ViSO: Visual Skill Distillation for Large-scale Routing Optimization

Decomposition enables large-scale routing optimization by allowing powerful solvers to focus on tractable subproblems. Yet selecting productive subproblems remains challenging, and existing approaches leave their selection experience largely implicit and difficult to reuse. We propose ViSO, a novel framework that guides routing decomposition with transferable visual skills for solving large-scale routing problems. ViSO distills solver feedback into transferable visual skills that direct optimization toward promising subproblems. A unified decomposition interface couples this guidance with off-the-shelf solvers across symmetric, asymmetric, and capacitated routing problems. By distilling optimization experience into reusable visual skills, ViSO enables decomposition strategies to generalize to unseen instances without updating model parameters. Across four routing families with up to 85,900 nodes, ViSO reduces mean TSP and CVRP gaps by 10.5% and 11.5% relative to LKH-3 and HGS, respectively, and achieves a mean ACVRP objective value 2.72 lower than PyVRP’s. ViSO outperforms neural and LLM/VLM solvers (e.g., achieving a 26.5% improvement on TSP over ViTSP and a 94.8% improvement on CVRP over NCO-LLM), while its skill-distillation procedure is able to improve existing divide-and-conquer frameworks (e.g., DRAGON).