From Tuning Trials to Multi-Level Experience: LLM-Guided MIP Solver Configuration

Mixed-integer programming (MIP) solvers play a vital role in solving large-scale combinatorial optimization problems, which often originate from important real-world applications. It is well-known that the parameter configuration of the MIP solvers has a significant impact on the solving efficiency, while users often rely on static defaults or a single dataset-wide configuration for all instances. However, different instances often favor substantially different configurations, as real-world MIP instances usually originate from diverse sources and they are highly heterogeneous. To tackle this problem, we propose **H**ierarchical **E**xperience **G**raph for LLM-Guided Parameter **Config**uration (**HEG-Config**), which uses an LLM to generate an instance-specific configuration by exploiting tuning experience accumulated across instances. The key challenges to develop HEG-Config are twofold: (1) LLMs lack specialized tuning experience, and (2) tuning itself must balance generalization and instance-specific adaptation. By introducing the novel **hierarchical experience graph**, which can effectively distill historical tuning trials into multi-level experience from instance-specific rules to general tuning strategies, HEG-Config can well address the aforementioned challenges simultaneously. Then, during inference, by retrieving relevant experience at different levels, HEG-Config enables the LLM to integrate general and instance‑specific tuning experience to generate effective configurations. Experiments demonstrate that HEG-Config achieves better aggregate performance than the baselines, consistently improving solving efficiency over the default configuration and reducing the primal-dual integral within the given time limit by 21%–31%.