Introduction to the special issue on variable neighborhood search

Abstract

Variable Neighborhood Search (VNS) is a metaheuristic for solving optimization problems based on systematic changes of structure within a search that may be performed in a deterministic way (Variable Neighborhood Descent, VND) or randomly (reduced VNS). Basic VNS combines random selection of a point in a shaking or perturbation step followed by a deterministic local search from that point. There are several extensions and hybrids of the basic VNS scheme suggested in the literature: if VND is used instead of local search, we have general VNS; the variable neighbourhood decomposition search (VNDS) method extends the basic VNS into a two-level VNS scheme based upon decomposition of the problem; the skewed VNS allows moves to a slightly worse but far solutions, etc. VNS has been successfully applied to a wide range of combinatorial and global optimization problems. In this special issue of Journal of Heuristics we collect several new successful applications of VNS as well as studies of advanced characteristics of VNS. Most of them were presented at the XVIII Mini EURO Conference (MEC), which was held at Tenerife, Spain, in November 2005. On that meeting, 61 VNS contributions by researches from 14 different countries and 4 continents were presented. The papers that make up this special issue on Variable Neighborhood Search illustrate breadth and depth of research in variable neighborhood search since they show some advanced features of the metaheuristic. Michael Polacek, Karl F. Doerner, Richard F. Hartl and Vittorio Maniezzo develop a basic variable neighborhood search algorithm to solve the Capacitated Arc Routing Problem with Intermediate Facilities that outperforms all known heuristics on four benchmark sets. The method uses only one exchange operator, the CROSS-exchange,