mlsanityData to 14 Oct 2026

Towards Omni-generalizable Neural Methods for Vehicle Routing Problems

arXiv 2305.19587 ↗First posted 31 May 2023cs.LG cs.AIcited by 69

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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.

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

53 of 80 references.

References · 53

  1. 2017Attention Is All You Needcited by 60,361
  2. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  3. 2015Distilling the Knowledge in a Neural Networkcited by 10,324
  4. 2017Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networkscited by 4,897
  5. 2019Distributionally Robust Neural Networks for Group Shifts: On the Importance of Regularization for Worst-Case Generalizationcited by 1,247
  6. 2018On First-Order Meta-Learning Algorithmscited by 1,018
  7. 2020Meta-Learning in Neural Networks: A Surveycited by 950
  8. 2015Pointer Networkscited by 895
  9. 2018Attention, Learn to Solve Routing Problems!cited by 656
  10. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  11. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 608
  12. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 561
38 more
  1. 2019Rapid Learning or Feature Reuse? Towards Understanding the Effectiveness of MAMLcited by 359
  2. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 348
  3. 2017Residual Gated Graph ConvNetscited by 346
  4. 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 333
  5. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 269
  6. 2020ReZero is All You Need: Fast Convergence at Large Depthcited by 264
  7. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 221
  8. 2018Learning a SAT Solver from Single-Bit Supervisioncited by 200
  9. 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 185
  10. 2019Learning Improvement Heuristics for Solving Routing Problemscited by 164
  11. 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 162
  12. 2020Learning to Dispatch for Job Shop Scheduling via Deep Reinforcement Learningcited by 140
  13. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 129
  14. 2020Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhoodcited by 125
  15. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 119
  16. 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
  17. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 109
  18. 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
  19. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 103
  20. 2020Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learningcited by 100
  21. 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
  22. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 100
  23. 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 91
  24. 2021Learning Collaborative Policies to Solve NP-hard Routing Problemscited by 86
  25. 2019Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learningcited by 78
  26. 2021Graph Neural Network Guided Local Search for the Traveling Salesperson Problemcited by 70
  27. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 62
  28. 2020Learning What to Defer for Maximum Independent Setscited by 54
  29. 2021Bootstrapped Meta-Learningcited by 45
  30. 2021Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustnesscited by 35
  31. 2022Learning to Solve Routing Problems via Distributionally Robust Optimizationcited by 31
  32. 2020It's Not What Machines Can Learn, It's What We Cannot Teachcited by 29
  33. 2022Learning to Solve Travelling Salesman Problem with Hardness-adaptive Curriculumcited by 27
  34. 2022How Good Is Neural Combinatorial Optimization? A Systematic Evaluation on the Traveling Salesman Problemcited by 27
  35. 2021A Bi-Level Framework for Learning to Solve Combinatorial Optimization on Graphscited by 26
  36. 2022On the Generalization of Neural Combinatorial Optimization Heuristicscited by 24
  37. 2020Evaluating Curriculum Learning Strategies in Neural Combinatorial Optimizationcited by 19
  38. 2021A Game-Theoretic Approach for Improving Generalization Ability of TSP Solverscited by 14

50 most cited of 53 All 53 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 5; 2024: 22; 2025: 26; 2026: 16.

69 papers.

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  1. 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
  2. 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Expertscited by 70
  3. 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 62
  4. 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
  5. 2023Algorithm Evolution Using Large Language Modelcited by 53
  6. 2024INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformercited by 44
  7. 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 42
  8. 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 37
  9. 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
  10. 2025Large Language Models as End-to-end Combinatorial Optimization Solverscited by 28
  11. 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attentioncited by 24
  12. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
38 more
  1. 2024DPN: Decoupling Partition and Navigation for Neural Solvers of Min-max Vehicle Routing Problemscited by 18
  2. 2024Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problemscited by 15
  3. 2024Graph Neural Networks for Job Shop Scheduling Problems: A Surveycited by 15
  4. 2024Reinforced In-Context Black-Box Optimizationcited by 14
  5. 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
  6. 2023Neural Multi-Objective Combinatorial Optimization with Diversity Enhancementcited by 13
  7. 2025MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solvercited by 13
  8. 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
  9. 2025Preference Optimization for Combinatorial Optimization Problemscited by 11
  10. 2024Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solvercited by 9
  11. 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
  12. 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 9
  13. 2024Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimizationcited by 8
  14. 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degreescited by 8
  15. 2025Learning for routing: A guided review of recent developments and future directionscited by 7
  16. 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDPcited by 7
  17. 2024Prompt Learning for Generalized Vehicle Routingcited by 6
  18. 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computationcited by 6
  19. 2024Moco: A Learnable Meta Optimizer for Combinatorial Optimizationcited by 5
  20. 2024Leader Reward for POMO-Based Neural Combinatorial Optimizationcited by 5
  21. 2024Neural Solver Selection for Combinatorial Optimizationcited by 5
  22. 2025An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problemscited by 5
  23. 2026Survey on Neural Routing Solverscited by 4
  24. 2024Adaptive Stabilization Based on Machine Learning for Column Generationcited by 3
  25. 2024Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solverscited by 3
  26. 2025Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problemscited by 3
  27. 2025GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scalescited by 3
  28. 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problemscited by 3
  29. 2023An Edge-Aware Graph Autoencoder Trained on Scale-Imbalanced Data for Traveling Salesman Problemscited by 2
  30. 2024FlagVNE: A Flexible and Generalizable Reinforcement Learning Framework for Network Resource Allocationcited by 2
  31. 2025TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problemscited by 2
  32. 2025Accelerating Vehicle Routing via AI-Initialized Genetic Algorithmscited by 2
  33. 2025UniCO: Towards a Unified Model for Combinatorial Optimization Problemscited by 2
  34. 2025Lifelong Learner: Discovering Versatile Neural Solvers for Vehicle Routing Problemscited by 2
  35. 2025FORGE: Foundational Optimization Representations from Graph Embeddingscited by 2
  36. 2026Game-Theoretic Co-Evolution for LLM-Based Heuristic Discoverycited by 2
  37. 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPscited by 2
  38. 2026SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solvercited by 2

50 most cited of 69 All 69 (JSON)