Metaheuristics with variable diversity control and neighborhood search for the Heterogeneous Site-Dependent Multi-depot Multi-trip Periodic Vehicle Routing Problem

The planning of vehicle routes is a major issue involved in supply chains. In real environment, we can find situations involving a very large number of clients or constraints which indicate that exact methods should be avoided. In this context, this paper presents two metaheuristcs which are used to solve a complex problem named the Heterogeneous Site-Dependent Multi-depot Multi-trip Periodic Vehicle Routing Problem (HSDMDMTPVRP). The HSDMDMTPVRP is a real problem found in the automotive industry and considers several well-known Vehicle Routing Problems (VRP). The first metaheuristic is an adaptation of the Unified Hybrid Genetic Search (UHGS) which considers an advanced diversity control, feasibility control and a restart mechanism. The second one is a new metaheuristic named Adaptive Variable Neighborhood Race (AVNR) which combines variable neighborhood search and adaptive mechanisms integrated with a shrinking population managed with a diversity mechanism. Both approaches are also used for solving some variants of the VRP: Heterogeneous VRP, Site dependent VRP, Periodic VRP and Multi-trip VRP. Our computational experiments used 398 available instances in the literature with generic code path and also present 20 new instances for the HSDMDMTPVRP. The metaheuristics solved all instances with only one set of parameters and the results outperform or present the same solutions found by several state-of-the-art algorithms, showing the good performance of the approaches. Out of the 398 previously tested literature instances, the proposed metaheuristics found 140 new best-known solutions and 209 of the best-known ones. For the remaining instances, both approaches found results very close to best ones known.