mlsanityData to 7 Oct 2026

Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learning

arXiv 2004.01608 ↗First posted 3 Apr 2020cs.LG cs.AI stat.MLcited by 100

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Abstract (arXiv)

Recent works using deep learning to solve the Traveling Salesman Problem (TSP) have focused on learning construction heuristics. Such approaches find TSP solutions of good quality but require additional procedures such as beam search and sampling to improve solutions and achieve state-of-the-art performance. However, few studies have focused on improvement heuristics, where a given solution is improved until reaching a near-optimal one. In this work, we propose to learn a local search heuristic based on 2-opt operators via deep reinforcement learning. We propose a policy gradient algorithm to learn a stochastic policy that selects 2-opt operations given a current solution. Moreover, we introduce a policy neural network that leverages a pointing attention mechanism, which unlike previous works, can be easily extended to more general k-opt moves. Our results show that the learned policies can improve even over random initial solutions and approach near-optimal solutions at a faster rate than previous state-of-the-art deep learning methods.

Key facts. Cited by 100 papers in the map (data through 7 Oct 2026). First posted on arXiv 3 Apr 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 17; 2022: 12; 2023: 16; 2024: 22; 2025: 24; 2026: 9.

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  1. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  2. 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
  3. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
  4. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
  5. 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
  6. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 102
  7. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 99
  8. 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
  9. 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
  10. 2021Learning Collaborative Policies to Solve NP-hard Routing Problemscited by 86
  11. 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
  12. 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 82
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  1. 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
  2. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
  3. 2021Graph Neural Network Guided Local Search for the Traveling Salesperson Problemcited by 70
  4. 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
  5. 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Expertscited by 69
  6. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
  7. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
  8. 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 57
  9. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  10. 2023Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problemcited by 49
  11. 2023H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problemcited by 43
  12. 2025Fast T2T: Optimization Consistency Speeds Up Diffusion-Based Training-to-Testing Solving for Combinatorial Optimizationcited by 43
  13. 2023Combinatorial Optimization with Policy Adaptation using Latent Space Searchcited by 41
  14. 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 36
  15. 2024PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimizationcited by 35
  16. 2024Self-Improvement for Neural Combinatorial Optimization: Sample without Replacement, but Improvementcited by 32
  17. 2021ScheduleNet: Learn to solve multi-agent scheduling problems with reinforcement learningcited by 31
  18. 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
  19. 2024Position: Rethinking Post-Hoc Search-Based Neural Approaches for Solving Large-Scale Traveling Salesman Problemscited by 24
  20. 2023Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimizationcited by 23
  21. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
  22. 2021Analytics and Machine Learning in Vehicle Routing Researchcited by 22
  23. 2021An Overview and Experimental Study of Learning-based Optimization Algorithms for Vehicle Routing Problemcited by 22
  24. 2021Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problemscited by 20
  25. 2022Learning to Control Local Search for Combinatorial Optimizationcited by 18
  26. 2022Learning to Solve Vehicle Routing Problems: A Surveycited by 16
  27. 2023Equity-Transformer: Solving NP-hard Min-Max Routing Problems as Sequential Generation with Equity Contextcited by 16
  28. 2024Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomycited by 16
  29. 2025Neural Deconstruction Search for Vehicle Routing Problemscited by 15
  30. 2022Reinforced Lin-Kernighan-Helsgaun Algorithms for the Traveling Salesman Problemscited by 12
  31. 2023Continuation Path Learning for Homotopy Optimizationcited by 12
  32. 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
  33. 2025Preference Optimization for Combinatorial Optimization Problemscited by 11
  34. 2024DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problemscited by 10
  35. 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
  36. 2024Hierarchical Neural Constructive Solver for Real-world TSP Scenarioscited by 9
  37. 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
  38. 2021Improving Generalization of Deep Reinforcement Learning-based TSP Solverscited by 8

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