A Combined Metaheuristic Algorithm for the Vehicle Routing Problem and its Open Version

Abstract: The Open Vehicle Routing Problem (OVRP) is one of the most important extensions of the vehicle routing problem (VRP) that has many applications in industrial and service. In the VRP, a set of customers with a specified demand of goods are given and a depot where a fleet of identical capacitated vehicles is located. We are also given the ‘‘traveling costs’’ between the depot and all the customers, and between each pair of customers. In the OVRP against to VRP, vehicles are not required to return to the depot after completing service. Because VRP and OVRP belong to NP-hard Problems, an efficient hybrid elite ant system called EACO is proposed for solving them in the paper. In this algorithm, a modified tabu search (TS), a new state transition rule and a modified pheromone updating rule are used for more improving solutions. These modifications lead that the proposed algorithm does not trapped at the local optimum and discovers different parts of the solution space. Computational results on fourteen standard benchmark instances for VRP and OVRP show that EACO finds the best known solutions for most of the instances and is comparable in terms of solutions quality to the best performing published metaheuristics in the literature.