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

2026/06/30 by Yidong Luo, Xuemin Chen, Chenguang Wang +3
Computer Science · #cs.LG

paper · pdf

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

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 (\textbf\underlineGeneral \textbf\underlineReasoning for \textbf\underlineInstance-specific \textbf\underlineMIP 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.

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