ChatGPT with Mixed-Integer Linear Programming for Precision Nutrition Recommendations

BackgroundThe growing interest in applying artificial intelligence in personalized nutrition is challenged by the complex nature of dietary advice that must balance health, economic, and personal factors. Though automated solutions using either Linear Programming (LP) or Large Language Models (LLMs) already exist, they have significant drawbacks. LP often lacks personalization, whereas LLMs can be unreliable for precise calculations. ObjectivesTo develop and assess a model that integrates a Mixed Integer Linear Programming (MILP) solver with an LLM to generate personalized meal plans and compare it with standalone LLM and MILP models. MethodsThe proposed hybrid MILP+LLM model first uses an LLM (GPT-4o) to filter a unified food dataset (n=297), which combines regional Central Asian and global food items, according to the users profile. The filtered list of food items is then received by a MILP solver which identifies the set of top 10 optimal solutions. Finally, given this set of solutions, LLM chooses the most appropriate meal plan. The model was evaluated using five synthesized, clinically complex patient profiles sourced from Adilmetova et al. [4]. The performance of this hybrid model was compared against standalone MILP and LLM using 5-point Likert scale with Kruskal-Wallis and post hoc Dunns tests for Nutrient Accuracy, Personalization, Practicality, and Variety. ResultsFindings demonstrated that the proposed MILP+LLM model reached balanced performance achieving scores of more than 3.6 points in all criteria, with high scores in Nutrient Accuracy (3.96), Personalization (3.81), and Practicality (3.99). The standalone LLM model performed the weakest in all criteria, with statistically significant lower scores compared to the other two methods. The standalone MILP model performed best in Nutrient Accuracy (4.93) and in Variety (4.10) but lagged behind the MILP+LLM model in Practicality and Personalization. Kruskal-Wallis and Dunns tests showed MILP and MILP+LLM outperformed LLM across all criteria. MILP was more accurate (p<0.0001), while MILP+LLM model was more practical (p=0.021). ConclusionsThe findings suggest that integrating the LLM with the MILP solver creates a model that combines qualitative personalization with quantitative precision. This model produces comprehensive, reliable meal plans, addressing the limitations of using either model alone.