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With elementary means, we prove a stronger run time guarantee for theunivariate marginal distribution algorithm (UMDA) optimizing the LeadingOnesbenchmark function in the desirable regime with low genetic drift. If thepopulation size is at least quasilinear, then, with high probability, the UMDAsamples the optimum within a number of iterations that is linear in the problemsize divided by the logarithm of the UMDA's selection rate. This improves overthe previous guarantee, obtained by Dang and Lehre (2015) via the deeplevel-based population method, both in terms of the run time and bydemonstrating further run time gains from small selection rates. With similararguments as in our upper-bound analysis, we also obtain the first lower boundfor this problem. Under similar assumptions, we prove that a bound that matchesour upper bound up to constant factors holds with high probability.

A Simplified Run Time Analysis of the Univariate Marginal Distribution Algorithm on LeadingOnes