Bi-Objective Optimization for Vehicle Routing Problems with a Mixed Fleet of Conventional and Electric Vehicles and Soft Time Windows

With the growing interest in environmental protection and congestion, electric vehicles are increasingly becoming the important transportation means. However, electric vehicles currently face several adoption barriers including high purchasing price and limited travelling range, so the fleets where electric vehicles and conventional vehicles coexist are closer to the current fleet management status. Considering the impact of charging facilities and carbon emission, this paper proposes a vehicle routing problem with a mixed fleet of conventional and electric vehicles and soft time windows. A bi-objective programming model is established to minimize total operational cost and time penalty cost. Finally, the nondominated sorting genetic algorithm II (NSGA-II) is employed to deal with this problem. Furthermore, single-objective optimization is carried out for the two objectives, respectively, and the linear weighting method is also used to solve the problem. Through the contrast of these results and the NSGA-II results, the effectiveness of the algorithm in this paper is further verified. The results indicate that two objectives are contradictory to some extent and decision-makers need a trade-off between two objectives.