A systematic assessment of Large Language Models for constructing two-level fractional factorial designs

Two-level fractional factorial designs permit the study multiple factors using a limited number of runs. Traditionally, these designs are obtained from catalogs available in standard textbooks or statistical software. However, modern Large Language Models (LLMs) can now produce two-level fractional factorial designs, but the quality of these designs has not been previously assessed. In this paper, we perform a systematic evaluation of two popular classes of LLMs, namely GPT and Gemini models, to construct two-level fractional factorial designs with 8, 16, and 32 runs, and 4 to 26 factors. To this end, we use prompting techniques to develop a high-quality set of design construction tasks for the LLMs. We compare the designs obtained by the LLMs with the best-known designs in terms of resolution and minimum aberration criteria. We show that the LLMs can effectively construct optimal 8-, 16-, and 32-run designs with up to eight factors.