Learning to Solve Vehicle Routing Problems: A Survey
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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.
Builds on
58 of 120 references.
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50 most cited of 58 All 58 (JSON)
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Citing papers per year: 2022: 1; 2023: 5; 2024: 7; 2025: 3.
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- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 85
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
- 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 34
- 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attentioncited by 24
- 2024AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Searchcited by 8
- 2023Routing Arena: A Benchmark Suite for Neural Routing Solverscited by 5
- 2023A Neural Separation Algorithm for the Rounded Capacity Inequalitiescited by 4
- 2023A Hierarchical Destroy and Repair Approach for Solving Very Large-Scale Travelling Salesman Problemcited by 4
- 2022Learning to repeatedly solve routing problemscited by 3
- 2025Reinforcement Learning for Solving the Pricing Problem in Column Generation: Applications to Vehicle Routingcited by 1
- 2024Pivoting Retail Supply Chain with Deep Generative Techniques: Taxonomy, Survey and Insightscited by 0
4 more
- 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleetcited by 0
- 2024A Coalition Game for On-demand Multi-modal 3D Automated Delivery Systemcited by 0
- 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Applicationcited by 0
- 2025OPTIC-ER: A Reinforcement Learning Framework for Real-Time Emergency Response and Equitable Resource Allocation in Underserved African Communitiescited by 0
- 2025OPTIC-ER: A Reinforcement Learning Framework for Real-Time Emergency Response and Equitable Resource Allocation in Underserved African Communities18 Aug 2025
- 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Application11 Apr 2025
- 2025Reinforcement Learning for Solving the Pricing Problem in Column Generation: Applications to Vehicle Routing3 Apr 2025
- 2024A Coalition Game for On-demand Multi-modal 3D Automated Delivery System23 Dec 2024
- 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention30 Nov 2024
- 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet7 Nov 2024
- 2024AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Search7 Oct 2024
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problems21 Jun 2024
- 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvement22 Mar 2024
- 2024Pivoting Retail Supply Chain with Deep Generative Techniques: Taxonomy, Survey and Insights29 Feb 2024
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time13 Dec 2023
- 2023Routing Arena: A Benchmark Suite for Neural Routing Solvers6 Oct 2023
4 more
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization25 Sep 2023
- 2023A Hierarchical Destroy and Repair Approach for Solving Very Large-Scale Travelling Salesman Problem9 Aug 2023
- 2023A Neural Separation Algorithm for the Rounded Capacity Inequalities29 Jun 2023
- 2022Learning to repeatedly solve routing problems15 Dec 2022
- 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 34
- 2024AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Searchcited by 8
- 2025Reinforcement Learning for Solving the Pricing Problem in Column Generation: Applications to Vehicle Routingcited by 1
- 2024A Coalition Game for On-demand Multi-modal 3D Automated Delivery Systemcited by 0
- 2025OPTIC-ER: A Reinforcement Learning Framework for Real-Time Emergency Response and Equitable Resource Allocation in Underserved African Communitiescited by 0
- 2025OPTIC-ER: A Reinforcement Learning Framework for Real-Time Emergency Response and Equitable Resource Allocation in Underserved African Communities18 Aug 2025
- 2025Reinforcement Learning for Solving the Pricing Problem in Column Generation: Applications to Vehicle Routing3 Apr 2025
- 2024A Coalition Game for On-demand Multi-modal 3D Automated Delivery System23 Dec 2024
- 2024AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Search7 Oct 2024
- 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvement22 Mar 2024
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 85
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
- 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attentioncited by 24
- 2023Routing Arena: A Benchmark Suite for Neural Routing Solverscited by 5
- 2023A Neural Separation Algorithm for the Rounded Capacity Inequalitiescited by 4
- 2023A Hierarchical Destroy and Repair Approach for Solving Very Large-Scale Travelling Salesman Problemcited by 4
- 2022Learning to repeatedly solve routing problemscited by 3
- 2024Pivoting Retail Supply Chain with Deep Generative Techniques: Taxonomy, Survey and Insightscited by 0
- 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleetcited by 0
- 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Applicationcited by 0
- 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Application11 Apr 2025
- 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention30 Nov 2024
- 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet7 Nov 2024
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problems21 Jun 2024
- 2024Pivoting Retail Supply Chain with Deep Generative Techniques: Taxonomy, Survey and Insights29 Feb 2024
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time13 Dec 2023
- 2023Routing Arena: A Benchmark Suite for Neural Routing Solvers6 Oct 2023
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization25 Sep 2023
- 2023A Hierarchical Destroy and Repair Approach for Solving Very Large-Scale Travelling Salesman Problem9 Aug 2023
- 2023A Neural Separation Algorithm for the Rounded Capacity Inequalities29 Jun 2023
- 2022Learning to repeatedly solve routing problems15 Dec 2022