A TABU SEARCH HEURISTIC FOR THE VEHICLE-ROUTING PROBLEM WITH SOFT TIME WINDOWS

This paper describes a tabu search heuristic for the vehicle routing p roblem with soft time windows. In this problem, lateness at customer l ocations is allowed although a penalty is incurred and added to the ob jective value. By adding large penalty values, the vehicle routing pro blem with hard time windows can be addressed as well. In the tabu sear ch, a neighborhood of the current solution is created through an excha nge procedure that swaps sequences of consecutive customers (or segmen ts) between two routes. The tabu search also exploits an adaptive memo ry that contains the routes of the best previously visited solutions. New starting points for the tabu search are produced through a combina tion of routes taken from different solutions found in this memory. Ma ny best-known solutions are reported on classical test problems.