通过多视角注意力内化几何对称性，提升路径规划模型的泛化能力。
MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing
- 设计多视角交替注意力机制，显式建模四重对称性
- 在TSP/CVRP上实现与主流方法相当的解质量，零样本泛化更强
- 适合需要强泛化能力的组合优化场景，如物流调度
组合路由问题如旅行商问题（TSP）和带容量限制的车辆路径问题（CVRP）是具有广泛现实应用的基本NP难问题。尽管近期深度强化学习方法表现良好，但通常仅通过数据增强处理几何对称性，导致决策不一致且泛化能力有限。为此，我们提出MViewRouter，一种将几何等变性作为结构归纳偏置内化的多视角框架，实现不同路由问题变体下的不变决策。该方法引入多视角交替注意力（MAA）机制，可在$D_4$对称群上并行处理，交替进行视图内关系建模与视图间特征对齐。此外，通过集体策略梯度聚合（CPGA）优化策略，利用多个对称视角的共识梯度稳定训练并加速收敛。在TSP、CVRP基准及真实世界TSPLIB实例上的实验表明，MViewRouter实现了具有竞争力的解质量与强大的零样本泛化能力。
原文摘要 · Abstract (English)
Combinatorial routing problems such as the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) are fundamental NP-hard problems with broad real-world applications. While recent deep reinforcement learning methods have shown promising performance, they typically handle geometric symmetries only through data augmentation, resulting in inconsistent decisions and limited generalization. To address this issue, we propose MViewRouter, a multi-view framework that internalizes geometric equivariance as a structural inductive bias to achieve invariant decision-making across routing problem variants. Our approach introduces a Multi-view Alternating Attention (MAA) mechanism that enables parallel processing over the $D_4$ symmetry group, alternating between intra-view relational modeling and inter-view feature alignment. Furthermore, we optimize the policy via Collective Policy Gradient Aggregation (CPGA), leveraging consensus gradients from multiple symmetric views to stabilize training and accelerate convergence. Experiments on TSP and CVRP benchmarks, as well as real-world TSPLIB instances, demonstrate that MViewRouter achieves competitive solution quality and strong zero-shot generalization.
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