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Neigborhood Selection in Variable Neighborhood Search

Variable neighborhood search (VNS) is a metaheuristic for solving optimization problems based on a simple principle: systematic changes of neighborhoods within the search, both in the descent to local minima and in the escape from the valleys which contain them. Designing these neighborhoods and applying them in a meaningful fashion is not an easy task. Moreover, an appropriate order in which they are applied must be determined. In this paper we attempt to investigate this issue. Assume that we are given an optimization problem that is intended to be solved by applying the VNS scheme, how many and which types of neighborhoods should be investigated and what could be appropriate selection criteria to apply these neighborhoods. More specifically, does it pay to "look ahead" (see, e.g., in the context of VNS and GRASP) when attempting to switch from one neighborhood to another?