Metaheuristics applied to mixed and simultaneous extensions of vehicle routing problems with backhauls

Metaheuristics are a class of approximate methods designed to solve hard combinatorial optimization problems arising within various different areas. The importance of metaheuristics results from their ability to continue the search beyond a local optimum so that near-optimal or optimal solutions are efficiently found. In order to solve the backhauling problem associated with mixed and simultaneous delivery and pick-ups, this paper presents a hybrid algorithm which is comprised of the two metaheuristics of tabu search and variable neighbourhood descent. The primary challenge associated with backhauling consists of creating routes in which vehicles are not only required to deliver goods, but also to perform pick-ups at customer locations. The problems associated with these two categories of problems, however, have received little attention in the literature to date. A set of examples taken from the literature with Euclidean cost matrices are presented. Finally, some numerical results are illustrated to show the effectiveness of the proposed approach.