Convergence analysis of UMDAC with finite populations: a case study on flat landscapes

This paper presents some new analytical results on the continuous Univariate Marginal Distribution Algorithm (UMDAC), which is a well known Estimation of Distribution Algorithm based on Gaussian distributions. As the extension of the current theoretical work built on the assumption of infinite populations, the convergence behavior of UMDAC with finite populations is formally analyzed. We show both analytically and experimentally that, on flat landscapes, the Gaussian model in UMDAC tends to collapse with high probability, which is an important fact that is not well understood before.

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