Multiple Variable Neighborhood Search Enriched with ILP Techniques for the Periodic Vehicle Routing Problem with Time Windows

In this work we extend a VNS for the periodic vehicle routing problem with time windows (PVRPTW) to a multiple VNS (mVNS) where several VNS instances are applied cooperatively in an intertwined way. The mVNS adaptively allocates VNS instances to promising areas of the search space. Further, an intertwined collaborative cooperation with a generic ILP solver applied on a suitable set covering ILP formulation with this mVNS is proposed, where the mVNS provides the exact method with feasible routes of the actual best solutions, and the ILP solver takes a global view and seeks to determine better feasible route combinations. Experimental results were conducted on newly derived instances and show the advantage of the mVNS as well as of the hybrid approach. The latter yields for almost all instances a statistically significant improvement over solely applying the VNS in a standard way, often requiring less runtime, too.