mlsanityData to 7 Oct 2026

Reinforcement Learning for Solving the Vehicle Routing Problem

arXiv 1802.04240 ↗First posted 12 Feb 2018cs.AI cs.LG stat.MLcited by 327

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Abstract (arXiv)

We present an end-to-end framework for solving the Vehicle Routing Problem (VRP) using reinforcement learning. In this approach, we train a single model that finds near-optimal solutions for problem instances sampled from a given distribution, only by observing the reward signals and following feasibility rules. Our model represents a parameterized stochastic policy, and by applying a policy gradient algorithm to optimize its parameters, the trained model produces the solution as a sequence of consecutive actions in real time, without the need to re-train for every new problem instance. On capacitated VRP, our approach outperforms classical heuristics and Google's OR-Tools on medium-sized instances in solution quality with comparable computation time (after training). We demonstrate how our approach can handle problems with split delivery and explore the effect of such deliveries on the solution quality. Our proposed framework can be applied to other variants of the VRP such as the stochastic VRP, and has the potential to be applied more generally to combinatorial optimization problems.

Key facts. Cited by 327 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Feb 2018.

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Citing papers per year: 2021: 60; 2022: 59; 2023: 51; 2024: 52; 2025: 58; 2026: 47.

327 papers.

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  1. 2023Large Language Models as Optimizerscited by 830
  2. 2021Combinatorial optimization and reasoning with graph neural networkscited by 267
  3. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  4. 2021End-to-End Constrained Optimization Learning: A Surveycited by 154
  5. 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
  6. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
  7. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
  8. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 108
  9. 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
  10. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 102
  11. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 99
  12. 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
38 more
  1. 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
  2. 2021Learning Collaborative Policies to Solve NP-hard Routing Problemscited by 86
  3. 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
  4. 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
  5. 2023BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimizationcited by 80
  6. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
  7. 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
  8. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
  9. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
  10. 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 61
  11. 2021The Transformer Network for the Traveling Salesman Problemcited by 59
  12. 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 57
  13. 2022Pareto Set Learning for Neural Multi-objective Combinatorial Optimizationcited by 56
  14. 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
  15. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  16. 2021CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraintscited by 49
  17. 2023Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problemcited by 49
  18. 2024Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalizationcited by 49
  19. 2021Learning to Select Cuts for Efficient Mixed-Integer Programmingcited by 48
  20. 2021Learning a Large Neighborhood Search Algorithm for Mixed Integer Programscited by 41
  21. 2022Equivariant quantum circuits for learning on weighted graphscited by 41
  22. 2022The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insightscited by 39
  23. 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 39
  24. 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 36
  25. 2021Reinforcement Learning for Ridesharing: An Extended Surveycited by 35
  26. 2021Heterogeneous Attentions for Solving Pickup and Delivery Problem via Deep Reinforcement Learningcited by 35
  27. 2024PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimizationcited by 35
  28. 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 32
  29. 2021ScheduleNet: Learn to solve multi-agent scheduling problems with reinforcement learningcited by 31
  30. 2021Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problemcited by 31
  31. 2021Provably Efficient Black-Box Action Poisoning Attacks Against Reinforcement Learningcited by 29
  32. 2022Efficient Neural Neighborhood Search for Pickup and Delivery Problemscited by 29
  33. 2022Backpropagation through Combinatorial Algorithms: Identity with Projection Workscited by 29
  34. 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
  35. 2022Learning to Solve Travelling Salesman Problem with Hardness-adaptive Curriculumcited by 27
  36. 2022Challenges and Opportunities in Deep Reinforcement Learning with Graph Neural Networks: A Comprehensive review of Algorithms and Applicationscited by 27
  37. 2023ASP: Learn a Universal Neural Solver!cited by 27
  38. 2022On the Generalization of Neural Combinatorial Optimization Heuristicscited by 24

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