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

How can Large Language Models (LLMs) be integrated into Bayesian Optimization (BO) to improve the efficiency and effectiveness of per-instance hyperparameter tuning for Mixed-Integer Programming (MIP) solvers? The authors aim to overcome the limitations of traditional surrogate models, which often struggle with high-dimensional search spaces and lack semantic understanding of problem structures.

The authors introduce GRIMIP, a framework that elevates the LLM from an auxiliary tool to a central, autonomous probabilistic surrogate. The system operates in three key stages:

1. Warm-Starting (WS): An initial 30-second exploratory solve extracts static and dynamic instance features, which the LLM uses to generate a diverse, informed set of initial configurations.
2. Automated Space Selection (ASS): The LLM analyzes the instance features to prune the massive Gurobi parameter space, focusing the search on a small subset (e.g., 6 parameters) most likely to impact performance.
3. LLM Probabilistic Surrogate (LLM-PS): The LLM iteratively proposes candidate configurations, predicts their performance (mean) and uncertainty (standard deviation), and uses an Expected Improvement (EI) acquisition function to guide the search toward the global optimum.

GRIMIP demonstrates state-of-the-art performance across seven diverse benchmarks, including MIPLIB and maritime routing problems. By leveraging the LLM's semantic reasoning, the framework achieves over 40% reduction in Primal-Dual Integral (PDI) on hard instances compared to standard baselines like SMAC and other LLM-assisted methods. The authors show that the ASS module is critical for performance, as it effectively mitigates the curse of dimensionality inherent in solver tuning.