GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs
2026-06-22 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the problem of tuning parameters for Mixed-Integer Programming (MIP) solvers, which is usually complex and instance-dependent. They introduce GRIMIP, a new method that combines the reasoning abilities of Large Language Models (LLMs) with the search efficiency of Bayesian Optimization (BO). This approach helps find better solver configurations faster and with fewer trials. Testing on multiple benchmarks showed that GRIMIP performs significantly better than existing methods. Overall, the authors demonstrate how combining AI reasoning with optimization techniques can improve solver performance.
Mixed-Integer ProgrammingHyperparameter tuningLarge Language ModelsBayesian OptimizationPrimal-Dual IntegralSolver configurationMIPLIBSample efficiency
Authors
Yidong Luo, Xuemin Chen, Chenguang Wang, Fangzhou Zhu, Tao Zhong, Tianshu Yu
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 \textbf{GRIMIP} (\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 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.