With elementary means, we prove a stronger run time guarantee for the univariate marginal distribution algorithm (UMDA) optimizing the LeadingOnes benchmark function in the desirable regime with low genetic drift. If the population size is at least quasilinear, then, with high probability, the UMDA samples the optimum in a number of iterations that is linear in the problem size divided by the logarithm of the UMDA's selection rate. This improves over the previous guarantee, obtained by Dang and Lehre (2015) via the deep level-based population method, both in terms of the run time and by demonstrating further run time gains from small selection rates. Under similar assumptions, we prove a lower bound that matches our upper bound up to constant factors.

通过基本手段，我们证明了单变量边际分布算法（UMDA）在较低遗传漂移的理想情况下优化LeadingOnes基准函数的运行时保证。如果总体大小至少是准线性的，则UMDA很有可能在多次迭代中对最优值进行采样，该迭代的问题大小除以UMDA选择率的对数是线性的。相对于Dang和Lehre（2015）通过基于深度级别的人口方法获得的先前保证，无论是在运行时间上还是在小选择率上证明了运行时间的增加，都得到了保证。在类似的假设下，我们证明了一个下限，该上限与我们的上限匹配到常数因子。