DeepMDV: Global Spatial Matching for Multi-depot Vehicle Routing Problems

The rapid growth of online retail and e-commerce has made effective and efficient Vehicle Routing Problem (VRP) solutions essential. To meet rising demand, companies are adding more depots, which changes the VRP problem to a complex optimization task of Multi-Depot VRP (MDVRP) where the routing decisions of vehicles from multiple depots are highly interdependent. The complexities render traditional VRP methods suboptimal and non-scalable for the MDVRP. In this paper, we propose a novel approach to solve MDVRP addressing these interdependencies, hence achieving more effective results. The key idea is, the MDVRP can be broken down into two core spatial tasks: assigning customers to depots and optimizing the sequence of customer visits. We adopt task-decoupling approach and propose a two-stage framework that is scalable: (i) an interdependent partitioning module that embeds spatial and tour context directly into the representation space to globally match customers to depots and assign them to tours; and (ii) an independent routing module that determines the optimal visit sequence within each tour. Extensive experiments on both synthetic and real-world datasets demonstrate that our method outperforms all baselines across varying problem sizes, including the adaptations of learning-based solutions for single-depot VRP. Its adaptability and performance make it a practical and readily deployable solution for real-world logistics challenges.