The Univariate Marginal Distribution Algorithm (UMDA) – a popular estimation-of-distribution algorithm – is studied from a run time perspective. On the classical OneMax benchmark function on bit strings of length n, a lower bound of $\mathrm{\Omega }(\lambda +\mu \sqrt{n}+n\log n)$, where μ and λ are algorithm-specific parameters, on its expected run time is proved. This is the first direct lower bound on the run time of UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation-of-distribution algorithms in general.

从运行时角度研究了单变量边际分布算法（UMDA）（一种流行的分布估计算法）。在长度为n的位串的下限的经典OneMax基准函数上$\mathrm{\Omega }（\lambda +\mu \sqrt{ñ}+ñ\mathrm{日志}ñ）$，其中μ和λ是算法特定的参数，证明了其预期的运行时间。这是UMDA运行时的第一个直接下限。它比一般的黑盒复杂性理论所遵循的界限更强大，并且与许多进化算法的运行时间相匹配。通过对算法保持的位值频率的随机变化进行高级分析，包括精心设计的潜在函数，可以获得结果。通常，这些技术可能在推进运行时分析领域方面很有用，以用于分布估计算法。