Rigorous time complexity analysis of Univariate Marginal Distribution Algorithm with margins

Univariate Marginal Distribution Algorithms (UMDAs) are a kind of Estimation of Distribution Algorithms (EDAs) which do not consider the dependencies among the variables. In this paper, on the basis of our proposed approach in [1], we present a rigorous proof for the result that the UMDA with margins (in [1] we merely showed the effectiveness of margins) cannot find the global optimum of the TRAPLEADINGONES problem [2] within polynomial number of generations with a probability that is super-polynomially close to 1. Such a theoretical result is significant in sheding light on the fundamental issues of what problem characteristics make an EDA hard/easy and when an EDA is expected to perform well/poorly for a given problem.