# OD-Gear: Online Decomposition and Group Sampling for Expert-Guided Adversarial Routing in Scalable Capacitated Vehicle Routing

arXiv: https://arxiv.org/abs/2602.00488 · HTML: https://mlsanity.com/paper/2602.00488/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 33 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 14 of 14)

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- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
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- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
- [Combinatorial optimization and reasoning with graph neural networks](https://mlsanity.com/paper/2102.09544/) (2021)
- [DIFUSCO: Graph-based Diffusion Solvers for Combinatorial Optimization](https://mlsanity.com/paper/2302.08224/) (2023)
- [End-to-End Constrained Optimization Learning: A Survey](https://mlsanity.com/paper/2103.16378/) (2021)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [GLOP: Learning Global Partition and Local Construction for Solving Large-scale Routing Problems in Real-time](https://mlsanity.com/paper/2312.08224/) (2023)
- [Learning to Search Feasible and Infeasible Regions of Routing Problems with Flexible Neural k-Opt](https://mlsanity.com/paper/2310.18264/) (2023)
- [Ant Colony Sampling with GFlowNets for Combinatorial Optimization](https://mlsanity.com/paper/2403.07041/) (2024)

## Abstract (arXiv)

Solving large-scale capacitated vehicle routing problems (CVRP) is hindered by the high complexity of classical heuristics and the limited generalization of neural solvers. To bridge this gap, we propose OD-Gear, an expert-guided adversarial framework that integrates hybrid genetic search (HGS) and online barycenter clustering (BCC) decomposition with group-relative optimization. OD-Gear internalizes expert heuristics into a graph attention network (GAT)-based policy via high-fidelity knowledge distillation. Our minimax adversarial training distills divide-and-conquer strategies into dense surrogate rewards, while a group-sampling strategy exploits relative solution advantages to promote both diversity and quality. This architecture enables high-quality, clustering-free inference on massive graphs, effectively bypassing the overhead of traditional decomposition. Empirical results demonstrate that OD-Gear achieves state-of-the-art (SOTA) performance across most benchmarks, remaining highly competitive at the 10,000-node scale. By providing heuristic-quality solutions with low-latency, OD-Gear offers a robust and scalable framework for large-scale CVRP.