一元边际分布算法对欺骗和上位性的处理
The Univariate Marginal Distribution Algorithm Copes Well With Deception and Epistasis
摘要：
在他们最近的工作中，Lehre和Nguyen（FOGA 2019）表明，单变量边际分布算法（UMDA）需要父种群大小的时间指数来优化DeceptiveLeadingBlocks（DLB）问题。他们从这一结果得出结论，单变量EDA有困难的欺骗和上位性。在这项工作中，我们表明，这种负面的发现是由一个不幸的选择的参数的UMDA。当选择足够大的群体大小以防止遗传漂变时，UMDA以最多$λ(\frac{n}{2} + 2 e \ln n)$适应度评估以高概率优化DLB问题。由于$n \log n$阶的后代群体大小$λ$可以防止遗传漂移，因此UMDA可以用$O(n^2 \log n)$适应度评估来解决DLB问题。相比之下，对于经典的进化算法没有更好的运行时间保证比$O(n^3)$是已知的（我们证明是紧的${(1+1)}$ EA），所以我们的结果，而不是表明，UMDA可以很好地应付欺骗和epistatis。从更广泛的角度来看，我们的研究结果表明，UMDA可以更好地应付局部最优比进化算法，这样的结果是以前只知道紧凑的遗传算法。结合Lehre和Nguyen的下界，我们的结果首次严格证明了在具有遗传漂移的制度中运行EDA会导致严重的性能损失。
英文摘要：
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 $λ(\frac{n}{2} + 2 e \ln n)$ fitness evaluations. Since an offspring population size $λ$ 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.
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