[Submitted on 22 Jun 2026 (v1), last revised 1 Nov 2026 (this version, v3)]
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.
Submission history
From: Yidong Luo [view email]
[v1] Mon, 22 Jun 2026 13:10:50 UTC (398 KB)
[v2] Wed, 5 Aug 2026 05:48:40 UTC (530 KB)
[v3] Sun, 1 Nov 2026 15:23:04 UTC (530 KB)
