Edge-aware Decoding for Neural Asymmetric Routing

2026-06-01

AI Summary

This work addresses a critical gap in existing approaches to asymmetric path planning, where a disconnect exists between representation and decision-making: while encoding captures pairwise costs, decoding relies solely on node-context compatibility and neglects directed edge-level transition information. To bridge this gap, the authors propose an edge-aware decoding mechanism that explicitly incorporates three candidate-specific signals—namely, the current directed edge cost, the return-to-depot closing cost, and lightweight static lookahead information—without modifying the backbone architecture. Integrated with SVD/Sinkhorn-based asymmetric backbones, the method enables zero-shot generalization from ATSP-100 to larger instances, reducing the optimality gap on ATSP-1000 from 4.13% to 2.73% and consistently improving performance on the Asymmetric Capacitated Vehicle Routing Problem (ACVRP).

Abstract

Neural asymmetric routing models increasingly encode directionality through matrix representations and asymmetry-aware attention. The final routing action, however, is not a node in isolation but a directed transition chosen under the current partial route. This creates a representation--decision mismatch: pairwise cost information may be encoded upstream while the final candidate logit is still largely parameterized as context--node compatibility. We propose a decoder-design principle for neural asymmetric routing: the final score should explicitly expose transition-level quantities suggested by the problem's cost-to-go structure. We instantiate this principle with an edge-aware decoder that adds candidate-specific terms for the current directed edge, return-to-start closure, and static lightweight lookahead, while keeping the representation backbone fixed. On a controlled SVD/Sinkhorn asymmetric backbone, the decoder improves over the RADAR reference when trained on ATSP-100 and evaluated zero-shot on ATSP-100/200/500/1000, reducing the ATSP-1000 gap from $4.13\%$ to $2.73\%$. On ACVRP, the same score-level modification shows the same qualitative trend under a richer routing state. ATSP ablations and directed-transition diagnostics sharpen the mechanism: the strongest evidence concerns sensitivity to the current directed edge, while closure and static lookahead act as heuristic continuation cues. The results support a mechanism study: a key decoder-side signal in neural asymmetric routing is decision-time exposure of transition-level edge information.

Problem

• neural asymmetric routing
• representation--decision mismatch
• directed transition
• edge-aware decoding
• ATSP

Innovation

• edge-aware decoding
• asymmetric routing
• transition-level scoring
• neural combinatorial optimization
• cost-to-go structure