# LLMs for Cold-Start Cutting Plane Separator Configuration

arXiv: https://arxiv.org/abs/2412.12038 · HTML: https://mlsanity.com/paper/2412.12038/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 67 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 30 of 37)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Automatic Prompt Optimization with "Gradient Descent" and Beam Search](https://mlsanity.com/paper/2305.03495/) (2023)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Learning Combinatorial Optimization Algorithms over Graphs](https://mlsanity.com/paper/1704.01665/) (2017)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Prompting Large Language Model for Machine Translation: A Case Study](https://mlsanity.com/paper/2301.07069/) (2023)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [DeepACO: Neural-enhanced Ant Systems for Combinatorial Optimization](https://mlsanity.com/paper/2309.14032/) (2023)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [Large Language Models for Supply Chain Optimization](https://mlsanity.com/paper/2307.03875/) (2023)
- [Learning To Cut By Looking Ahead: Cutting Plane Selection via Imitation Learning](https://mlsanity.com/paper/2206.13414/) (2022)
- [Smaller, Weaker, Yet Better: Training LLM Reasoners via Compute-Optimal Sampling](https://mlsanity.com/paper/2408.16737/) (2024)
- [Augmenting Operations Research with Auto-Formulation of Optimization Models from Problem Descriptions](https://mlsanity.com/paper/2209.15565/) (2022)
- [MIP-GNN: A Data-Driven Framework for Guiding Combinatorial Solvers](https://mlsanity.com/paper/2205.14210/) (2022)
- [Autoformulation of Mathematical Optimization Models Using LLMs](https://mlsanity.com/paper/2411.01679/) (2024)
- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [OptiMUS-0.3: Using Large Language Models to Model and Solve Optimization Problems at Scale](https://mlsanity.com/paper/2407.19633/) (2024)
- [Sample Complexity of Tree Search Configuration: Cutting Planes and Beyond](https://mlsanity.com/paper/2106.04033/) (2021)
- [Holy Grail 2.0: From Natural Language to Constraint Models](https://mlsanity.com/paper/2308.01589/) (2023)
- [Sequential Large Language Model-Based Hyper-parameter Optimization](https://mlsanity.com/paper/2410.20302/) (2024)
- [Structural Analysis of Branch-and-Cut and the Learnability of Gomory Mixed Integer Cuts](https://mlsanity.com/paper/2204.07312/) (2022)

## Built on by (most cited first, 8 of 8)

- [EquivaMap: Leveraging LLMs for Automatic Equivalence Checking of Optimization Formulations](https://mlsanity.com/paper/2502.14760/) (2025)
- [EvoCut: Strengthening Integer Programs via Evolution-Guided Language Models](https://mlsanity.com/paper/2508.11850/) (2025)
- [DualSchool: How Reliable are LLMs for Optimization Education?](https://mlsanity.com/paper/2505.21775/) (2025)
- [From Natural Language to Solver-Ready Power System Optimization: An LLM-Assisted, Validation-in-the-Loop Framework](https://mlsanity.com/paper/2508.08147/) (2025)
- [LISTEN to Your Preferences: An LLM Framework for Multi-Objective Selection](https://mlsanity.com/paper/2510.25799/) (2025)
- [Structure-Aware Commitment Reduction for Network-Constrained Unit Commitment with Solver-Preserving Guarantees](https://mlsanity.com/paper/2604.02788/) (2026)
- [Agentic MIP Research: Accelerated Constraint Handler Generation](https://mlsanity.com/paper/2605.09186/) (2026)
- [FLARE: Verifying MILP Reformulations with LLM-Based Theorem Proving](https://mlsanity.com/paper/2608.25220/) (2026)

## Abstract (arXiv)

Mixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users. Existing machine learning (ML) approaches require training on thousands of related instances, generalize poorly and can be difficult to integrate into existing solver workflows. We propose a large language model (LLM)-based framework that configures cutting plane separators using problem descriptions and solver-specific separator summaries. To reduce variance in LLM outputs, we introduce an ensembling strategy that clusters and aggregates candidate configurations into a small portfolio of high-performing configurations. Our method requires no custom solver interface, generates configurations in seconds via simple API calls, and requires solving only a small number of instances. Extensive experiments on standard synthetic and real-world MILPs show our approach matches or outperforms state-of-the-art configuration methods with a fraction of the data and computation.