{"type":"ScholarlyArticle","title":"LLM-guided Cutting-plane Management for Mixed-integer Linear Programming","authors":[{"name":"Zetao Zheng","slug":"zetao-zheng","given":"Zetao","family":"Zheng","affiliation":""},{"name":"Zhe Wang","slug":"zhe-wang","given":"Zhe","family":"Wang","affiliation":""},{"name":"Jie Shao","slug":"jie-shao","given":"Jie","family":"Shao","affiliation":""}],"abstract":"Cutting planes are central to mixed-integer linear programming (MILP) solving, yet their effectiveness hinges on expert tuning of separator configurations and hard-crafted cut-selection heuristics, creating a high barrier for non-specialists. Learning-based methods can reduce manual effort, but typically require large training datasets and often generalize poorly beyond the instance classes they are trained on. We propose an LLM-guided cutting-plane management framework that integrates large language models into the MILP solving pipeline. First, using chain-of-thought (CoT) prompting, the LLM infers an instance-specific separator configuration, deciding which separators to activate and how to set key parameters from the problem type and structural features. Then, it translates the evolving branch-and-bound state in natural language to perform stage-aware cut selection, choosing a high-quality subset of cuts that tightens the relaxation and improves overall solver performance. Leveraging the LLM's reasoning capabilities and rich background knowledge, our work removes dependence on domain-specific training data and substantially reduces reliance on expert-crafted configurations. Experiments show consistent improvements over SCIP's default settings, hard-crafted heuristics, and recent learning-based cut selection baselines.","doi":"10.24963/ijcai.2026/736","url":"https://ijcai.org/proceedings/2026/736","pdf":"https://ijcai.org/proceedings/2026/0736.pdf","markdown":"https://ijcai.org/proceedings/2026/736.md","bibtex":"https://ijcai.org/proceedings/2026/bibtex/736","volume":{"slug":"2026","title":"Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2026","url":"https://ijcai.org/proceedings/2026/","year":2026,"location":"Bremen, Germany","dates":"15-21 August 2026","editors":"Diego Calvanese","isbn":"978-1-956792-09-6","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2026"},"section":"AI4Tech: AI Enabling Technologies","track":"AI4Tech: AI Enabling Technologies","number":736,"pages":{"first":6617,"last":6625},"keywords":["Advanced AI4Tech: Generative and LLMs-driven AI4Tech","Advanced AI4Tech: Other advances"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}