Variable neighborhood search: Principles and applications

Systematic change of neighborhood within a possibly randomized local search algorithm yields a simple and e€ective metaheuristic for combinatorial and global optimization, called variable neighborhood search (VNS). We present a basic scheme for this purpose, which can easily be implemented using any local search algorithm as a subroutine. Its e€ectiveness is illustrated by solving several classical combinatorial or global optimization problems. Moreover, several extensions are proposed for solving large problem instances: using VNS within the successive approximation method yields a two-level VNS, called variable neighborhood decomposition search (VNDS); modifying the basic scheme to explore easily valleys far from the incumbent solution yields an ecient skewed VNS (SVNS) heuristic. Finally, we show how to stabilize column generation algorithms with help of VNS and discuss various ways to use VNS in graph theory, i.e., to suggest, disprove or give hints on how to prove conjectures, an area where metaheuristics do not appear to have been applied before.