Exploring the True Potential: Evaluating the Black-box Optimization Capability of Large Language Models

Large language models (LLMs) have gained widespread popularity and demonstrated exceptional performance not only in natural language processing (NLP) tasks but also in non-linguistic domains. Their potential as artificial general intelligence extends beyond NLP, showcasing promising capabilities in diverse optimization scenarios. Despite this rising trend, whether the integration of LLMs into these black-box optimization problems is genuinely beneficial remains unexplored. This paper endeavors to tackle this issue by offering deeper insights into the potential of LLMs in optimization tasks through a comprehensive investigation. Our approach involves a comprehensive evaluation, covering both discrete and continuous optimization problems, aiming to assess the efficacy and distinctive characteristics that LLMs bring to the realm of optimization. Our findings reveal both the limitations and advantages of LLMs in optimization. On one hand, despite consuming the significant power required to run the model, LLMs exhibit subpar performance and lack desirable properties in pure numerical tasks, primarily due to a mismatch between the problem domain and their processing capabilities. On the other hand, although LLMs may not be ideal for traditional numerical optimization, their potential in broader optimization contexts remains promising. LLMs exhibit the ability to solve problems in non-numerical domains and can leverage heuristics from the prompt to enhance their performance. To the best of our knowledge, this work presents the first systematic evaluation of LLMs for numerical optimization, offering a progressive, wide-coverage, and behavioral analysis. Our findings pave the way for a deeper understanding of LLMs' role in optimization and guide future application in diverse scenarios for LLMs.