Title: MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing

Abstract:

Fundamental NP-hard challenges with extensive practical utility, such as the Traveling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP), are central to combinatorial routing. Although recent deep reinforcement learning techniques have demonstrated considerable promise, they generally rely on data augmentation to manage geometric symmetries. This conventional approach often leads to unpredictable decision-making and constrained generalization capabilities. To overcome these limitations, we introduce MViewRouter, a novel multi-view framework that embeds geometric equivariance as a structural inductive bias, thereby ensuring invariant decision-making across various routing problem configurations. Central to our method is the Multi-view Alternating Attention (MAA) mechanism, which facilitates parallel processing across the $D_4$ symmetry group by alternating between aligning features between views and modeling relationships within views. Additionally, we refine the policy using Collective Policy Gradient Aggregation (CPGA), which utilizes consensus gradients derived from multiple symmetric perspectives to enhance training stability and speed up convergence. Empirical evaluations on standard TSP and CVRP benchmarks, alongside real-world instances from TSPLIB, reveal that MViewRouter delivers competitive solution quality and robust zero-shot generalization.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC