OD-DEAL: Dynamic Expert-Guided Adversarial Learning with Online Decomposition for Scalable Capacitated Vehicle Routing

Solving large-scale capacitated vehicle routing problems (CVRP) is hindered by the high complexity of heuristics and the limited generalization of neural solvers on massive graphs. We propose OD-DEAL, an adversarial learning framework that tightly integrates hybrid genetic search (HGS) and online barycenter clustering (BCC) decomposition, and leverages high-fidelity knowledge distillation to transfer expert heuristic behavior. OD-DEAL trains a graph attention network (GAT)-based generative policy through a minimax game, in which divide-and-conquer strategies from a hybrid expert are distilled into dense surrogate rewards. This enables high-quality, clustering-free inference on large-scale instances. Empirical results demonstrate that OD-DEAL achieves state-of-the-art (SOTA) real-time CVRP performance, solving 10000-node instances with near-constant neural scaling. This uniquely enables the sub-second, heuristic-quality inference required for dynamic large-scale deployment.