# UDC: A Unified Neural Divide-and-Conquer Framework for Large-Scale Combinatorial Optimization Problems

arXiv: https://arxiv.org/abs/2407.00312 · HTML: https://mlsanity.com/paper/2407.00312/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2024.

## Built on by (most cited first, 30 of 47)

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- [Improving Generalization of Neural Combinatorial Optimization for Vehicle Routing Problems via Test-Time Projection Learning](https://mlsanity.com/paper/2506.02392/) (2025)
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- [Collaboration! Towards Robust Neural Methods for Routing Problems](https://mlsanity.com/paper/2410.04968/) (2024)
- [Rethinking Neural Combinatorial Optimization for Vehicle Routing Problems with Different Constraint Tightness Degrees](https://mlsanity.com/paper/2505.24627/) (2025)
- [URS: A Unified Neural Routing Solver for Cross-Problem Zero-Shot Generalization](https://mlsanity.com/paper/2509.23413/) (2025)
- [RADAR: Learning to Route with Asymmetry-aware DistAnce Representations](https://mlsanity.com/paper/2603.03388/) (2026)
- [PARCO: Parallel AutoRegressive Models for Multi-Agent Combinatorial Optimization](https://mlsanity.com/paper/2409.03811/) (2024)
- [VRPAgent: LLM-Driven Discovery of Heuristic Operators for Vehicle Routing Problems](https://mlsanity.com/paper/2510.07073/) (2025)
- [Multi-Task Vehicle Routing Solver via Mixture of Specialized Experts under State-Decomposable MDP](https://mlsanity.com/paper/2510.21453/) (2025)
- [Neural Solver Selection for Combinatorial Optimization](https://mlsanity.com/paper/2410.09693/) (2024)
- [Learning to Segment for Vehicle Routing Problems](https://mlsanity.com/paper/2507.01037/) (2025)
- [RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models](https://mlsanity.com/paper/2505.20242/) (2025)
- [Survey on Neural Routing Solvers](https://mlsanity.com/paper/2602.21761/) (2026)
- [GELD: A Unified Neural Model for Efficiently Solving Traveling Salesman Problems Across Different Scales](https://mlsanity.com/paper/2506.06634/) (2025)
- [Towards Efficient Constraint Handling in Neural Solvers for Routing Problems](https://mlsanity.com/paper/2602.16012/) (2026)
- [LocalEscaper: A Weakly-supervised Framework with Regional Reconstruction for Scalable Neural TSP Solvers](https://mlsanity.com/paper/2502.12484/) (2025)
- [CADO: From Imitation to Cost Minimization for Heatmap-based Solvers in Combinatorial Optimization](https://mlsanity.com/paper/2602.08210/) (2026)
- [SPACE: Unifying Symmetric and Asymmetric Routing Problems for Generalist Neural Solver](https://mlsanity.com/paper/2605.24484/) (2026)
- [DeepMDV: Global Spatial Matching for Multi-depot Vehicle Routing Problems](https://mlsanity.com/paper/2411.17080/) (2024)
- [Solving the Min-Max Multiple Traveling Salesmen Problem via Learning-Based Path Generation and Optimal Splitting](https://mlsanity.com/paper/2508.17087/) (2025)
- [ViTSP: A Vision Language Models Guided Framework for Solving Large-Scale Traveling Salesman Problems](https://mlsanity.com/paper/2509.23465/) (2025)
- [Efficient Decoder Scaling Strategy for Neural Routing Solvers](https://mlsanity.com/paper/2603.00430/) (2026)
- [Aligning LLMs with Graph Neural Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2603.27169/) (2026)

## Abstract (arXiv)

Single-stage neural combinatorial optimization solvers have achieved near-optimal results on various small-scale combinatorial optimization (CO) problems without requiring expert knowledge. However, these solvers exhibit significant performance degradation when applied to large-scale CO problems. Recently, two-stage neural methods motivated by divide-and-conquer strategies have shown efficiency in addressing large-scale CO problems. Nevertheless, the performance of these methods highly relies on problem-specific heuristics in either the dividing or the conquering procedure, which limits their applicability to general CO problems. Moreover, these methods employ separate training schemes and ignore the interdependencies between the dividing and conquering strategies, often leading to sub-optimal solutions. To tackle these drawbacks, this article develops a unified neural divide-and-conquer framework (i.e., UDC) for solving general large-scale CO problems. UDC offers a Divide-Conquer-Reunion (DCR) training method to eliminate the negative impact of a sub-optimal dividing policy. Employing a high-efficiency Graph Neural Network (GNN) for global instance dividing and a fixed-length sub-path solver for conquering divided sub-problems, the proposed UDC framework demonstrates extensive applicability, achieving superior performance in 10 representative large-scale CO problems. The code is available at https://github.com/CIAM-Group/NCO_code/tree/main/single_objective/UDC-Large-scale-CO-master.