ABSTRACT The vehicle routing problem (VRP) has garnered significant interest due to its central role in logistics and transportation systems. However, existing deep reinforcement learning (DRL) approaches often underexploit the structural information encoded in graph topologies, and tend to generate solution trajectories with limited diversity, restricting effective exploration of the solution space. To overcome these limitations, we present a Graph‐based Diverse Trajectory‐driven Attention Model (GDTAM) for solving VRPs across a range of scales and types. Built upon a transformer backbone, GDTAM operates directly on undirected graphs and integrates an edge‐driven graph attention block within the encoder, enabling the joint modeling of node‐ and edge‐level topological features. To enhance adaptability to dynamic environments, we introduce a feature integrator that bridges the encoder and decoder, enabling the fusion of real‐time state features with static graph representations. Moreover, GDTAM incorporates a multi‐decoder architecture with identical structures but independently network parameters, promoting the generation of diverse routing trajectories through a Jensen–Shannon divergence regularization term. We evaluate GDTAM on four canonical VRP variants, i.e., the traveling salesman problem (TSP), the capacitated VRP (CVRP), the orienteering problem (OP), and the asymmetric traveling salesman problem (ATSP). Experimental results demonstrate that GDTAM represents a meaningful advancement over mainstream heuristic and DRL‐based baselines, while exhibiting strong generalization across various problem scales, underscoring its effectiveness and robustness for real‐world routing applications.
Ou et al. (Mon,) studied this question.