Research map / Probabilistic and scientific modeling / Molecules and proteins

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

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Equivariant and disentangled latent representations · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes SPACE, a generalist neural routing solver that unifies symmetric and asymmetric VRPs via a coordinate-free bidirectional Fréchet pivot embedding (furthest pivot sampling) and weight-decomposed adaptive decoding built on URS.

Problem

Generalist neural VRP solvers either handle only symmetric instances or degrade on asymmetric ones, because coordinate-based encodings are unavailable or inconsistent for asymmetric costs.

Approach

Represent each node by its outgoing and incoming distances to a furthest-pivot-sampled set (bidirectional Fréchet representation, motivated by Bourgain's embedding), and decode with a DoRA-style weight-decomposed adapter composed from active constraint attributes, so geometry perception is decoupled from problem constraints.

Key results

• On 1000-node CVRPB, SPACE reaches -11.63% average gap versus URS -0.09%, with asymmetric gap -19.10%.
• On 12 seen VRPs, SPACE's ACVRP100 gap is 2.67% versus URS 3.06%, but on CVRPTW100 SPACE is 5.36% vs URS 6.13%.
• On CVRPLIB Set-X and Set-XXL, SPACE achieves 8.34% overall gap vs URS 9.20%, solving 34/34 instances.

Surprising findings

• Removing explicit coordinates entirely (URS-Dist) degrades symmetric performance, showing the trade-off between symmetric and asymmetric settings.
• On some symmetric unseen variants (e.g., MDCVRPLTW, OCVRPBTW-like cases), SPACE is not the best, and on constraint-heavy variants it underperforms ReLD-MTL on seen problems.

Limitations

• Deliberately reduces reliance on problem-specific constraint states, using a model-agnostic masking, which can weaken constraint-aware performance on constraint-heavy variants.
• Theoretical lower-bound/non-contraction guarantee requires an additional pivot-separation condition; only non-expansiveness holds unconditionally.

Experimental setup

Datasets: on-the-fly generated synthetic VRP instances (12 training variants) CVRPLIB Set-X CVRPLIB Set-XXL

Benchmarks: 110 VRP variants (12 seen, 98 unseen) CVRPLIB Set-X CVRPLIB Set-XXL 1000-node CVRPB, OCVRP, CVRPTW

Metrics: optimality gap inference time

Baselines: MVMoE MTPOMO ReLD-MTL RouteFinder CaDA GOAL-MTL URS

Builds on: URS Bourgain's embedding theorem DoRA Attention Model POMO

Closest papers by meaning

• Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP (NeurIPS 2025 · similarity 0.89)
• A Mixed-Curvature based Pre-training Paradigm for Multi-Task Vehicle Routing Solver (ICML 2025 · similarity 0.89)
• Rethinking Light Decoder-based Solvers for Vehicle Routing Problems (ICLR 2025 · similarity 0.88)
• MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts (ICML 2024 · similarity 0.88)
• Learning to Solve Compositional Geometry Routing Problems (NeurIPS 2026 · similarity 0.88)
• DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems (ICML 2024 · similarity 0.86)