Self-Improved Learning for Scalable Neural Combinatorial Optimization
Not on the map. Why?
Abstract (arXiv)
The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale problems, hindering their practical applicability. To overcome this limitation, this work proposes a novel Self-Improved Learning (SIL) method for better scalability of neural combinatorial optimization. Specifically, we develop an efficient self-improved mechanism that enables direct model training on large-scale problem instances without any labeled data. Powered by an innovative local reconstruction approach, this method can iteratively generate better solutions by itself as pseudo-labels to guide efficient model training. In addition, we design a linear complexity attention mechanism for the model to efficiently handle large-scale combinatorial problem instances with low computation overhead. Comprehensive experiments on the Travelling Salesman Problem (TSP) and the Capacitated Vehicle Routing Problem (CVRP) with up to 100K nodes in both uniform and real-world distributions demonstrate the superior scalability of our method.
Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). Builds on 23 of its 40 references that are in the map. First posted on arXiv 28 Mar 2024.
Builds on
23 of 40 references.
References · 23
- 2017Attention Is All You Needcited by 59,932
- 2015Pointer Networkscited by 882
- 2018Attention, Learn to Solve Routing Problems!cited by 646
- 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
- 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
- 2020POMO: Policy Optimization with Multiple Optima for Reinforcement Learningcited by 341
- 2019An Efficient Graph Convolutional Network Technique for the Travelling Salesman Problemcited by 265
- 2023DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimizationcited by 216
- 2020Generalize a Small Pre-trained Model to Arbitrarily Large TSP Instancescited by 161
- 2023Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalizationcited by 140
- 2022DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problemscited by 127
- 2020Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhoodcited by 122
11 more
- 2022Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimizationcited by 118
- 2019Neural Large Neighborhood Search for the Capacitated Vehicle Routing Problemcited by 117
- 2021Learning to Delegate for Large-scale Vehicle Routingcited by 108
- 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
- 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
- 2023BQ-NCO: Bisimulation Quotienting for Efficient Neural Combinatorial Optimizationcited by 80
- 2023H-TSP: Hierarchically Solving the Large-Scale Travelling Salesman Problemcited by 43
Built on by
Citing papers per year: 2024: 6; 2025: 16; 2026: 7.
29 papers.
Sort:
By area:
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
- 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 39
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2025Destroy and Repair Using Hyper Graphs for Routingcited by 14
- 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
- 2025BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimizationcited by 14
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 10
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
- 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
- 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimizationcited by 7
- 2025Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Schedulingcited by 7
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 7
17 more
- 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degreescited by 7
- 2025Learning to Segment for Vehicle Routing Problemscited by 5
- 2024Take a Step and Reconsider: Sequence Decoding for Self-Improved Neural Combinatorial Optimizationcited by 4
- 2025LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solverscited by 2
- 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimizationcited by 1
- 2025Elevating Visual Question Answering through Implicitly Learned Reasoning Pathways in LVLMscited by 0
- 2025Multi-Dimensional AGV Path Planning in 3D Warehouses Using Ant Colony Optimization and Advanced Neural Networkscited by 0
- 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Applicationcited by 0
- 2025RsGCN: Subgraph-Based Rescaling Enhances Generalization of GCNs for Solving Traveling Salesman Problemscited by 0
- 2025Parametrized Multi-Agent Routing via Deep Attention Modelscited by 0
- 2026Enabling Population-Based Architectures for Neural Combinatorial Optimizationcited by 0
- 2026EGAM: Extended Graph Attention Model for Solving Routing Problemscited by 0
- 2026Rethinking Efficiency in Neural Combinatorial Optimization: Batched Preference Optimization with Mambacited by 0
- 2026Self-Improvement Imitation with Biologically Guided Search for Protein Design Under Oracle Budgetscited by 0
- 2026COMPASS: Ordered Clustered Routing at 100K Scalecited by 0
- 2026Compute Time Scaling with Recursive Models for Combinatorial Optimizationcited by 0
- 2026Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimizationcited by 0
- 2026Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimization28 Sep 2026
- 2026Compute Time Scaling with Recursive Models for Combinatorial Optimization28 Sep 2026
- 2026COMPASS: Ordered Clustered Routing at 100K Scale17 Sep 2026
- 2026Self-Improvement Imitation with Biologically Guided Search for Protein Design Under Oracle Budgets26 May 2026
- 2026Rethinking Efficiency in Neural Combinatorial Optimization: Batched Preference Optimization with Mamba24 Feb 2026
- 2026EGAM: Extended Graph Attention Model for Solving Routing Problems29 Jan 2026
- 2026Enabling Population-Based Architectures for Neural Combinatorial Optimization13 Jan 2026
- 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimization5 Sep 2025
- 2025Parametrized Multi-Agent Routing via Deep Attention Models30 Jul 2025
- 2025Learning to Segment for Vehicle Routing Problems22 Jun 2025
- 2025RsGCN: Subgraph-Based Rescaling Enhances Generalization of GCNs for Solving Traveling Salesman Problems31 May 2025
- 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees30 May 2025
17 more
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimization27 May 2025
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solver20 May 2025
- 2025Graph Reduction with Unsupervised Learning in Column Generation: A Routing Application11 Apr 2025
- 2025Multi-Dimensional AGV Path Planning in 3D Warehouses Using Ant Colony Optimization and Advanced Neural Networks30 Mar 2025
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimization20 Mar 2025
- 2025Elevating Visual Question Answering through Implicitly Learned Reasoning Pathways in LVLMs18 Mar 2025
- 2025BOPO: Neural Combinatorial Optimization via Best-anchored and Objective-guided Preference Optimization10 Mar 2025
- 2025Learning to Reduce Search Space for Generalizable Neural Routing Solver5 Mar 2025
- 2025Destroy and Repair Using Hyper Graphs for Routing22 Feb 2025
- 2025Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Scheduling18 Feb 2025
- 2025LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solvers18 Feb 2025
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problems28 Oct 2024
- 2024Collaboration! Towards Robust Neural Methods for Routing Problems7 Oct 2024
- 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization5 Sep 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
- 2024RouteFinder: Towards Foundation Models for Vehicle Routing Problemscited by 54
- 2024GOAL: A Generalist Combinatorial Optimization Agent Learnercited by 39
- 2024Learning to Handle Complex Constraints for Vehicle Routing Problemscited by 29
- 2025Destroy and Repair Using Hyper Graphs for Routingcited by 14
- 2025Learning to Reduce Search Space for Generalizable Neural Routing Solvercited by 14
- 2025RRNCO: Towards Real-World Routing with Neural Combinatorial Optimizationcited by 10
- 2025Learning to Insert for Constructive Neural Vehicle Routing Solvercited by 10
- 2024Collaboration! Towards Robust Neural Methods for Routing Problemscited by 9
- 2024PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimizationcited by 7
- 2025Learning-Guided Rolling Horizon Optimization for Long-Horizon Flexible Job-Shop Schedulingcited by 7
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimizationcited by 7
- 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degreescited by 7
12 most cited of 26 All 26 (JSON)
- 2026Just Initialize: A Training-Free Initialization Component for Large-Scale Routing Optimization28 Sep 2026
- 2026Compute Time Scaling with Recursive Models for Combinatorial Optimization28 Sep 2026
- 2026COMPASS: Ordered Clustered Routing at 100K Scale17 Sep 2026
- 2026Self-Improvement Imitation with Biologically Guided Search for Protein Design Under Oracle Budgets26 May 2026
- 2026EGAM: Extended Graph Attention Model for Solving Routing Problems29 Jan 2026
- 2026Enabling Population-Based Architectures for Neural Combinatorial Optimization13 Jan 2026
- 2025Recurrent State Encoders for Efficient Neural Combinatorial Optimization5 Sep 2025
- 2025Parametrized Multi-Agent Routing via Deep Attention Models30 Jul 2025
- 2025Learning to Segment for Vehicle Routing Problems22 Jun 2025
- 2025RsGCN: Subgraph-Based Rescaling Enhances Generalization of GCNs for Solving Traveling Salesman Problems31 May 2025
- 2025Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees30 May 2025
- 2025Generalizable Heuristic Generation Through LLMs with Meta-Optimization27 May 2025
12 newest of 26 All 26 (JSON)