mlsanityData to 7 Oct 2026

INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer

arXiv 2402.02317 ↗First posted 4 Feb 2024cs.LGcited by 43

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Abstract (arXiv)

Recently, deep reinforcement learning has shown promising results for learning fast heuristics to solve routing problems. Meanwhile, most of the solvers suffer from generalizing to an unseen distribution or distributions with different scales. To address this issue, we propose a novel architecture, called Invariant Nested View Transformer (INViT), which is designed to enforce a nested design together with invariant views inside the encoders to promote the generalizability of the learned solver. It applies a modified policy gradient algorithm enhanced with data augmentations. We demonstrate that the proposed INViT achieves a dominant generalization performance on both TSP and CVRP problems with various distributions and different problem scales.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). Builds on 30 of its 45 references that are in the map. First posted on arXiv 4 Feb 2024.

Builds on

30 of 45 references.

References · 30

  1. 2017Attention Is All You Needcited by 59,932
  2. 2013Playing Atari with Deep Reinforcement Learningcited by 3,211
  3. 2015Pointer Networkscited by 882
  4. 2018Attention, Learn to Solve Routing Problems!cited by 646
  5. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  6. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 557
  7. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  8. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 341
  9. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
  10. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
  11. 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 161
  12. 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
18 more
  1. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
  2. 2020Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhoodcited by 122
  3. 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
  4. 2021Efficient Active Search for Combinatorial Optimization Problemscited by 99
  5. 2020Learning the Travelling Salesperson Problem Requires Rethinking Generalizationcited by 96
  6. 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
  7. 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 82
  8. 2019Combinatorial Optimization by Graph Pointer Networks and Hierarchical Reinforcement Learningcited by 78
  9. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
  10. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
  11. 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 61
  12. 2023Unsupervised Learning for Solving the Travelling Salesman Problemcited by 57
  13. 2023Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problemcited by 49
  14. 2023H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problemcited by 43
  15. 2022Learning to Solve Routing Problems via Distributionally Robust Optimizationcited by 31
  16. 2021Improving Generalization of Deep Reinforcement Learning-based TSP Solverscited by 8
  17. 2021Generalization in Deep RL for TSP Problems via Equivariance and Local Searchcited by 8
  18. 2023Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problemscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 5; 2025: 19; 2026: 19.

43 papers.

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  1. 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 36
  2. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
  3. 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
  4. 2025BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimizationcited by 14
  5. 2025MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solvercited by 13
  6. 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
  7. 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
  8. 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
  9. 2024Bridging Large Language Models and Optimization: A Unified Framework for Text-attributed Combinatorial Optimizationcited by 8
  10. 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degreescited by 7
  11. 2025URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalizationcited by 7
  12. 2025Hybrid-Balance GFlowNet for Solving Vehicle Routing Problemscited by 7
31 more
  1. 2024Neural Solver Selection for Combinatorial Optimizationcited by 5
  2. 2025Learning to Segment for Vehicle Routing Problemscited by 5
  3. 2026Survey on Neural Routing Solverscited by 4
  4. 2024Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solverscited by 3
  5. 2025GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scalescited by 3
  6. 2025Efficient Neural Combinatorial Optimization Solver for the Min-max Heterogeneous Capacitated Vehicle Routing Problemcited by 3
  7. 2025LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solverscited by 2
  8. 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problemscited by 2
  9. 2025ASAP: Exploiting the Satisficing Generalization Edge in Neural Combinatorial Optimizationcited by 1
  10. 2025Lifelong Learning with Behavior Consolidation for Vehicle Routingcited by 1
  11. 2025ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problemscited by 1
  12. 2025Empowering Targeted Neighborhood Search via Hyper Tour for Large-Scale TSPcited by 1
  13. 2026Efficient Decoder Scaling Strategy for Neural Routing Solverscited by 1
  14. 2026Aligning LLMs with Graph Neural Solvers for Combinatorial Optimizationcited by 1
  15. 2026Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solvercited by 1
  16. 2026Learning with Foresight: Enhancing Neural Routing Policy via Multi-Node Lookahead Predictioncited by 1
  17. 2026SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solvercited by 1
  18. 2026Leveraging Structural Constraints for Diffusion-based Neural TSP Solverscited by 1
  19. 2026HyCO: A Hybrid Neural Solver for Combinatorial Optimizationcited by 1
  20. 2025RsGCN: Subgraph-Based Rescaling Enhances Generalization of GCNs for Solving Traveling Salesman Problemscited by 0
  21. 2025NeuFACO: Neural Focused Ant Colony Optimization for Traveling Salesman Problemcited by 0
  22. 2026SEAFormer: A Spatial Proximity and Edge-Aware Transformer for Real-World Vehicle Routing Problemscited by 0
  23. 2026Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Taskscited by 0
  24. 2026Neural Cluster First, Route Second: Capacitated Vehicle Routing via Differentiable Optimal Transportcited by 0
  25. 2026MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routingcited by 0
  26. 2026Beyond Static Priors: Dynamic Neural Guidance for Large-Scale Ant Colony Optimizationcited by 0
  27. 2026AGDN: Learning to Solve Traveling Salesman Problem with Anisotropic Graph Diffusion Networkcited by 0
  28. 2026LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solverscited by 0
  29. 2026Depot-Closed Multi-Component Construction for Neural Vehicle Routingcited by 0
  30. 2026Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimizationcited by 0
  31. 2026MiLoop: Selective Memory Propagation for Neural Combinatorial Optimizationcited by 0