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We discuss the geometrical interpretation of a well-known smoothing operator applied to the Molecular Distance Geometry Problem, and we then describe a heuristic approach based on Variable Neighbourhood Search on the smoothed and original problem. This algorithm often manages to find solutions having higher accuracy than other methods. This is important as small differences in the objective fun...

Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these t...