Edge-enhanced attentions for drone delivery in presence of winds and recharging stations

Existing variants of vehicle routing problems have limited capabilities in describing real-world drone delivery scenarios in terms of drone physical restrictions, mission constraints, and stochastic operating environments. To that end, this paper proposes a specific drone delivery problem with recharging (DDP-R) characterized by directional edges and stochastic edge costs subject to wind conditions. To address it, the DDP-R is cast into a Markov decision process over a graph, with the next node chosen according to a stochastic policy based on the evolving observation. An edge-enhanced attention model (AM-E) is then suggested to map the optimal policy via the deep reinforcement learning (DRL) approach. The AM-E comprises a succession of edge-enhanced dot-product attention layers and is designed with the aim of capturing the heterogeneous node relationship for DDP-Rs by incorporating adjacent edge information. Simulations show that edge enhancement facilitates the training process, achieving superior performance with less trainable parameters and simpler architecture in comparison with other deep learning models. Furthermore, a stochastic drone energy cost model in consideration of winds is incorporated into validation simulations, which provides a practical insight into drone delivery problems. In terms of both nonwind and windy cases, extensive simulations demonstrate that the proposed DRL method outperforms state-of-the-art heuristics for solving DDP-Rs, especially at large sizes.