A Multistage Very Large-Scale Neighborhood Search for the Vehicle Routing Problem with Soft Time Windows

This paper considers the VRP Problem with Soft Time-Windows (VRPSTW), a challenging routing problem due to its combination of hard time windows and a lexicographic objective function minimizing the number of vehicles, the violations of the soft time windows, and the total travel distance. The paper presents a multi-stage, variable neighborhood search algorithm for the VRPSTW, which uses the same very large-scale neighborhood (VLSN) for each of its three steps with different objective functions. Experimental results indicate that the multi-stage VLSN algorithm improves best-known solutions on 90% and 100% of the Type 1 and Type 3 instances respectively. Equally interesting is the fact that the multi-stage algorithm decreases the number of routes in 33% of the instances and the soft time-window violations in 92% of the remaining instances.