In this paper, a heuristic algorithm based on Tabu Search Approach for solving the Vehicle Routing Problem with Backhauls (VRPB) is proposed. The problem considers a set of customers divided in two subsets: Linehaul and Backhaul customers. Each Linehaul customer requires the delivery of a given quantity of product from the depot, whereas a given quantity of product must be picked up from each Backhaul customer and transported to the depot. In the proposed algorithm, each route consists of one sub-route in which only the delivery task is done, and one sub-route in which only the collection process is performed. The search process allows obtaining a correct order to visit all the customers on each sub-route. In addition, the proposed algorithm determines the best connections among the sub-routes in order to obtain a global solution with the minimum traveling cost. The efficiency of the algorithm is evaluated on a set of benchmark instances taken from the literature. The results show that the computing times are greatly reduced with a high quality of solutions. Finally, conclusions and suggestions for future works are presented.

This paper presents a multiobjective ant colony algorithm for the Multi-Depot Vehicle Routing Problem with Backhauls (MDVRPB) where three objectives of traveled distance, traveling times and total consumption of energy are minimized. An ant colony algorithm is proposed to solve the MDVRPB. The solution scheme allows one to find a set of ordered solutions in Pareto fronts by considering the concept of dominance. The effectiveness of the proposed approach is examined by considering a set of instances adapted from the literature. The computational results show high quality results within short computing times.