Improving LLM-based Global Optimization with Search Space Partitioning

Large Language Models (LLMs) have recently emerged as effective surrogate models and candidate generators within global optimization frameworks for expensive blackbox functions. Despite promising results, LLM-based methods often struggle in high-dimensional search spaces or when lacking domain-specific priors, leading to sparse or uninformative suggestions. To overcome these limitations, we propose HOLLM, a novel global optimization algorithm that enhances LLM-driven sampling by partitioning the search space into promising subregions. Each subregion acts as a ``meta-arm'' selected via a bandit-inspired scoring mechanism that effectively balances exploration and exploitation. Within each selected subregion, an LLM then proposes high-quality candidate points, without any explicit domain knowledge. Empirical evaluation on standard optimization benchmarks shows that HOLLM consistently matches or surpasses leading Bayesian optimization and trust-region methods, while substantially outperforming global LLM-based sampling strategies.