An interactive GRAMPS algorithm for the heterogeneous fixed fleet vehicle routing problem with and without backhauls

In this article, a visual interactive approach based on a new greedy randomised adaptive memory programming search (GRAMPS) algorithm is proposed to solve the heterogeneous fixed fleet vehicle routing problem (HFFVRP) and a new extension of the HFFVRP, which is called heterogeneous fixed fleet vehicle routing problem with backhauls (HFFVRPB). This problem involves two different sets of customers. Backhaul customers are pickup points and linehaul customers are delivery points that are to be serviced from a single depot by a heterogeneous fixed fleet of vehicles, each of which is restricted in the capacity it can carry, with different variable travelling costs. The proposed approach is implemented within a visual decision support system, which was developed to allow users to produce and judge alternative decisions by using their knowledge and experience about the requirements of the HFFVRP. The computational results are provided on classical problem instances for HFFVRP and a new best-known solution has been reported. A new set of problem instances for HFFVRPB is proposed. The results show that the proposed approach can find high quality solutions in very short time and the system is able to create alternative solutions in order to satisfy the user's expectations.