# Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policy

arXiv: https://arxiv.org/abs/2308.14104 · HTML: https://mlsanity.com/paper/2308.14104/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 51 references that are in the map.
- First posted on arXiv 27 Aug 2023.

## Builds on (most cited first, 25 of 25)

- [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)
- [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)
- [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)
- [An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problem](https://mlsanity.com/paper/1906.01227/) (2019)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [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)
- [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)
- [Learning the Travelling Salesperson Problem Requires Rethinking Generalization](https://mlsanity.com/paper/2006.07054/) (2020)
- [Towards Omni-generalizable Neural Methods for Vehicle Routing Problems](https://mlsanity.com/paper/2305.19587/) (2023)
- [Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation](https://mlsanity.com/paper/2210.07686/) (2022)
- [Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problem](https://mlsanity.com/paper/2304.09407/) (2023)
- [Learning to Solve Routing Problems via Distributionally Robust Optimization](https://mlsanity.com/paper/2202.07241/) (2022)
- [Probabilistic Mixture-of-Experts for Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2104.09122/) (2021)
- [How Good Is Neural Combinatorial Optimization? A Systematic Evaluation on the Traveling Salesman Problem](https://mlsanity.com/paper/2209.10913/) (2022)
- [On the Generalization of Neural Combinatorial Optimization Heuristics](https://mlsanity.com/paper/2206.00787/) (2022)
- [Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimization](https://mlsanity.com/paper/2306.02688/) (2023)

## Built on by (most cited first, 30 of 62)

- [ReEvo: Large Language Models as Hyper-Heuristics with Reflective Evolution](https://mlsanity.com/paper/2402.01145/) (2024)
- [MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts](https://mlsanity.com/paper/2405.01029/) (2024)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2402.16891/) (2024)
- [INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer](https://mlsanity.com/paper/2402.02317/) (2024)
- [Rethinking Light Decoder-based Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2503.00753/) (2025)
- [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)
- [Learning to Reduce Search Space for Generalizable Neural Routing Solver](https://mlsanity.com/paper/2503.03137/) (2025)
- [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)
- [DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems](https://mlsanity.com/paper/2406.19705/) (2024)
- [RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization](https://mlsanity.com/paper/2503.16159/) (2025)
- [Preference Optimization for Combinatorial Optimization Problems](https://mlsanity.com/paper/2505.08735/) (2025)
- [Hierarchical Neural Constructive Solver for Real-world TSP Scenarios](https://mlsanity.com/paper/2408.03585/) (2024)
- [Learning to Insert for Constructive Neural Vehicle Routing Solver](https://mlsanity.com/paper/2505.13904/) (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)
- [An Efficient Diffusion-based Non-Autoregressive Solver for Traveling Salesman Problem](https://mlsanity.com/paper/2501.13767/) (2025)
- [Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees](https://mlsanity.com/paper/2505.24627/) (2025)
- [URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2509.23413/) (2025)
- [RADAR: Learning to Route with Asymmetry-aware DistAnce Representations](https://mlsanity.com/paper/2603.03388/) (2026)
- [PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization](https://mlsanity.com/paper/2409.03811/) (2024)
- [Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2510.04792/) (2025)
- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [Leader Reward for POMO-Based Neural Combinatorial Optimization](https://mlsanity.com/paper/2405.13947/) (2024)
- [Neural Solver Selection for Combinatorial Optimization](https://mlsanity.com/paper/2410.09693/) (2024)
- [Learning to Segment for Vehicle Routing Problems](https://mlsanity.com/paper/2507.01037/) (2025)
- [An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problems](https://mlsanity.com/paper/2510.16701/) (2025)

## Abstract (arXiv)

Machine learning has been adapted to help solve NP-hard combinatorial optimization problems. One prevalent way is learning to construct solutions by deep neural networks, which has been receiving more and more attention due to the high efficiency and less requirement for expert knowledge. However, many neural construction methods for Vehicle Routing Problems~(VRPs) focus on synthetic problem instances with specified node distributions and limited scales, leading to poor performance on real-world problems which usually involve complex and unknown node distributions together with large scales. To make neural VRP solvers more practical, we design an auxiliary policy that learns from the local transferable topological features, named local policy, and integrate it with a typical construction policy (which learns from the global information of VRP instances) to form an ensemble policy. With joint training, the aggregated policies perform cooperatively and complementarily to boost generalization. The experimental results on two well-known benchmarks, TSPLIB and CVRPLIB, of travelling salesman problem and capacitated VRP show that the ensemble policy significantly improves both cross-distribution and cross-scale generalization performance, and even performs well on real-world problems with several thousand nodes.