Bi-objective challenge of the Brazilian diet: a linear programming model for the balance between planetary health and cultural acceptability

This paper presents a model of Mixed Integer Linear Programming (PLIM) to investigate the conflict between the adherence of Brazilians to the Planetary Health Diet Index (PHDI) and the cultural acceptability of the Brazilian population. Using data from the National Food Survey (INA 2017-2018), the model seeks to simultaneously maximize the PHDI score and cultural acceptability, modeled via Goal Programming to penalize deviations from the consumption percentiles observed in the INA. The conditional nature of the PHDI was treated using the Big-M linearization technique. The resolution of the 108 instances present in the survey was carried out using the preemptive scheme and allowed the identification of the lexicographic points of the Pareto Frontier. The results show a trade-off between the objectives, suggesting that the transition to sustainable dietary patterns in Brazil faces significant cultural barriers, represented by the degradation of one objective by prioritizing the other in the optimization process.