Matheuristics for the Periodic Vehicle Routing Problem with Time Windows

We investigate two matheuristic strategies using the periodic vehicle routing problem with time windows as a testbed. Two different metaheuristics are suitably combined with parts of a developed column generation approach: On the one hand a variable neighborhood search (VNS) acts as the sole provider of columns for a set covering model, hence realizing a pure metaheuristic column generation. Hereby, the VNS and the resolving of the model are performed in an intertwined way. On the other hand the solution to the linear programming (LP) relaxation of the set covering model, i.e. the columns (routes) and their respective (accumulated) LP values, found by a classical column generation approach are successfully exploited in a subsequent evolutionary algorithm. Both matheuristics often yield significantly better results than their pure metaheuristic counterparts. These approaches are applicable to other classes of combinatorial optimization problems as well.