Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillation
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Abstract (arXiv)
Recent neural methods for vehicle routing problems always train and test the deep models on the same instance distribution (i.e., uniform). To tackle the consequent cross-distribution generalization concerns, we bring the knowledge distillation to this field and propose an Adaptive Multi-Distribution Knowledge Distillation (AMDKD) scheme for learning more generalizable deep models. Particularly, our AMDKD leverages various knowledge from multiple teachers trained on exemplar distributions to yield a light-weight yet generalist student model. Meanwhile, we equip AMDKD with an adaptive strategy that allows the student to concentrate on difficult distributions, so as to absorb hard-to-master knowledge more effectively. Extensive experimental results show that, compared with the baseline neural methods, our AMDKD is able to achieve competitive results on both unseen in-distribution and out-of-distribution instances, which are either randomly synthesized or adopted from benchmark datasets (i.e., TSPLIB and CVRPLIB). Notably, our AMDKD is generic, and consumes less computational resources for inference.
Key facts. Cited by 61 papers in the map (data through 7 Oct 2026). Builds on 40 of its 58 references that are in the map. First posted on arXiv 14 Oct 2022.
Builds on
40 of 58 references.
References · 40
- 2017Attention Is All You Needcited by 59,932
- 2015Distilling the Knowledge in a Neural Networkcited by 10,076
- 2019TinyBERT: Distilling BERT for Natural Language Understandingcited by 1,153
- 2015Pointer Networkscited by 882
- 2018Attention, Learn to Solve Routing Problems!cited by 646
- 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
- 2017Learning Combinatorial Optimization Algorithms over Graphscited by 557
- 2018Born Again Neural Networkscited by 539
- 2015Policy Distillationcited by 414
- 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 341
- 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 327
- 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
28 more
- 2020FastBERT: a Self-distilling BERT with Adaptive Inference Timecited by 224
- 2021Does Knowledge Distillation Really Work?cited by 187
- 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 183
- 2020Self-Distillation Amplifies Regularization in Hilbert Spacecited by 171
- 2019Learning Improvement Heuristics for Solving Routing Problemscited by 162
- 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 161
- 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
- 2021Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformercited by 108
- 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 102
- 2020Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learningcited by 100
- 2020Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problemscited by 100
- 2021Efficient Active Search for Combinatorial Optimization Problemscited by 99
- 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
- 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 89
- 2021Learning Collaborative Policies to Solve NP-hard Routing Problemscited by 86
- 2021One Teacher is Enough? Pre-trained Language Model Distillation from Multiple Teacherscited by 39
- 2021Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustnesscited by 35
- 2021Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problemcited by 31
- 2022Learning to Solve Routing Problems via Distributionally Robust Optimizationcited by 31
- 2020A Deep Reinforcement Learning Algorithm Using Dynamic Attention Model for Vehicle Routing Problemscited by 30
- 2022Efficient Neural Neighborhood Search for Pickup and Delivery Problemscited by 29
- 2022Learning to Solve Travelling Salesman Problem with Hardness-adaptive Curriculumcited by 27
- 2021Meta-Learning-Based Deep Reinforcement Learning for Multiobjective Optimization Problemscited by 20
- 2022Quantifying the Knowledge in a DNN to Explain Knowledge Distillation for Classificationcited by 19
- 2018Attention-Guided Answer Distillation for Machine Reading Comprehensioncited by 18
- 2021A Game-Theoretic Approach for Improving Generalization Ability of TSP Solverscited by 14
- 2018Progressive Reinforcement Learning with Distillation for Multi-Skilled Motion Controlcited by 12
- 2022Learning to Solve Multiple-TSP with Time Window and Rejections via Deep Reinforcement Learningcited by 8
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Citing papers per year: 2023: 17; 2024: 15; 2025: 15; 2026: 14.
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- 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 82
- 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
- 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
- 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Expertscited by 69
- 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
- 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 61
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
- 2024INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformercited by 43
- 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 39
- 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 36
38 more
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2023ASP: Learn a Universal Neural Solver!cited by 27
- 2024Cross-Problem Learning for Solving Vehicle Routing Problemscited by 24
- 2023Meta-SAGE: Scale Meta-Learning Scheduled Adaptation with Guided Exploration for Mitigating Scale Shift on Combinatorial Optimizationcited by 23
- 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
- 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attentioncited by 23
- 2023Distilling Autoregressive Models to Obtain High-Performance Non-Autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speedcited by 19
- 2023Equity-Transformer: Solving NP-hard Min-Max Routing Problems as Sequential Generation with Equity Contextcited by 16
- 2024Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problemscited by 15
- 2023Neural Multi-Objective Combinatorial Optimization with Diversity Enhancementcited by 13
- 2025MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solvercited by 13
- 2023Promoting Generalization for Exact Solvers via Adversarial Instance Augmentationcited by 12
- 2025Preference Optimization for Combinatorial Optimization Problemscited by 11
- 2024DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problemscited by 10
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
- 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
- 2025Hybrid-Balance GFlowNet for Solving Vehicle Routing Problemscited by 7
- 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDPcited by 7
- 2023Efficient Training of Multi-task Neural Solver for Combinatorial Optimizationcited by 6
- 2024Prompt Learning for Generalized Vehicle Routingcited by 6
- 2024Neural Solver Selection for Combinatorial Optimizationcited by 5
- 2024Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solverscited by 3
- 2025Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problemscited by 3
- 2025TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problemscited by 2
- 2025UniCO: Towards a Unified Model for Combinatorial Optimization Problemscited by 2
- 2025Lifelong Learner: Discovering Versatile Neural Solvers for Vehicle Routing Problemscited by 2
- 2026Game-Theoretic Co-Evolution for LLM-Based Heuristic Discoverycited by 2
- 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problemscited by 2
- 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPscited by 2
- 2024On Size and Hardness Generalization in Unsupervised Learning for the Travelling Salesman Problemcited by 1
- 2025Knowledge-Guided Machine Learning for Stabilizing Near-Shortest Path Routingcited by 1
- 2025Lifelong Learning with Behavior Consolidation for Vehicle Routingcited by 1
- 2025Enhancing the Cross-Size Generalization for Solving Vehicle Routing Problems via Continual Learningcited by 1
- 2026Efficient Decoder Scaling Strategy for Neural Routing Solverscited by 1
- 2026Leveraging Structural Constraints for Diffusion-based Neural TSP Solverscited by 1
- 2026Reinforcement Learning Enhanced LLM Agents for Complex Vehicle Routing Problemscited by 1
- 2023LLQL: Logistic Likelihood Q-Learning for Reinforcement Learningcited by 0
- 2023Learning from A Single Graph is All You Need for Near-Shortest Path Routing in Wireless Networkscited by 0
50 most cited of 61 All 61 (JSON)
- 2026Understanding Decision-Making Mechanisms in Neural Routing Solvers28 Sep 2026
- 2026Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimization28 Sep 2026
- 2026Reinforcement Learning Enhanced LLM Agents for Complex Vehicle Routing Problems1 Sep 2026
- 2026Optimizing Nursing Care Taxi Dispatch Leveraging Integer Linear Programming Solvers and Machine Learning29 Jun 2026
- 2026Leveraging Structural Constraints for Diffusion-based Neural TSP Solvers8 Jun 2026
- 2026Towards Generalization-Oriented Models for Vehicle Routing Problems with Mixture-of-Experts26 May 2026
- 2026Learning to Solve Compositional Geometry Routing Problems18 May 2026
- 2026CDEoH: Category-Driven Automatic Algorithm Design With Large Language Models8 Mar 2026
- 2026Learning to Solve Orienteering Problem with Time Windows and Variable Profits6 Mar 2026
- 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs2 Mar 2026
- 2026Efficient Decoder Scaling Strategy for Neural Routing Solvers28 Feb 2026
- 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problems17 Feb 2026
38 more
- 2026Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery30 Jan 2026
- 2026Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks30 Jan 2026
- 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP24 Oct 2025
- 2025Enhancing the Cross-Size Generalization for Solving Vehicle Routing Problems via Continual Learning11 Oct 2025
- 2025Hybrid-Balance GFlowNet for Solving Vehicle Routing Problems6 Oct 2025
- 2025Lifelong Learning with Behavior Consolidation for Vehicle Routing26 Sep 2025
- 2025Knowledge-Guided Machine Learning for Stabilizing Near-Shortest Path Routing8 Sep 2025
- 2025Lifelong Learner: Discovering Versatile Neural Solvers for Vehicle Routing Problems8 Aug 2025
- 2025On Distributional Dependent Performance of Classical and Neural Routing Solvers4 Aug 2025
- 2025LRM-1B: Towards Large Routing Model4 Jul 2025
- 2025MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solver3 Jun 2025
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solver20 May 2025
- 2025Preference Optimization for Combinatorial Optimization Problems13 May 2025
- 2025UniCO: Towards a Unified Model for Combinatorial Optimization Problems7 May 2025
- 2025TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problems16 Mar 2025
- 2025Learning Constraints-Based Adaptive Hypergraph Neural Networks for Solving Vehicle Routing Problems13 Mar 2025
- 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problems2 Mar 2025
- 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attention30 Nov 2024
- 2024Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers14 Nov 2024
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problems28 Oct 2024
- 2024Neural Solver Selection for Combinatorial Optimization13 Oct 2024
- 2024Collaboration! Towards Robust Neural Methods for Routing Problems7 Oct 2024
- 2024DISCO: Efficient Diffusion Solver for Large-Scale Combinatorial Optimization Problems28 Jun 2024
- 2024GOAL: A Generalist Combinatorial Optimization Agent Learner21 Jun 2024
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problems21 Jun 2024
- 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectives1 Jun 2024
- 2024Prompt Learning for Generalized Vehicle Routing20 May 2024
- 2024MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts2 May 2024
- 2024Cross-Problem Learning for Solving Vehicle Routing Problems17 Apr 2024
- 2024On Size and Hardness Generalization in Unsupervised Learning for the Travelling Salesman Problem29 Mar 2024
- 2024INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformer4 Feb 2024
- 2024Distance-aware Attention Reshaping: Enhance Generalization of Neural Solver for Large-scale Vehicle Routing Problems13 Jan 2024
- 2023Distilling Autoregressive Models to Obtain High-Performance Non-Autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed19 Dec 2023
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time13 Dec 2023
- 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt27 Oct 2023
- 2023Graph Attention-based Deep Reinforcement Learning for solving the Chinese Postman Problem with Load-dependent costs24 Oct 2023
- 2023Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement22 Oct 2023
- 2023Promoting Generalization for Exact Solvers via Adversarial Instance Augmentation22 Oct 2023
50 newest of 61 All 61 (JSON)
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 82
- 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
- 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 77
- 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 70
- 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 68
- 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 61
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
- 2024INViT: A Generalizable Routing Problem Solver with Invariant Nested View Transformercited by 43
- 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 39
- 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 36
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2023ASP: Learn a Universal Neural Solver!cited by 27
12 most cited of 55 All 55 (JSON)
- 2026Understanding Decision-Making Mechanisms in Neural Routing Solvers28 Sep 2026
- 2026Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimization28 Sep 2026
- 2026Optimizing Nursing Care Taxi Dispatch Leveraging Integer Linear Programming Solvers and Machine Learning29 Jun 2026
- 2026Learning to Solve Compositional Geometry Routing Problems18 May 2026
- 2026CDEoH: Category-Driven Automatic Algorithm Design With Large Language Models8 Mar 2026
- 2026Learning to Solve Orienteering Problem with Time Windows and Variable Profits6 Mar 2026
- 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPs2 Mar 2026
- 2026Efficient Decoder Scaling Strategy for Neural Routing Solvers28 Feb 2026
- 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problems17 Feb 2026
- 2026Game-Theoretic Co-Evolution for LLM-Based Heuristic Discovery30 Jan 2026
- 2026Keep Rehearsing and Refining: Lifelong Learning Vehicle Routing under Continually Drifting Tasks30 Jan 2026
- 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP24 Oct 2025
12 newest of 55 All 55 (JSON)