Variable Neighborhood Search

Abstract

Variable neighborhood search (VNS) is a metaheuristic for solving combinatorial and global optimization problems. Its basic idea is systematic change of neighborhood both within a descent phase to find a local optimum and in a perturbation phase to get out of the corresponding valley. In this chapter we present the basic schemes of variable neighborhood search and some of its extensions. We next present four families of applications of VNS in which it has proved to be very successful: (i) finding feasible solutions to large mixed-integer linear programs, by hybridization of VNS and local branching, (ii) finding good feasible solutions to continuous nonlinear programs, (iii) finding programs in automatic fashion (artificial intelligence field) by building variable neighborhood programming methodology, and (iv) exploring graph theory in order to find conjectures, refutations, and proofs or ideas of proofs.