A matheuristic for the asymmetric capacitated vehicle routing problem

In this paper, we propose a novel matheuristic for the Asymmetric Capacitated Vehicle Routing Problem (ACVRP). This optimization-based approach combines some heuristic concepts with compact mixed-integer linear programming (MILP) formulations. Basically, the proposed matheuristic includes three sequential stages. First, the problem size is heuristically reduced by discarding unpromising arcs. Second, a starting feasible solution is derived. Finally, an optimization-based improvement procedure is invoked to iteratively generate near-optimal solutions. This latter procedure requires solving a sequence of two- or three-vehicle ACVRP reduced instances. A peculiar feature of the solution strategy is that all the three stages are solely based on solving compact MILP formulations using a commercial solver and it does not resort to any constructive heuristic nor metaheuristic. We describe the results of extensive computational experiments, that were carried out on a large set of benchmark instances with up to 200 nodes, and we provide empirical evidence that the proposed matheuristic often delivers high-quality solutions.