OptiSkill: A Hierarchical and Evolving SkillBank for LLM-Based Optimization Modeling

Automated operations research (OR) modeling requires LLMs to translate natural-language decision problems into correct mathematical programs. Existing methods can improve individual formulations, but they often solve problems in isolation, retaining little reusable experience and repeating similar formulation errors. Prior memory-based approaches store examples, thoughts, or insights as references, while OR modeling requires reusable formulation skills that transfer across problem narratives and guide concrete modeling decisions. We propose OptiSkill, a skill-augmented framework that builds a hierarchical and evolving SkillBank for LLM-based OR modeling. SkillBank stores solver-verified experience as reusable skills, with Global Strategies for problem-level formulation skeletons and Step Experiences for local error-prevention rules. It is further refined through stable batch-level test-time evolution, where candidate skills are incorporated only after validation. Experiments on eight OR modeling benchmarks show that OptiSkill improves formulation accuracy across LLM backbones, outperforms strong agentic baselines, and gains further by expanding SkillBank coverage and reliability. Code and data are available at https://github.com/rachhhhing/OptiSkill