---
title: "LLM-guided Cutting-plane Management for Mixed-integer Linear Programming"
authors:
  - "Zetao Zheng"
  - "Zhe Wang"
  - "Jie Shao"
doi: "10.24963/ijcai.2026/736"
url: "https://ijcai.org/proceedings/2026/736"
pdf: "https://ijcai.org/proceedings/2026/0736.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "6617-6625"
track: "AI4Tech: AI Enabling Technologies"
keywords:
  - "Advanced AI4Tech: Generative and LLMs-driven AI4Tech"
  - "Advanced AI4Tech: Other advances"
---

# LLM-guided Cutting-plane Management for Mixed-integer Linear Programming

Zetao Zheng, Zhe Wang, Jie Shao

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 6617-6625. DOI: [10.24963/ijcai.2026/736](https://doi.org/10.24963/ijcai.2026/736)

## 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.