# Cross-Problem Learning for Solving Vehicle Routing Problems

arXiv: https://arxiv.org/abs/2404.11677 · HTML: https://mlsanity.com/paper/2404.11677/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 57 references that are in the map.
- First posted on arXiv 17 Apr 2024.

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [Unified Language Model Pre-training for Natural Language Understanding and Generation](https://mlsanity.com/paper/1905.03197/) (2019)
- [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)
- [GCC: Graph Contrastive Coding for Graph Neural Network Pre-Training](https://mlsanity.com/paper/2006.09963/) (2020)
- [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)
- [LST: Ladder Side-Tuning for Parameter and Memory Efficient Transfer Learning](https://mlsanity.com/paper/2206.06522/) (2022)
- [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)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems](https://mlsanity.com/paper/2210.04123/) (2022)
- [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)
- [NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problem](https://mlsanity.com/paper/2110.07983/) (2021)

## Built on by (most cited first, 24 of 24)

- [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)
- [GOAL: A Generalist Combinatorial Optimization Agent Learner](https://mlsanity.com/paper/2406.15079/) (2024)
- [Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives](https://mlsanity.com/paper/2406.00415/) (2024)
- [MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver](https://mlsanity.com/paper/2506.02935/) (2025)
- [URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2509.23413/) (2025)
- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [EFormer: An Effective Edge-based Transformer for Vehicle Routing Problems](https://mlsanity.com/paper/2506.16428/) (2025)
- [Survey on Neural Routing Solvers](https://mlsanity.com/paper/2602.21761/) (2026)
- [Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2503.10421/) (2025)
- [Towards Efficient Constraint Handling in Neural Solvers for Routing Problems](https://mlsanity.com/paper/2602.16012/) (2026)
- [TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problems](https://mlsanity.com/paper/2503.12662/) (2025)
- [Lifelong Learner: Discovering Versatile Neural Solvers for Vehicle Routing Problems](https://mlsanity.com/paper/2508.11679/) (2025)
- [Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs](https://mlsanity.com/paper/2603.01667/) (2026)
- [SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver](https://mlsanity.com/paper/2605.24484/) (2026)
- [Boosting Cross-problem Generalization in Diffusion-Based Neural Combinatorial Solver via Inference Time Adaptation](https://mlsanity.com/paper/2502.12188/) (2025)
- [Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2603.27169/) (2026)
- [Vision-Assisted Foundation Model for Solving Multi-Task Vehicle Routing Problems](https://mlsanity.com/paper/2606.10431/) (2026)
- [LRM-1B: Towards Large Routing Model](https://mlsanity.com/paper/2507.03300/) (2025)
- [GAMA: A Neural Neighborhood Search Method with Graph-aware Multi-modal Attention for Vehicle Routing Problem](https://mlsanity.com/paper/2511.07850/) (2025)
- [Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks](https://mlsanity.com/paper/2601.22509/) (2026)
- [Can Computational Reducibility Lead to Transferable Models for Graph Combinatorial Optimization?](https://mlsanity.com/paper/2603.02462/) (2026)
- [Enhancing Cross-Problem Vehicle Routing via Federated Learning](https://mlsanity.com/paper/2604.10652/) (2026)
- [LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers](https://mlsanity.com/paper/2607.17708/) (2026)

## Abstract (arXiv)

Existing neural heuristics often train a deep architecture from scratch for each specific vehicle routing problem (VRP), ignoring the transferable knowledge across different VRP variants. This paper proposes the cross-problem learning to assist heuristics training for different downstream VRP variants. Particularly, we modularize neural architectures for complex VRPs into 1) the backbone Transformer for tackling the travelling salesman problem (TSP), and 2) the additional lightweight modules for processing problem-specific features in complex VRPs. Accordingly, we propose to pre-train the backbone Transformer for TSP, and then apply it in the process of fine-tuning the Transformer models for each target VRP variant. On the one hand, we fully fine-tune the trained backbone Transformer and problem-specific modules simultaneously. On the other hand, we only fine-tune small adapter networks along with the modules, keeping the backbone Transformer still. Extensive experiments on typical VRPs substantiate that 1) the full fine-tuning achieves significantly better performance than the one trained from scratch, and 2) the adapter-based fine-tuning also delivers comparable performance while being notably parameter-efficient. Furthermore, we empirically demonstrate the favorable effect of our method in terms of cross-distribution application and versatility.