A solution for multi-objective commodity vehicle routing problem by NSGA-II

Vehicle routing is considered the basic issue in distribution management. In real-world problems, customer demand for some commodities increases on special situations. On the one hand, one of the factors that are very important for customers is the timely delivery of the demanded commodities. In this research, customers had several different kinds of demands. Therefore, a new routing model was introduced in the form of integer linear programming by combining the concepts of time windows and multiple demands and by considering the two contradictory goals of minimizing travel cost and maximizing demand coverage. Moreover, two approaches were designed for the problem-solving model based on the NSGA-II algorithm with diversification of the mutation operator structure. The two criteria of spread and coverage of non-dominated solutions were used to compare algorithms. Study of some typical created problems indicated the validity of the model and the computational efficiency of the proposed algorithm. The proposed algorithm could increase the criterion of solution spread by about 10%, and increased the number of obtained solutions on the Pareto border compared to other algorithms, which indicated its high efficiency.