Behaviour of the UMDAc algorithm with truncationselection on monotone functions

Of late, much progress has been made in developing Estimation of DistributionAlgorithms (EDA), algorithms that use probabilistic modelling of high quality solutionsto guide their search. While experimental results on EDA behaviour are widelyavailable, theoretical results are still rare. This is especially the case for continuousEDA. In this article, we develop theory that predicts the behaviour of the UnivariateMarginal Distribution Algorithm in the continuous domain (UMDAc) with truncationselection on monotonous ¯tness functions. Monotonous functions are commonlyused to model the algorithm behaviour far from the optimum.[...]