GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using Large Language Models

Yidong Luo, Tianshu Yu

Keywords: Mixed Integer Programming, Combinatorial Optimization, Bayesian Optimization, Large Language Models

Abstract: Tuning the numerous internal hyperparameters of Mixed Integer Programming (MIP) solvers is critical for achieving optimal performance but remains a significant challenge. Default configurations are often suboptimal for specific problem instances, and traditional automated tuning methods either provide generic ``one-size-fits-all'' solutions or demand significant domain expertise. This paper introduces \textbf{GRIMIP}, which stands for \textbf{\underline{G}}eneral \textbf{\underline{R}}easoning for \textbf{\underline{I}}nstance-specific \textbf{\underline{MIP}} configuration, a novel hybrid intelligence framework that synergistically integrates the reasoning capabilities of Large Language Models (LLMs) with the sample-efficient search of Bayesian Optimization (BO). A key innovation is that while a pure LLM approach is insufficient for BO’s exploration–exploitation trade-off, GRIMIP enables the LLM to function as a complete probabilistic surrogate by jointly predicting performance mean and its uncertainty (standard deviation), a capability that is essential for the Bayesian Optimization exploration–exploitation trade-off. Unlike conventional surrogates such as Gaussian Processes or small neural networks, our LLM-based estimator integrates reasoning about instance-specific structure and uncertainty into a single prompt without additional training, achieving both higher flexibility and lower engineering overhead. The framework leverages an LLM to interpret high-level, instance-specific problem descriptions and generate an initial portfolio of hyperparameter configurations. By tailoring these configurations to individual instances and offering a generalizable approach capable of handling diverse parameter sets, GRIMIP provides a more effective and versatile optimization strategy than traditional methods, enabling adaptive, context-aware parameter recommendations for any given MIP instance.

Primary Area: optimization

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Submission Number: 5589