Relational Trajectory-Entropy Augmented MADRL for Truck-Drone Collaborative Deliver With Mobile Charging Optimization

The truck-drone collaborative delivery problem, modeled as a Traveling Salesman Problem with Drones (TSP-D), presents critical challenges in coordinating heterogeneous vehicles with distinct operational constraints. A key optimization opportunity lies in using trucks as mobile charging stations, enabling extended drone operations beyond battery limitations. While existing approaches struggle with scalability and inefficient exploration of this mobile charging paradigm, we propose a relational trajectory-entropy augmented (R-TEA) Multi-Agent Deep Reinforcement Learning (MADRL) framework that synergizes Relational Graph Convolutional Networks (R-GCN) with Trajectory-Entropy Reward (TER). Our method addresses three core challenges: 1) modeling spatiotemporal dependencies between trucks and drones via R-GCN’s relational inductive biases, including critical charging coordination; 2) escaping local optima via trajectory exploration that considers dynamic charging opportunities; and 3) balancing time-cost trade-offs via a compound reward design that accounts for charging efficiency. Extensive experiments on TSPLib and synthetic benchmarks demonstrate R-TEA’s superiority over heuristic, attention-based RL, and evolutionary baselines.