OD-DEAL: Dynamic Expert-Guided Adversarial Learning with Online Decomposition for Scalable Capacitated Vehicle Routing
Dongbin Jiao, Zisheng Chen, Xianyi Wang, Jintao Shi, Shengcai Liu, Shi Yan
TL;DR
OD-DEAL tackles large-scale CVRP by marrying a GAT-based policy with an online decomposition expert (HGS+BCC) within an adversarial GFlowNet framework. The discriminator provides dense reward signals, enabling trajectory balance-based training to align the neural policy with expert-like distribution while internalizing the divide-and-conquer logic. Empirically, OD-DEAL achieves state-of-the-art real-time CVRP performance, maintaining sub-second inference up to 10,000-node instances with near-constant neural scaling, and demonstrates strong generalization to CVRPLib/TSPLib and XL benchmarks. This framework thus bridges the gap between high-quality heuristic search and scalable neural inference, offering a practical solution for dynamic large-scale routing in logistics.
Abstract
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.