary algorithms.

The results highlight the importance of parameter tuning in EDAs for complex optimization problems.

Abstract

In their recent work, Lehre and Nguyen (FOGA 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 an unfortunate 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 $\lambda(\frac{n}{2} + 2 e \ln n)$ fitness evaluations. Since an offspring population size $\lambda$ of order $n \log n$ can prevent genetic drift, the UMDA can solve the DLB problem with $O(n^2 \log n)$ fitness evaluations. In contrast, for classic evolutionary algorithms no better run time guarantee than $O(n^3)$ 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 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.