The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis
Conference: European Conference on Evolutionary Computation in Combinatorial Optimisation 2020
Speaker: Martin S. Krejca
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 DeceivingLeadingBlocks (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, so our result rather suggests that the UMDA can cope well with deception and epistatis. Together with the result 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.
This is joined work with Benjamin Doerr.