Hyper-heuristics are search methods that aim to solve optimization problems by selecting or generating heuristics. Selection hyper-heuristics choose from a pool of heuristics a good one to be applied at the current stage of the optimization process. The selection mechanism is the main part of a selection hyper-heuristic and have a great impact on its performance. In this paper a deterministic selection mechanism based on the concepts of the Multi-Armed Bandit (MAB) problem is proposed. The proposed approach is integrated into the HyFlex framework and is compared to twenty other hyper-heuristics using the methodology adapted by the CHeSC 2011 Challenge. The results obtained were good and comparable to those attained by the best hyper-heuristics. Therefore, it is possible to affirm that the use of a MAB mechanism as a selection method in a hyper-heuristic is a promising approach.