mlsanityData to 14 Oct 2026

MVMoE: Multi-Task Vehicle Routing Solver with Mixture-of-Experts

arXiv 2405.01029 ↗First posted 2 May 2024cs.AI cs.LGcited by 70

On the map: Mixture-of-experts → Expert routing strategies

Abstract (arXiv)

Learning to solve vehicle routing problems (VRPs) has garnered much attention. However, most neural solvers are only structured and trained independently on a specific problem, making them less generic and practical. In this paper, we aim to develop a unified neural solver that can cope with a range of VRP variants simultaneously. Specifically, we propose a multi-task vehicle routing solver with mixture-of-experts (MVMoE), which greatly enhances the model capacity without a proportional increase in computation. We further develop a hierarchical gating mechanism for the MVMoE, delivering a good trade-off between empirical performance and computational complexity. Experimentally, our method significantly promotes zero-shot generalization performance on 10 unseen VRP variants, and showcases decent results on the few-shot setting and real-world benchmark instances. We further conduct extensive studies on the effect of MoE configurations in solving VRPs, and observe the superiority of hierarchical gating when facing out-of-distribution data. The source code is available at: https://github.com/RoyalSkye/Routing-MVMoE.

Key facts. Cited by 70 papers in the map (data through 14 Oct 2026). Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts. Builds on 63 of its 85 references that are in the map. First posted on arXiv 2 May 2024.

Builds on

63 of 85 references.

Closest ancestors · 3

Same direction, newest first

  1. 2022Mixture-of-Experts with Expert Choice Routing18 Feb
  2. 2021Taming Sparsely Activated Transformer with Stochastic Experts8 Oct
  3. 2021Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity11 Jan

Other references · 60

  1. 2017Attention Is All You Needcited by 60,361
  2. 2023Llama 2: Open Foundation and Fine-Tuned Chat Modelscited by 13,028
  3. 2020Scaling Laws for Neural Language Modelscited by 6,586
  4. 2021Prefix-Tuning: Optimizing Continuous Prompts for Generationcited by 3,915
  5. 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
  6. 2020GShard: Scaling Giant Models with Conditional Computation and Automatic Shardingcited by 1,631
  7. 2015Pointer Networkscited by 895
  8. 2021Scaling Vision with Sparse Mixture of Expertscited by 747
  9. 2018Attention, Learn to Solve Routing Problems!cited by 656
  10. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  11. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 608
  12. 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 348
38 more
  1. 2021BASE Layers: Simplifying Training of Large, Sparse Modelscited by 320
  2. 2013Learning Factored Representations in a Deep Mixture of Expertscited by 278
  3. 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 269
  4. 2023From Sparse to Soft Mixtures of Expertscited by 248
  5. 2021Hash Layers For Large Sparse Modelscited by 237
  6. 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 221
  7. 2024OpenMoE: An Early Effort on Open Mixture-of-Experts Language Modelscited by 187
  8. 2018Learning to Perform Local Rewriting for Combinatorial Optimizationcited by 185
  9. 2024Scaling Laws for Fine-Grained Mixture of Expertscited by 173
  10. 2019Learning Improvement Heuristics for Solving Routing Problemscited by 164
  11. 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 162
  12. 2022A Review of Sparse Expert Models in Deep Learningcited by 148
  13. 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 142
  14. 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 129
  15. 2020Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhoodcited by 125
  16. 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 119
  17. 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
  18. 2021Learning to Delegate for Large-scale Vehicle Routingcited by 109
  19. 2021NeuroLKH: Combining Deep Learning Model with Lin-Kernighan-Helsgaun Heuristic for Solving the Traveling Salesman Problemcited by 103
  20. 2020Learning 2-opt Heuristics for the Traveling Salesman Problem via Deep Reinforcement Learningcited by 100
  21. 2021Deep Policy Dynamic Programming for Vehicle Routing Problemscited by 94
  22. 2021Matrix Encoding Networks for Neural Combinatorial Optimizationcited by 91
  23. 2023Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Optcited by 81
  24. 2023DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimizationcited by 78
  25. 2023RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmarkcited by 71
  26. 2023Towards Omni-generalizable Neural Methods for Vehicle Routing Problemscited by 69
  27. 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 62
  28. 2023Towards Generalizable Neural Solvers for Vehicle Routing Problems via Ensemble with Transferrable Local Policycited by 62
  29. 2022Winner Takes It All: Training Performant RL Populations for Combinatorial Optimizationcited by 58
  30. 2023Unsupervised Learning for Solving the Travelling Salesman Problemcited by 58
  31. 2024Ant Colony Sampling with GFlowNets for Combinatorial Optimizationcited by 53
  32. 2024Multi-Task Learning for Routing Problem with Cross-Problem Zero-Shot Generalizationcited by 50
  33. 2021Independent Prototype Propagation for Zero-Shot Compositionalitycited by 42
  34. 2023Combinatorial Optimization with Policy Adaptation using Latent Space Searchcited by 41
  35. 2021Generalization of Neural Combinatorial Solvers Through the Lens of Adversarial Robustnesscited by 35
  36. 2024PolyNet: Learning Diverse Solution Strategies for Neural Combinatorial Optimizationcited by 35
  37. 2023Demystifying Softmax Gating Function in Gaussian Mixture of Expertscited by 33
  38. 2021Deep Reinforcement Learning for Solving the Heterogeneous Capacitated Vehicle Routing Problemcited by 31

50 most cited of 60 All 60 (JSON)

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 13; 2025: 29; 2026: 28.

70 papers.

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By area:

  1. 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 55
  2. 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 42
  3. 2025Rethinking Light Decoder-based Solvers for Vehicle Routing Problemscited by 37
  4. 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
  5. 2024CaDA: Cross-Problem Routing Solver with Constraint-Aware Dual-Attentioncited by 24
  6. 2024Neural Combinatorial Optimization Algorithms for Solving Vehicle Routing Problems: A Comprehensive Survey with Perspectivescited by 23
  7. 2024Graph Neural Networks for Job Shop Scheduling Problems: A Surveycited by 15
  8. 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
  9. 2025BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimizationcited by 14
  10. 2025ARS: Automatic Routing Solver with Large Language Modelscited by 13
  11. 2025MTL-KD: Multi-Task Learning Via Knowledge Distillation for Generalizable Neural Vehicle Routing Solvercited by 13
  12. 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
38 more
  1. 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 11
  2. 2024Instance-Conditioned Adaptation for Large-scale Generalization of Neural Routing Solvercited by 9
  3. 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
  4. 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 9
  5. 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degreescited by 8
  6. 2025URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalizationcited by 8
  7. 2026RADAR: Learning to Route with Asymmetry-aware DistAnce Representationscited by 8
  8. 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimizationcited by 7
  9. 2025Learning for routing: A guided review of recent developments and future directionscited by 7
  10. 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDPcited by 7
  11. 2025Preference-Driven Multi-Objective Combinatorial Optimization with Conditional Computationcited by 6
  12. 2024Leader Reward for POMO-Based Neural Combinatorial Optimizationcited by 5
  13. 2024Neural Solver Selection for Combinatorial Optimizationcited by 5
  14. 2025An Agentic Framework with LLMs for Solving Complex Vehicle Routing Problemscited by 5
  15. 2026Survey on Neural Routing Solverscited by 4
  16. 2024Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solverscited by 3
  17. 2025LMask: Learn to Solve Constrained Routing Problems with Lazy Maskingcited by 3
  18. 2025Efficient Neural Combinatorial Optimization Solver for the Min-max Heterogeneous Capacitated Vehicle Routing Problemcited by 3
  19. 2025Refining Hybrid Genetic Search for CVRP via Reinforcement Learning-Finetuned LLMcited by 3
  20. 2025RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domainscited by 3
  21. 2026Towards Efficient Constraint Handling in Neural Solvers for Routing Problemscited by 3
  22. 2025TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problemscited by 2
  23. 2025Beyond Simple Graphs: Neural Multi-Objective Routing on Multigraphscited by 2
  24. 2026Chain-of-Context Learning: Dynamic Constraint Understanding for Multi-Task VRPscited by 2
  25. 2026SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solvercited by 2
  26. 2025ASAP: Exploiting the Satisficing Generalization Edge in Neural Combinatorial Optimizationcited by 1
  27. 2025USPR: Learning a Unified Solver for Profiled Routingcited by 1
  28. 2025Hierarchical Optimization via LLM-Guided Objective Evolution for Mobility-on-Demand Systemscited by 1
  29. 2026A Learning Method with Gap-Aware Generation for Heterogeneous DAG Schedulingcited by 1
  30. 2026Automated Large-scale CVRP Solver Design via LLM-assisted Flexible MCTScited by 1
  31. 2026Rethinking Constraint Awareness for Efficient State Embedding of Neural Routing Solvercited by 1
  32. 2026Vision-Assisted Foundation Model for Solving Multi-Task Vehicle Routing Problemscited by 1
  33. 2024Multi-Agent Environments for Vehicle Routing Problemscited by 0
  34. 2025Onboard Mission Replanning for Adaptive Cooperative Multi-Robot Systemscited by 0
  35. 2025LRM-1B: Towards Large Routing Modelcited by 0
  36. 2025Deep Reinforcement Learning for Drone Route Optimization in Post-Disaster Road Assessmentcited by 0
  37. 2025Optimizing delivery for quick commerce factoring qualitative assessment of generated routescited by 0
  38. 2025A Unified Model for Multi-Task Drone Routing in Post-Disaster Road Assessmentcited by 0

50 most cited of 70 All 70 (JSON)

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Close in wording, no citation either way

  1. 2025Hierarchical Learning-based Graph Partition for Large-scale Vehicle Routing Problems
  2. 2026Two Black Boxes, One Solver: Encoder Probing and Decoder Attribution for Neural Multi-Attribute VRP under Hard-Mask and Recourse Decoders
  3. 2024Memory-Enhanced Neural Solvers for Routing Problems
  4. 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet
  5. 2026Two-Stage Learned Decomposition for Scalable Routing on Multigraphs
  6. 2026OD-Gear: Online Decomposition and Group Sampling for Expert-Guided Adversarial Routing in Scalable Capacitated Vehicle Routing
  7. 2023Distilling Autoregressive Models to Obtain High-Performance Non-Autoregressive Solvers for Vehicle Routing Problems with Faster Inference Speed
  8. 2026Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems