mlsanityData to 7 Oct 2026

Learning to Solve Routing Problems via Distributionally Robust Optimization

arXiv 2202.07241 ↗First posted 15 Feb 2022cs.LG cs.AIcited by 31

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Abstract (arXiv)

Recent deep models for solving routing problems always assume a single distribution of nodes for training, which severely impairs their cross-distribution generalization ability. In this paper, we exploit group distributionally robust optimization (group DRO) to tackle this issue, where we jointly optimize the weights for different groups of distributions and the parameters for the deep model in an interleaved manner during training. We also design a module based on convolutional neural network, which allows the deep model to learn more informative latent pattern among the nodes. We evaluate the proposed approach on two types of well-known deep models including GCN and POMO. The experimental results on the randomly synthesized instances and the ones from two benchmark dataset (i.e., TSPLib and CVRPLib) demonstrate that our approach could significantly improve the cross-distribution generalization performance over the original models.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). Builds on 22 of its 39 references that are in the map. First posted on arXiv 15 Feb 2022.

Builds on

22 of 39 references.

References · 22

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2015Pointer Networkscited by 882
  3. 2018Attention, Learn to Solve Routing Problems!cited by 646
  4. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
  5. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  6. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 557
  7. 2018Fairness Without Demographics in Repeated Loss Minimizationcited by 363
  8. 2018Quantifying Generalization in Reinforcement Learningcited by 345
  9. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 341
  10. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  11. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
  12. 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 183
10 more
  1. 2019Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learningcited by 169
  2. 2019Learning Improvement Heuristics for Solving Routing Problemscited by 162
  3. 2016Variance-based regularization with convex objectivescited by 153
  4. 2019Distributionally Robust Language Modelingcited by 142
  5. 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
  6. 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
  7. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 102
  8. 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
  9. 2021Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problemcited by 31
  10. 2020Towards Feature-free TSP Solver Selection: A Deep Learning Approachcited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 10; 2024: 7; 2025: 7; 2026: 6.

31 papers.

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  1. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
  2. 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
  3. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
  4. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
  5. 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 61
  6. 2023Pointerformer: Deep Reinforced Multi-Pointer Transformer for the Traveling Salesman Problemcited by 49
  7. 2024Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalizationcited by 49
  8. 2024INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformercited by 43
  9. 2024Cross-Problem Learning for Solving Vehicle Routing Problemscited by 24
  10. 2023Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimizationcited by 23
  11. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
  12. 2023Promoting Generalization for Exact Solvers via Adversarial Instance Augmentationcited by 12
19 more
  1. 2023Too Big, so Fail? -- Enabling Neural Construction Methods to Solve Large-Scale Routing Problemscited by 6
  2. 2024Less Is More -- On the Importance of Sparsification for Transformers and Graph Neural Networks for TSPcited by 6
  3. 2024Prompt Learning for Generalized Vehicle Routingcited by 6
  4. 2025Learning for routing: A guided review of recent developments and future directionscited by 6
  5. 2024Neural Solver Selection for Combinatorial Optimizationcited by 5
  6. 2026Survey on Neural Routing Solverscited by 4
  7. 2023Revisit the Algorithm Selection Problem for TSP with Spatial Information Enhanced Graph Neural Networkscited by 3
  8. 2025SFT-GO: Supervised Fine-Tuning with Group Optimization for Large Language Modelscited by 2
  9. 2025Lifelong Learner: Discovering Versatile Neural Solvers for Vehicle Routing Problemscited by 2
  10. 2026Game-Theoretic Co-Evolution for LLM-Based Heuristic Discoverycited by 2
  11. 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problemscited by 2
  12. 2025Bandit based Dynamic Candidate Edge Selection in Solving Traveling Salesman Problemscited by 1
  13. 2025Lifelong Learning with Behavior Consolidation for Vehicle Routingcited by 1
  14. 2025Enhancing the Cross-Size Generalization for Solving Vehicle Routing Problems via Continual Learningcited by 1
  15. 2023Graph Attention-based Deep Reinforcement Learning for solving the Chinese Postman Problem with Load-dependent costscited by 0
  16. 2025LRM-1B: Towards Large Routing Modelcited by 0
  17. 2026Generating Diverse TSP Tours via a Combination of Graph Pointer Network and Dispersioncited by 0
  18. 2026Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Taskscited by 0
  19. 2026Towards Generalization-Oriented Models for Vehicle Routing Problems with Mixture-of-Expertscited by 0