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In the current work we introduce a novel estimation of distribution algorithmto tackle a hard combinatorial optimization problem, namely the single-machinescheduling problem, with uncertain delivery times. The majority of the existingresearch coping with optimization problems in uncertain environment aims atfinding a single sufficiently robust solution so that random noise andunpredictable circumstances would have the least possible detrimental effect onthe quality of the solution. The measures of robustness are usually based onvarious kinds of empirically designed averaging techniques. In contrast to theprevious work, our algorithm aims at finding a collection of robust schedulesthat allow for a more informative decision making. The notion of robustness ismeasured quantitatively in terms of the classical mathematical notion of a normon a vector space. We provide a theoretical insight into the relationshipbetween the properties of the probability distribution over the uncertaindelivery times and the robustness quality of the schedules produced by thealgorithm after a polynomial runtime in terms of approximation ratios.

Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments