用大模型+贝叶斯优化自动调优混合整数规划求解器，提速超40%。
GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs
- 让大模型充当贝叶斯优化的智能代理，自主指导参数搜索
- 在7个基准上对难例的原对偶积分降低40%以上
- 适合需要高效求解复杂优化问题的研究与工程人员
混合整数规划（MIP）求解器的超参数配置是一个高维、依赖实例的优化问题，次优设置可使求解时间下降数个数量级。默认配置通常不理想，传统调优方法要么存在冷启动问题、搜索效率低，要么严重依赖专家经验。本文提出GRIMIP（通用推理用于实例化MIP配置），一种融合大语言模型（LLM）语义推理能力与贝叶斯优化（BO）样本高效搜索优势的新型混合智能框架。GRIMIP使LLM在BO循环中充当完整的概率代理，显著提升性能并降低采样与评估成本。在包含MIPLIB在内的7个基准上，GRIMIP对难例的原对偶积分减少超过40%，优于SMAC及其他基于大模型的贝叶斯优化方法。通过赋予大模型充分自主性，该方法结合了大模型的专家级推理与贝叶斯优化的高效搜索，达到当前最优性能。
原文摘要 · Abstract (English)
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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