A biased-randomized metaheuristic for the vehicle routing problem with clustered and mixed backhauls

This article analyzes the Vehicle Routing Problem with Backhauls, where delivery and pick‐up customers are served from a central depot. Initially, we focus in the version with clustered backhauls (VRPCB), where all the customers in the delivery group of the same route have to be served before the first customer in the pick‐up group can be visited. The article presents a relatively simple‐to‐implement yet efficient metaheuristic algorithm that integrates a biased‐randomized version of the popular savings heuristic within a metaheuristic framework. A skewed probability distribution is used to induce a biased (oriented) randomization effect on the savings list of routing edges, and a penalty cost is assigned to those edges connecting delivery customers with pick‐up customers in order to promote a sequential order in delivery and pick‐up activities. In the proposed approach, the fleet size constraint is implicitly relaxed. This feature allows the perturbation process to explore unfeasible but promising regions in the solution space. Then, whenever the number of routes does not match the number of available vehicles, a ‘recursive corrective operator’ is employed to transform the new solution into a feasible one. Some classical benchmark instances for the VRPCB are selected in order to compare our approach with other state‐of‐the‐art algorithms, and a new best‐know solution for a classical benchmark set is obtained. Finally, we analyze the flexibility of our approach by employing it, after a minor adaptation, in the Vehicle Routing Problem with Mixed Backhauls, where linehaul and backhaul customers might appear in any order during a route.