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

2026-05-31

AI Summary

This work addresses the limitations in decision consistency and generalization arising from the neglect of geometric symmetries in combinatorial routing problems such as the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP). To this end, the authors propose MViewRouter, a novel framework that explicitly incorporates D₄ geometric equivariance as a structural inductive bias within its architecture. MViewRouter employs a multi-view alternating attention mechanism to process symmetry group transformations in parallel, modeling intra-view relational structures while aligning inter-view features. The framework further integrates collective policy gradient aggregation for end-to-end strategy optimization. Evaluated on standard TSP and CVRP benchmarks as well as real-world TSPLIB instances, MViewRouter achieves competitive solution quality while significantly enhancing zero-shot generalization and decision consistency.

Abstract

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.

Problem

• combinatorial routing
• geometric equivariance
• Traveling Salesman Problem
• Capacitated Vehicle Routing Problem
• generalization

Innovation

• geometric equivariance
• multi-view alternating attention
• combinatorial routing
• inductive bias
• collective policy gradient