Variable Neighborhood Search (VNS)

Variable Neighborhood Search (VNS) is a metaheuristic optimization framework introduced by Mladenović and Hansen in 1997. It escapes local optima by systematically switching among a predefined set of neighborhood structures — first perturbing the current solution (shaking) to reach a different region of the search space, then applying a local search within that region, and finally accepting the new solution only if it improves the incumbent. The method is flexible enough to handle combinatorial problems (routing, scheduling, graph problems) as well as continuous optimization, making it one of the most widely used neighborhood-based metaheuristics in operations research.