# Towards Omni-generalizable Neural Methods for Vehicle Routing Problems

arXiv: https://arxiv.org/abs/2305.19587 · HTML: https://mlsanity.com/paper/2305.19587/

## Key facts

- Cited by 69 papers in the map (data through 14 Oct 2026).
- Builds on 53 of its 80 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalization](https://mlsanity.com/paper/1911.08731/) (2019)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [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)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAML](https://mlsanity.com/paper/1909.09157/) (2019)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Residual Gated Graph ConvNets](https://mlsanity.com/paper/1711.07553/) (2017)
- [Reinforcement Learning for Solving the Vehicle Routing Problem](https://mlsanity.com/paper/1802.04240/) (2018)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [ReZero is All You Need: Fast Convergence at Large Depth](https://mlsanity.com/paper/2003.04887/) (2020)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [Learning a SAT Solver from Single-Bit Supervision](https://mlsanity.com/paper/1802.03685/) (2018)
- [Learning to Perform Local Rewriting for Combinatorial Optimization](https://mlsanity.com/paper/1810.00337/) (2018)
- [Learning Improvement Heuristics for Solving Routing Problems](https://mlsanity.com/paper/1912.05784/) (2019)
- [Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instances](https://mlsanity.com/paper/2012.10658/) (2020)
- [Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learning](https://mlsanity.com/paper/2010.12367/) (2020)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [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 Delegate for Large-scale Vehicle Routing](https://mlsanity.com/paper/2107.04139/) (2021)
- [Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer](https://mlsanity.com/paper/2110.02544/) (2021)

## Built on by (most cited first, 30 of 69)

- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (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)
- [Algorithm Evolution Using Large Language Model](https://mlsanity.com/paper/2311.15249/) (2023)
- [INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer](https://mlsanity.com/paper/2402.02317/) (2024)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [Learning to Handle Complex Constraints for Vehicle Routing Problems](https://mlsanity.com/paper/2410.21066/) (2024)
- [Large Language Models as End-to-end Combinatorial Optimization Solvers](https://mlsanity.com/paper/2509.16865/) (2025)
- [CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention](https://mlsanity.com/paper/2412.00346/) (2024)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problems](https://mlsanity.com/paper/2405.17272/) (2024)
- [Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problems](https://mlsanity.com/paper/2401.06979/) (2024)
- [Graph Neural Networks for Job Shop Scheduling Problems: A Survey](https://mlsanity.com/paper/2406.14096/) (2024)
- [Reinforced In-Context Black-Box Optimization](https://mlsanity.com/paper/2402.17423/) (2024)
- [Learning to Reduce Search Space for Generalizable Neural Routing Solver](https://mlsanity.com/paper/2503.03137/) (2025)
- [Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement](https://mlsanity.com/paper/2310.15195/) (2023)
- [MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver](https://mlsanity.com/paper/2506.02935/) (2025)
- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
- [Preference Optimization for Combinatorial Optimization Problems](https://mlsanity.com/paper/2505.08735/) (2025)
- [Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solver](https://mlsanity.com/paper/2405.01906/) (2024)
- [Collaboration! Towards Robust Neural Methods for Routing Problems](https://mlsanity.com/paper/2410.04968/) (2024)
- [Generalizable Heuristic Generation Through LLMs with Meta-Optimization](https://mlsanity.com/paper/2505.20881/) (2025)
- [Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimization](https://mlsanity.com/paper/2408.12214/) (2024)
- [Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees](https://mlsanity.com/paper/2505.24627/) (2025)
- [Learning for routing: A guided review of recent developments and future directions](https://mlsanity.com/paper/2507.00218/) (2025)
- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [Prompt Learning for Generalized Vehicle Routing](https://mlsanity.com/paper/2405.12262/) (2024)
- [Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computation](https://mlsanity.com/paper/2506.08898/) (2025)

## Abstract (arXiv)

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.