mlsanityData to 14 Oct 2026

Learning to Solve Vehicle Routing Problems: A Survey

arXiv 2205.02453 ↗First posted 5 May 2022cs.LGcited by 16

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Abstract (arXiv)

This paper provides a systematic overview of machine learning methods applied to solve NP-hard Vehicle Routing Problems (VRPs). Recently, there has been a great interest from both machine learning and operations research communities to solve VRPs either by pure learning methods or by combining them with the traditional hand-crafted heuristics. We present the taxonomy of the studies for learning paradigms, solution structures, underlying models, and algorithms. We present in detail the results of the state-of-the-art methods demonstrating their competitiveness with the traditional methods. The paper outlines the future research directions to incorporate learning-based solutions to overcome the challenges of modern transportation systems.

Key facts. Cited by 16 papers in the map (data through 14 Oct 2026). Builds on 58 of its 120 references that are in the map. First posted on arXiv 5 May 2022.

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58 of 120 references.

References · 58

  1. 2017Attention Is All You Needcited by 60,361
  2. 2017Proximal Policy Optimization Algorithmscited by 15,215
  3. 2014Neural Machine Translation by Jointly Learning to Align and Translatecited by 4,548
  4. 2015Continuous control with deep reinforcement learningcited by 3,407
  5. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,258
  6. 2015Deep Reinforcement Learning with Double Q-learningcited by 1,745
  7. 2017Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environmentscited by 1,558
  8. 2015Prioritized Experience Replaycited by 1,099
  9. 2017Counterfactual Multi-Agent Policy Gradientscited by 751
  10. 2018Attention, Learn to Solve Routing Problems!cited by 656
  11. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  12. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 608
38 more
  1. 2019Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithmscited by 567
  2. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 561
  3. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 348
  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. 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
  7. 2020Reinforcement Learning for Combinatorial Optimization: A Surveycited by 236
  8. 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 185
  9. 2018A Survey and Critique of Multiagent Deep Reinforcement Learningcited by 177
  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. 2017Deep Decentralized Multi-task Multi-Agent Reinforcement Learning under Partial Observabilitycited by 148
  13. 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
  14. 2018Strong mixed-integer programming formulations for trained neural networkscited by 115
  15. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 109
  16. 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
  17. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 103
  18. 2020Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learningcited by 100
  19. 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
  20. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 100
  21. 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
  22. 2019Deep Reinforcement Learning for Multi-objective Optimizationcited by 90
  23. 2021Learning Collaborative Policies to Solve NP-hard Routing Problemscited by 86
  24. 2019Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learningcited by 78
  25. 2020Learning Combinatorial Optimization on Graphs: A Survey with Applications to Networkingcited by 70
  26. 2020Combining Reinforcement Learning and Constraint Programming for Combinatorial Optimizationcited by 63
  27. 2020Reinforcement Learning with Combinatorial Actions: An Application to Vehicle Routingcited by 61
  28. 2018Learning to Solve NP-Complete Problems - A Graph Neural Network for Decision TSPcited by 58
  29. 2020Learning to Solve Combinatorial Optimization Problems on Real-World Graphs in Linear Timecited by 39
  30. 2021Heterogeneous Attentions for Solving Pickup and Delivery Problem via Deep Reinforcement Learningcited by 36
  31. 2021Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problemcited by 31
  32. 2020A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problemscited by 30
  33. 2020Multi-Vehicle Routing Problems with Soft Time Windows: A Multi-Agent Reinforcement Learning Approachcited by 30
  34. 2020Learning to Solve Vehicle Routing Problems with Time Windows through Joint Attentioncited by 29
  35. 2018Learning Permutations with Sinkhorn Policy Gradientcited by 26
  36. 2020Deep Reinforcement Learning for Electric Vehicle Routing Problem with Time Windowscited by 25
  37. 2019On Learning Paradigms for the Travelling Salesman Problemcited by 24
  38. 2020Learn to Design the Heuristics for Vehicle Routing Problemcited by 24

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Citing papers per year: 2022: 1; 2023: 5; 2024: 7; 2025: 3.

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  1. 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 85
  2. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
  3. 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
  4. 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 34
  5. 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attentioncited by 24
  6. 2024AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Searchcited by 8
  7. 2023Routing Arena: A Benchmark Suite for Neural Routing Solverscited by 5
  8. 2023A Neural Separation Algorithm for the Rounded Capacity Inequalitiescited by 4
  9. 2023A Hierarchical Destroy and Repair Approach for Solving Very Large-Scale Travelling Salesman Problemcited by 4
  10. 2022Learning to repeatedly solve routing problemscited by 3
  11. 2025Reinforcement Learning for Solving the Pricing Problem in Column Generation: Applications to Vehicle Routingcited by 1
  12. 2024Pivoting Retail Supply Chain with Deep Generative Techniques: Taxonomy, Survey and Insightscited by 0
4 more
  1. 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleetcited by 0
  2. 2024A Coalition Game for On-demand Multi-modal 3D Automated Delivery Systemcited by 0
  3. 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Applicationcited by 0
  4. 2025OPTIC-ER: A Reinforcement Learning Framework for Real-Time Emergency Response and Equitable Resource Allocation in Underserved African Communitiescited by 0