Parallel Processing Algorithms for the Vehicle Routing Problem and Its Variants: A Literature Review with a Look into the Future

Abstract

Vehicle Routing Problems (VRPs) are well-know combinatorial optimization problems used to design an optimal route for a fleet of vehicles to service a set of customers under a number of constraints. Due to their NP-hard complexity, a number of purely computational techniques have been proposed in recent years in order to solve them. Among these techniques, nature-inspired algorithms have proven their effectiveness in terms of accuracy and convergence speed. Some of these methods are also designed in such a way to decompose the basic problem into a number of sub-problems which are subsequently solved in parallel computing environments. It is therefore the purpose of this paper to review the fresh corpus of the literature dealing with the main approaches proposed over the past few years to solve combinatorial optimization problems in general and, in particular, the VRP and its different variants. Bibliometric and review studies are conducted with a special attention paid to metaheuristic strategies involving procedures with parallel architectures. The obtained results show an expansion of the use of parallel algorithms for solving various VRPs. Nevertheless, the regression in the number of citations in this framework proves that the interest of the research community has declined somewhat in recent years. This decline may be explained by the lack of rigorous mathematical results and practical interfaces under famous calculation softwares.