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

• URL: http://arxiv.org/abs/2606.23299v1
• Date: Mon, 22 Jun 2026 13:10:50 GMT
• Title: GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs
• Abstract summary: This paper introduces textbfGRIMIP (textbfunderlineGeneral textbfunderlineReasoning for textbfunderlineInstance-specific textbfunderlineMIP configuration), a novel hybrid intelligence framework.
• Score: 9.2939109839777
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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