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

arXiv: https://arxiv.org/abs/2609.22987 · HTML: https://mlsanity.com/paper/2609.22987/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 57 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [ExpeL: LLM Agents Are Experiential Learners](https://mlsanity.com/paper/2308.10144/) (2023)
- [SkillWeaver: Web Agents can Self-Improve by Discovering and Honing Skills](https://mlsanity.com/paper/2504.07079/) (2025)
- [Synapse: Trajectory-as-Exemplar Prompting with Memory for Computer Control](https://mlsanity.com/paper/2306.07863/) (2023)
- [Trace2Skill: Distill Trajectory-Local Lessons into Transferable Agent Skills](https://mlsanity.com/paper/2603.25158/) (2026)
- [NL4Opt Competition: Formulating Optimization Problems Based on Their Natural Language Descriptions](https://mlsanity.com/paper/2303.08233/) (2023)
- [ORLM: A Customizable Framework in Training Large Models for Automated Optimization Modeling](https://mlsanity.com/paper/2405.17743/) (2024)
- [AutoSkill: Experience-Driven Lifelong Learning via Skill Self-Evolution](https://mlsanity.com/paper/2603.01145/) (2026)
- [LLMOPT: Learning to Define and Solve General Optimization Problems from Scratch](https://mlsanity.com/paper/2410.13213/) (2024)
- [XSkill: Continual Learning from Experience and Skills in Multimodal Agents](https://mlsanity.com/paper/2603.12056/) (2026)
- [Seed2.0 Model Card: Towards Intelligence Frontier for Real-World Complexity](https://mlsanity.com/paper/2607.00248/) (2026)
- [OptMATH: A Scalable Bidirectional Data Synthesis Framework for Optimization Modeling](https://mlsanity.com/paper/2502.11102/) (2025)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Contextual Experience Replay for Self-Improvement of Language Agents](https://mlsanity.com/paper/2506.06698/) (2025)
- [Solver-Informed RL: Grounding Large Language Models for Authentic Optimization Modeling](https://mlsanity.com/paper/2505.11792/) (2025)
- [Investigate-Consolidate-Exploit: A General Strategy for Inter-Task Agent Self-Evolution](https://mlsanity.com/paper/2401.13996/) (2024)
- [StepORLM: A Self-Evolving Framework With Generative Process Supervision For Operations Research Language Models](https://mlsanity.com/paper/2509.22558/) (2025)
- [OptiTree: Hierarchical Thoughts Generation with Tree Search for LLM Optimization Modeling](https://mlsanity.com/paper/2510.22192/) (2025)
- [OR-R1: Automating Modeling and Solving of Operations Research Optimization Problem via Test-Time Reinforcement Learning](https://mlsanity.com/paper/2511.09092/) (2025)
- [BPP-Search: Enhancing Tree of Thought Reasoning for Mathematical Modeling Problem Solving](https://mlsanity.com/paper/2411.17404/) (2024)
- [AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Library](https://mlsanity.com/paper/2510.18428/) (2025)
- [Large-Scale Optimization Model Auto-Formulation: Harnessing LLM Flexibility via Structured Workflow](https://mlsanity.com/paper/2601.09635/) (2026)
- [ReLoop: Structured Modeling and Behavioral Verification for Reliable LLM-Based Optimization](https://mlsanity.com/paper/2602.15983/) (2026)
- [MIRROR: A Multi-Agent Framework with Iterative Adaptive Revision and Hierarchical Retrieval for Optimization Modeling in Operations Research](https://mlsanity.com/paper/2602.03318/) (2026)

## Abstract (arXiv)

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