OptRoute: Evolving Trees that Couple Skill Organization and Retrieval for LLM-Based Optimization Modeling

Large language models (LLMs) have shown strong potential for automating optimization modeling from natural-language problem descriptions. Prompt-based methods are particularly attractive because they can reuse external modeling knowledge at inference time without updating model parameters. However, as reusable modeling knowledge grows, it becomes increasingly challenging to organize related skills while ensuring that the right knowledge can be reliably retrieved for new problems. Existing approaches typically organize skills using flat catalogs or predefined hierarchies, leaving skill organization disconnected from how the stored knowledge is subsequently retrieved. We propose OptRoute, a framework that couples skill organization and retrieval through an evolving tree. Within the tree, paradigm nodes organize related formulation families and provide hierarchical routing, while leaf nodes preserve complete, solver-ready skills. As new reference-grounded skills are added, OptRoute jointly updates skill content and tree structure, refining existing skills and evolving paradigms that distinguish formulation families relevant to future retrieval. At inference time, a new problem is routed through the resulting hierarchy to retrieve relevant skills for solver-code generation. Experiments on eight OR benchmarks show that OptRoute achieves 79.2% macro-average Pass@1 accuracy with DeepSeek-V4, outperforming the evaluated baselines. These results demonstrate the effectiveness of coupling skill organization and retrieval for scalable reuse of optimization modeling knowledge.