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

2026-06-22

AI Summary

This work addresses the challenge of instance-dependent hyperparameter configuration for mixed-integer programming (MIP) solvers, a task traditionally hindered by cold-start issues, inefficient search, or reliance on expert knowledge. The authors propose GRIMIP, a novel framework that, for the first time, employs a large language model (LLM) as a full probabilistic surrogate within Bayesian optimization (BO). By integrating the LLM’s semantic reasoning capabilities with BO’s sample efficiency in an end-to-end tuning loop, GRIMIP enables instance-specific automatic hyperparameter optimization. The approach substantially advances beyond existing tuning paradigms, achieving an average reduction of over 40% in the Primal-Dual Integral on hard instances across seven benchmarks—including MIPLIB—significantly outperforming both SMAC and current LLM-assisted BO methods.

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.

Problem

• Mixed-integer programming
• hyperparameter configuration
• instance-specific optimization
• solver performance
• cold-start problem

Innovation

• Large Language Models
• Bayesian Optimization
• MIP Solver Configuration
• Hybrid Intelligence
• Probabilistic Surrogate