Generalize Learned Heuristics to Solve Large-scale Vehicle Routing Problems in Real-time

Large-scale Vehicle Routing Problems (VRPs) are widely used in logistics, transportation, supply chain, and robotic system. Recently, data-driven VRP heuristics are proposed to generate real-time VRP solutions with up to 100 nodes. However, current heuristics for large-scale VRPs still face three challenges: 1) Hard to generalize the heuristics learned on small-scale VRPs to large-scale VRPs in zero-shot way; 2) Hard to generate real-time solutions for large-scale VRPs; 3) Hard to embed global constraints in learned heuristics. We contribute in the three directions: We propose a Two-stage Divide Method (TAM) to generate sub-route sequence rather than node sequence for generalizing the heuristics learned on small-scale-VRPs to solve large-scale VRPs in real-time. A two-step reinforcement learning method with new reward and padding techniques is proposed to train our TAM. A global mask function is proposed to keep the global constraints satisfied when dividing a large-scale VRP into several small-scale Traveling Salesman Problems (TSPs). As result, we can solve the small-scale TSPs in parallel quickly. The experiments on synthetic and real-world large-scale VRPs show our method could generalize the learned heuristics trained on datasets of VRP 100 to solve VRPs with over 5000 nodes in real-time while keeping the solution quality better than data-driven heuristics and competitive with traditional heuristics.