A deep reinforcement learning-based algorithm for regional drone routing problem with nonlinear fuel consumption

With the boom of e-commerce and increasing policy support, regional logistics serving medium- and short-distance transportation have grown rapidly. Large fuel-powered drones are increasingly adopted in this field due to their flexibility and efficiency, yet their deployment has raised concerns regarding pollutant emissions and environmental sustainability. To balance logistics efficiency with environmental responsibility, this paper proposes a regional drone routing problem using large fuel-powered drones, accounting for nonlinear fuel consumption and multiple pollutant emissions. The problem is formulated as a mixed-integer nonlinear programming model to minimize the total cost, including fuel consumption cost, pollutant emission cost, and operational cost. To accurately estimate fuel consumption, a nonlinear fuel consumption function is formulated by comprehensively considering variable payload, fluctuating fuel load, empty weight, the entire flight process, and wind. A deep reinforcement learning-based algorithm, namely a double-deep Q-network with attention mechanism based large neighborhood search algorithm, is designed to solve the model. The effectiveness of the algorithm and the nonlinear fuel consumption function is validated by comparative experiments on simulated instances, and then the impacts of refueling availability and wind conditions on the total cost are further investigated. Furthermore, based on a real-world case, this paper shows that drones can reduce the total cost, while sensitivity analyses evaluate the impact of key factors on environmental and economic performance. The results indicate that the proposed model and algorithm can effectively enhance operational efficiency and environmental performance.