Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problem
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Abstract (arXiv)
Learning how to automatically solve optimization problems has the potential to provide the next big leap in optimization technology. The performance of automatically learned heuristics on routing problems has been steadily improving in recent years, but approaches based purely on machine learning are still outperformed by state-of-the-art optimization methods. To close this performance gap, we propose a novel large neighborhood search (LNS) framework for vehicle routing that integrates learned heuristics for generating new solutions. The learning mechanism is based on a deep neural network with an attention mechanism and has been especially designed to be integrated into an LNS search setting. We evaluate our approach on the capacitated vehicle routing problem (CVRP) and the split delivery vehicle routing problem (SDVRP). On CVRP instances with up to 297 customers, our approach significantly outperforms an LNS that uses only handcrafted heuristics and a well-known heuristic from the literature. Furthermore, we show for the CVRP and the SDVRP that our approach surpasses the performance of existing machine learning approaches and comes close to the performance of state-of-the-art optimization approaches.
Key facts. Cited by 117 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Nov 2019.
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Citing papers per year: 2021: 16; 2022: 19; 2023: 20; 2024: 22; 2025: 24; 2026: 16.
117 papers.
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- 2022Learning Generalizable Models for Vehicle Routing Problems via Knowledge Distillationcited by 61
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- 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learningcited by 12
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- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 10
50 most cited of 117 All 117 (JSON)
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- 2026GeoRouteNet: A Geometry-Aware Non-Autoregressive Neural Solver for the Euclidean Traveling Salesman Problem22 Jun 2026
- 2026MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing31 May 2026
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- 2026Towards Generalization-Oriented Models for Vehicle Routing Problems with Mixture-of-Experts26 May 2026
- 2026A Unified Knowledge Embedded Reinforcement Learning-based Framework for Generalized Capacitated Vehicle Routing Problems14 May 2026
- 2026Two-Stage Learned Decomposition for Scalable Routing on Multigraphs6 May 2026
- 2026FiLMMeD: Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing30 Apr 2026
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38 more
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- 2025Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP24 Oct 2025
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- 2025A Unified Deep Reinforcement Learning Approach for Close Enough Traveling Salesman Problem3 Oct 2025
- 2025Test-Time Search in Neural Graph Coarsening Procedures for the Capacitated Vehicle Routing Problem1 Oct 2025
- 2025Experience-Guided Reflective Co-Evolution of Prompts and Heuristics for Automatic Algorithm Design29 Sep 2025
- 2025Edge-Selector Model Applied for Local Search Neighborhood for Solving Vehicle Routing Problems12 Aug 2025
- 2025Hybrid Node-Destroyer Model with Large Neighborhood Search for Solving the Capacitated Vehicle Routing Problem12 Aug 2025
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- 2025On Distributional Dependent Performance of Classical and Neural Routing Solvers4 Aug 2025
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- 2025Learning for routing: A guided review of recent developments and future directions30 Jun 2025
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- 2025Latent Guided Sampling for Combinatorial Optimization4 Jun 2025
- 2025Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning3 Jun 2025
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimization27 May 2025
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solver20 May 2025
- 2025USPR: Learning a Unified Solver for Profiled Routing8 May 2025
- 2025ABCDWaveNet: Advancing Robust Road Ponding Detection in Fog through Dynamic Frequency-Spatial Synergy7 Apr 2025
- 2025Reinforcement Learning for Solving the Pricing Problem in Column Generation: Applications to Vehicle Routing3 Apr 2025
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization20 Mar 2025
- 2025TuneNSearch: a hybrid transfer learning and local search approach for solving vehicle routing problems16 Mar 2025
- 2025Learning to Reduce Search Space for Generalizable Neural Routing Solver5 Mar 2025
- 2025Neural Deconstruction Search for Vehicle Routing Problems7 Jan 2025
- 2024Learn to Solve Vehicle Routing Problems ASAP: A Neural Optimization Approach for Time-Constrained Vehicle Routing Problems with Finite Vehicle Fleet7 Nov 2024
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problems28 Oct 2024
- 2024Robotic warehousing operations: a learn-then-optimize approach to large-scale neighborhood search29 Aug 2024
- 2024Feature-Guided Metaheuristic with Diversity Management for Solving the Capacitated Vehicle Routing Problem30 Jul 2024
- 2024Take a Step and Reconsider: Sequence Decoding for Self-Improved Neural Combinatorial Optimization24 Jul 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
50 newest of 117 All 117 (JSON)
- 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
- 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
- 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
- 2021Learning to Delegate for Large-scale Vehicle Routingcited by 108
- 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
- 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
- 2022Simulation-guided Beam Search for Neural Combinatorial Optimizationcited by 84
- 2023GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-timecited by 82
12 most cited of 114 All 114 (JSON)
- 2026SPO: Discovering Adaptive Large Neighborhood Search Operators via Stackelberg Program Optimization25 Sep 2026
- 2026Drive, Pack, Fly: The Travelling Thief Problem with Drone17 Aug 2026
- 2026LaT: LLM-as-Trainer for Multi-Task Vehicle Routing Solvers20 Jul 2026
- 2026GeoRouteNet: A Geometry-Aware Non-Autoregressive Neural Solver for the Euclidean Traveling Salesman Problem22 Jun 2026
- 2026MViewRouter: Internalizing Geometric Equivariance via Multi-view Alternating Attention for Combinatorial Routing31 May 2026
- 2026Solving Integer Linear Programming with Parallel Tempering28 May 2026
- 2026LoRe: Adaptive Interaction-Evaluation Routing with Per-Step Interaction Budgets for Iterative Graph Solvers27 May 2026
- 2026A Unified Knowledge Embedded Reinforcement Learning-based Framework for Generalized Capacitated Vehicle Routing Problems14 May 2026
- 2026Two-Stage Learned Decomposition for Scalable Routing on Multigraphs6 May 2026
- 2026FiLMMeD: Feature-wise Linear Modulation for Cross-Problem Multi-Depot Vehicle Routing30 Apr 2026
- 2026A First Guess is Rarely the Final Answer: Learning to Search in the Traveling Salesperson Problem8 Apr 2026
- 2026Large Neighborhood Search meets Iterative Neural Constraint Heuristics21 Mar 2026
12 newest of 114 All 114 (JSON)