# GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs

arXiv: https://arxiv.org/abs/2606.23299 · HTML: https://mlsanity.com/paper/2606.23299/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 71 references that are in the map.
- First posted on arXiv 22 Jun 2026.

## Builds on (most cited first, 29 of 29)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Large Language Models to Enhance Bayesian Optimization](https://mlsanity.com/paper/2402.03921/) (2024)
- [Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets](https://mlsanity.com/paper/1605.07079/) (2016)
- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [HEBO Pushing The Limits of Sample-Efficient Hyperparameter Optimisation](https://mlsanity.com/paper/2012.03826/) (2020)
- [Towards Learning Universal Hyperparameter Optimizers with Transformers](https://mlsanity.com/paper/2205.13320/) (2022)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [PFNs4BO: In-Context Learning for Bayesian Optimization](https://mlsanity.com/paper/2305.17535/) (2023)
- [Using Large Language Models for Hyperparameter Optimization](https://mlsanity.com/paper/2312.04528/) (2023)
- [The Machine Learning for Combinatorial Optimization Competition (ML4CO): Results and Insights](https://mlsanity.com/paper/2203.02433/) (2022)
- [A Survey of Methods for Automated Algorithm Configuration](https://mlsanity.com/paper/2202.01651/) (2022)
- [In-Context Freeze-Thaw Bayesian Optimization for Hyperparameter Optimization](https://mlsanity.com/paper/2404.16795/) (2024)
- [Sequential Large Language Model-Based Hyper-parameter Optimization](https://mlsanity.com/paper/2410.20302/) (2024)
- [Optuna vs Code Llama: Are LLMs a New Paradigm for Hyperparameter Tuning?](https://mlsanity.com/paper/2504.06006/) (2025)
- [Efficient Heuristics Generation for Solving Combinatorial Optimization Problems Using Large Language Models](https://mlsanity.com/paper/2505.12627/) (2025)
- [Large Language Model-Enhanced Multi-Armed Bandits](https://mlsanity.com/paper/2502.01118/) (2025)
- [Instance-wise algorithm configuration with graph neural networks](https://mlsanity.com/paper/2202.04910/) (2022)
- [Efficient Global Optimization using Deep Gaussian Processes](https://mlsanity.com/paper/1809.04632/) (2018)
- [Beyond the Heatmap: A Rigorous Evaluation of Component Impact in MCTS-Based TSP Solvers](https://mlsanity.com/paper/2411.09238/) (2024)
- [A learning-based mathematical programming formulation for the automatic configuration of optimization solvers](https://mlsanity.com/paper/2401.04237/) (2024)
- [Are Your Generated Instances Truly Useful? GenBench-MILP: A Benchmark Suite for MILP Instance Generation](https://mlsanity.com/paper/2505.24779/) (2025)

## Built on by (most cited first, 1 of 1)

- [HeurEvo: Agentic Evolution of Hybrid Solver-Augmented Heuristics for Time-Critical Mathematical Optimization](https://mlsanity.com/paper/2609.36303/) (2026)

## Abstract (arXiv)

Configuring the hyperparameters of Mixed-integer programming (MIP) solvers is a high-dimensional, instance-dependent optimization problem where suboptimal settings can degrade solving time by orders of magnitude. Default configurations are often suboptimal, while traditional tuning methods either suffer from the ``cold-start'' problem and inefficient search or heavily rely on expert experience. This paper introduces GRIMIP (textbfunderlineGeneral textbfunderlineReasoning for textbfunderlineInstance-specific textbfunderlineMIP configuration), a novel hybrid intelligence framework that synergistically integrates the semantic reasoning capabilities of Large Language Models (LLMs) with the sample-efficient search of Bayesian Optimization (BO). GRIMIP enables the LLM to function as a complete probabilistic surrogate within the BO loop, significantly improving performance and reducing sampling and evaluation costs. On seven benchmarks including MIPLIB, GRIMIP achieves over 40% reduction in Primal-Dual Integral on hard instances, outperforming SMAC and other LLM-assisted BO methods. By granting LLMs sufficient autonomy, GRIMIP combines the expert-level reasoning of LLMs with the efficient search of BO, achieving state-of-the-art performance.