A heuristic for the vehicle routing problem with time windows

In this paper we propose a heuristic algorithm to solve the Vehicle Routing Problem with Time Windows. Its framework is a smart combination of three s imple procedures: the classical k-opt exchanges improve the solution, an ad hoc procedure reduces the number of vehicles and a second objective functi on drives the search out of local optima. No parameter tuning is required a nd no random choice is made: these are the distinguishing features with res pect to the recent literature. The algorithm has been tested on benchmark p roblems which prove it to be more effective than comparable algorithms.