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

Researchers propose MViewRouter, a deep reinforcement learning framework that solves combinatorial routing problems like TSP and CVRP by embedding geometric symmetries directly into the model architecture rather than relying on data augmentation. The approach uses multi-view alternating attention and collective policy gradient aggregation to achieve more consistent decision-making and improved generalization across problem variants.

MViewRouter addresses a fundamental limitation in how current neural routing solvers handle geometric transformations. Traditional deep reinforcement learning approaches treat symmetries as data preprocessing concerns, augmenting training datasets with rotated and reflected variants. This reactive approach leads to inconsistent model behavior when encountering unfamiliar geometric configurations and poor transfer learning performance. The proposed framework internalizes symmetry as a structural bias, leveraging the D4 symmetry group—rotations and reflections in 2D space—directly within the model's attention mechanisms.

The Multi-view Alternating Attention mechanism processes the routing problem simultaneously across symmetric perspectives, maintaining separate representations while enforcing consistency through inter-view alignment. This architectural choice forces the model to learn invariant decision rules rather than memorizing symmetric variants. The Collective Policy Gradient Aggregation component aggregates gradient signals across all symmetric views, creating a consensus-based optimization signal that stabilizes training dynamics and accelerates convergence.

For the optimization community, this represents meaningful progress on notoriously difficult NP-hard problems. Competitive performance on TSP and CVRP benchmarks alongside strong zero-shot generalization to unseen problem instances suggests the approach captures genuine structural patterns rather than superficial correlations. The real-world TSPLIB validation adds credibility beyond academic benchmarks.

Developers building logistics optimization systems and researchers in combinatorial optimization should monitor refinements to this approach. The framework's emphasis on geometric structure suggests similar techniques could apply to other spatially-informed problems. Long-term impact depends on whether this architecture scales effectively to larger problem instances and whether competing approaches adopt similar symmetry-aware designs.

• →MViewRouter internalizes geometric equivariance as a structural bias rather than treating symmetries through data augmentation alone
• →The Multi-view Alternating Attention mechanism enables parallel processing across symmetric variants while enforcing decision consistency
• →Collective Policy Gradient Aggregation stabilizes training by consensus across multiple symmetric perspectives
• →Framework demonstrates competitive performance on TSP/CVRP benchmarks with strong zero-shot generalization to unseen instances
• →Approach addresses fundamental limitations in how neural routing solvers handle geometric transformations and problem variants