A simplified run time analysis of the univariate marginal distribution algorithm on LeadingOnes

Benjamin Doerr (1, 2, 3) , Martin Krejca (4)

1 X - École polytechnique
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
3 IP Paris - Institut Polytechnique de Paris
4 Hasso Plattner Institute [Potsdam, Germany]

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.

Domains: Computer Science [cs]

Benjamin Doerr, Martin Krejca. A simplified run time analysis of the univariate marginal distribution algorithm on LeadingOnes. Theoretical Computer Science, 2021, 851, pp.121-128. ⟨10.1016/J.TCS.2020.11.028⟩. ⟨hal-04485607⟩