SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver

2026-05-23

AI Summary

This work addresses the challenge that existing general-purpose neural solvers struggle to uniformly handle both symmetric and asymmetric variants of the Vehicle Routing Problem (VRP). To overcome this limitation, the authors propose a coordinate-agnostic unified embedding framework that constructs spatial representations based on relative distances to pivot nodes. The approach incorporates bidirectional Fréchet representations and a farthest-pivot sampling strategy to generate problem-setting-invariant node embeddings. Additionally, a weight-decomposed adaptive decoding mechanism is introduced to decouple geometric awareness from constraint-aware decision making. Evaluated across 110 VRP variants—including 55 symmetric/asymmetric pairs—the method demonstrates strong zero-shot generalization performance, achieving, for the first time, joint modeling and efficient solution of both symmetric and asymmetric VRPs within a single framework.

Abstract

Generalist neural routing solvers have shown great potential in solving diverse vehicle routing problems (VRPs) with a unified model. However, existing solvers are typically limited to symmetric settings or degrade in performance when switching to asymmetric settings due to input inconsistencies or inherent structural differences, substantially limiting their practicality in real-world scenarios that encompass both scenarios. To address this limitation, we define the spatial position of each node based on the relative distances to a specific set of pivots and further propose a Spatial Pivot-Aligned Coordinate-free Embedding (SPACE) framework that unifies node representation and solution generation across symmetric and asymmetric VRPs. Specifically, we construct a bidirectional Frechet representation using a novel furthest pivot sampling strategy to enable invariant node representations across distinct problem settings. Furthermore, we introduce a weight-decomposed adaptive decoding mechanism that decouples geometric perception from problem representations, mitigating the overfitting of constraint decisions to a specific geometry setting. Extensive experiments on 110 VRP variants, comprising 55 symmetric problems and their asymmetric counterparts, demonstrate that SPACE achieves promising zero-shot generalization in both symmetric and asymmetric VRPs.

Problem

• vehicle routing problems
• symmetric routing
• asymmetric routing
• generalist neural solver
• zero-shot generalization

Innovation

• SPACE
• coordinate-free embedding
• asymmetric VRP
• zero-shot generalization
• pivot-based representation