# RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization

arXiv: https://arxiv.org/abs/2503.16159 · HTML: https://mlsanity.com/paper/2503.16159/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 60 references that are in the map.
- First posted on arXiv 20 Mar 2025.

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/1911.09539/) (2019)
- [Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer](https://mlsanity.com/paper/2110.02544/) (2021)
- [Efficient Active Search for Combinatorial Optimization Problems](https://mlsanity.com/paper/2106.05126/) (2021)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [Matrix Encoding Networks for Neural Combinatorial Optimization](https://mlsanity.com/paper/2106.11113/) (2021)
- [Learning Collaborative Policies to Solve NP-hard Routing Problems](https://mlsanity.com/paper/2110.13987/) (2021)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark](https://mlsanity.com/paper/2306.17100/) (2023)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy](https://mlsanity.com/paper/2308.14104/) (2023)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)
- [PyVRP: a high-performance VRP solver package](https://mlsanity.com/paper/2403.13795/) (2023)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2407.00312/) (2024)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Combinatorial Optimization with Policy Adaptation using Latent Space Search](https://mlsanity.com/paper/2311.13569/) (2023)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)

## Built on by (most cited first, 11 of 11)

- [RADAR: Learning to Route with Asymmetry-aware DistAnce Representations](https://mlsanity.com/paper/2603.03388/) (2026)
- [Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design](https://mlsanity.com/paper/2509.24509/) (2025)
- [Efficient Neural Combinatorial Optimization Solver for the Min-max Heterogeneous Capacitated Vehicle Routing Problem](https://mlsanity.com/paper/2507.21386/) (2025)
- [Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs](https://mlsanity.com/paper/2603.01667/) (2026)
- [USPR: Learning a Unified Solver for Profiled Routing](https://mlsanity.com/paper/2505.05119/) (2025)
- [Recurrent State Encoders for Efficient Neural Combinatorial Optimization](https://mlsanity.com/paper/2509.05084/) (2025)
- [Beyond Solving: Prescriptive Probing for Neural Routing Solvers](https://mlsanity.com/paper/2602.07216/) (2026)
- [Two-Stage Learned Decomposition for Scalable Routing on Multigraphs](https://mlsanity.com/paper/2605.05389/) (2026)
- [Edge-aware Decoding for Neural Asymmetric Routing](https://mlsanity.com/paper/2606.02136/) (2026)
- [Geometric Self-Supervised Pre-training for Neural Combinatorial Optimization](https://mlsanity.com/paper/2608.00270/) (2026)
- [GREAT-ESDD: Graph Edge Attention Network for Effectively Steered Delivery Decisions](https://mlsanity.com/paper/2610.14792/) (2026)

## Abstract (arXiv)

The practical deployment of Neural Combinatorial Optimization (NCO) for Vehicle Routing Problems (VRPs) is hindered by a critical sim-to-real gap. This gap stems not only from training on oversimplified Euclidean data but also from node-based architectures incapable of handling the node-and-edge-based features with correlated asymmetric cost matrices, such as those for real-world distance and duration. We introduce RRNCO, a novel architecture specifically designed to address these complexities. RRNCO's novelty lies in two key innovations. First, its Adaptive Node Embedding (ANE) efficiently fuses spatial coordinates with real-world distance features using a learned contextual gating mechanism. Second, its Neural Adaptive Bias (NAB) is the first mechanism to jointly model asymmetric distance, duration, and directional angles, enabling it to capture complex, realistic routing constraints. Moreover, we introduce a new VRP benchmark grounded in real-world data crucial for bridging this sim-to-real gap, featuring asymmetric distance and duration matrices from 100 diverse cities, enabling the training and validation of NCO solvers on tasks that are more representative of practical settings. Experiments demonstrate that RRNCO achieves state-of-the-art performance on this benchmark, significantly advancing the practical applicability of neural solvers for real-world logistics. Our code, dataset, and pretrained models are available at https://github.com/ai4co/real-routing-nco.