A novel multi-objective optimization model for the vehicle routing problem with drone delivery and dynamic flight endurance

• A novel optimization model for the vehicle routing problem with drone delivery is proposed. • Economic and environmental objectives are optimized simultaneously in the model. • The flight endurance of drones is modelled dynamically with their loading rate. • An extended non-dominated sorting genetic algorithm is presented to solve the model. With growing environmental concerns and tough carbon–neutral objectives, logistics providers have to consider not only economic benefits but also environmental impact in the delivery process. This study proposes a novel multi-objective optimization model for the vehicle routing problem with drone delivery. The proposed model involves improving delivery efficiency and reducing environmental impact by extending the conventional ground vehicle (i.e. truck) delivery model with the implementation of drone delivery as well as the optimization of the total energy consumption of trucks. Drones need to collaborate with trucks to serve customers because of their limited flight endurance. Moreover, the fact that flight endurance is dynamic and influenced by the loading rate of drones is also considered to satisfy practical application scenarios. An extended non-dominated sorting genetic algorithm is presented to solve the proposed model. A new encoding and decoding method is incorporated to represent multiple feasible routes of drones and trucks, several crossover and mutation operators are integrated to accelerate the algorithmic convergence, and a multi-dimensional local search strategy is employed to enhance the diversity of population. Finally, the experimental results demonstrate that the presented algorithm is effective in obtaining high-quality non-dominated solutions by comparing it with three other baseline multi-objective algorithms.