Neigborhood Selection in Variable Neighborhood Search

Variable neighborhood search (VNS) [4, 5] 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. VNS applications have been numerous and successful. Many extensions have been made, mainly to be able to solve large problem instances. Nevertheless, a main driver behind VNS is to keep the simplicity of the basic scheme. Variable neighborhood descend (VND) belongs to the family of methods within VNS. The idea behind VND is to systematically switch between different neighborhoods where a local search is comprehensively performed within one neighborhood until no further improvements are possible. Given the found local optimum, VND continues with a local search within the next neighborhood. If an improved solution is found one may resort to the first neighborhood; otherwise the search continues with the next neighborhood, etc. Designing these neighborhoods and applying them in a meaningful fashion is not an easy task. Moreover, incorporating these neighborhoods, e.g., into VNS may still need a considerable degree of ingenuity and may be confronted with the following research questions (among others): • Which neighborhoods can be designed? • How should they be explored and how efficient are they? • How structurally different are they? • In which order should they be applied?