Optimization of Sustainable Diets under Cultural Acceptability Constraints: An Approach via Genetic Algorithms for the Brazilian Population

This work proposes a nonlinear optimization model to maximize the adherence of the Brazilian population to the Planetary Diet, measured by the Planetary Health Diet Index (PHDI), under caloric, economic and cultural acceptability restrictions. A meta-heuristic based on Genetic Algorithms (GA) was used, calibrated through $7,200$ executions to identify robust parameters. The results indicate that the restriction of cultural acceptability is the main limiting factor of the model, evidencing a gap between the national dietary pattern and the recommendations of the EAT-Lancet Commission. The average PHDI total score reached $84.85 points out of a maximum of 150 points, reflecting tensions between nutritional goals and the habits of the population. The analysis of the convergence profiles demonstrates that single-objective optimization diagnoses this incompatibility, pointing to the need for future multiobjective approaches to balance the nutritional, environmental, economic and social dimensions of sustainability in the Brazilian context.