A Reinforcement Learning Framework for Traveling Salesman and Vehicle Routing Problem with Drones

The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two classical combinatorial optimization problems. In recent years, their drone-assisted variants, the Traveling Salesman Problem with Drones (TSP-D) and the Vehicle Routing Problem with Drones (VRP-D) have attracted growing attention. Generally, these problems are solved using exact algorithms or metaheuristic algorithms. However, as the problem complexity increases and the scale of instances grows, these approaches often become less efficient. In this paper, we propose a reinforcement learning method with a shared attention encoder and a hierarchical dual-decoder architecture, where truck–drone coordination is achieved by first decoding the truck’s next node and then conditionally decoding the drone action. To further explore the solution space of large-scale instances, the proposed method adopts a multi-rollout learning strategy. We conducted experiments on large-scale TSP-D and VRP-D instances, and the results show that this model outperforms traditional metaheuristic algorithms in terms of both solution quality and computational efficiency.