A matheuristic algorithm for the mixed capacitated general routing problem

We study the general routing problem de ned on a mixed graph and subject to capacity constraints. Such a problem aims to nd the set of routes of minimum overall cost servicing a subset of required elements like vertices, arcs and edges, without exceeding the capacity of a eet of homogeneous vehicles based at the same depot. The problem is a generalization of a large variety of node and arc routing problems. It belongs to the family of NP-hard combinatorial problems. Instances with a small number of vehicles and required elements can be e ectively solved by means of exact methods. Instead, heuristic approaches are helpful to obtain feasible solutions for medium to large size instances. In this paper we present a matheuristic approach to the problem, in which a set of neighborhoods is iteratively searched and a branch-and-cut algorithm is used to improve the quality of the feasible solutions found during the search. The search is iterated within a de ned global number of steps, in which the solution space is explored. We demonstrate the e ectiveness of this approach through an extensive computational study on several benchmark instances.