The menu planning problem: a multi-objective approach for the Brazilian schools context

In this work, we developed a genetic algorithm for solving the automatic menu planning for the Brazilian school context. Our objectives are to create menus that: (i) minimize the total cost and, simultaneously, (ii) minimize the nutritional error according to the Brazilian reference. Those menus also satisfy requirements of the Brazilian government, for example: (i) student age group, (ii) school category, (iii) school duration time, (iv) school location, (v) variety of preparations, (vi) harmony of preparations and, (vii) maximum amount to be paid for each meal. To tackle this problem, we transformed our multiobjective in a mono-objective problem using the linear scalarization method and solved it with a genetic algorithm. We also developed a multiobjective algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). Our results demonstrate that the multiobjective approach is 5 times faster, with 30 times more non-dominated solutions and give solutions that are statistically better compared with the mono-objective algorithm. Another advantage of this the approach is the diversity of solutions, allowing the professional (nutritionist) choose one among the various menus obtained by the algorithm, giving priority to the objective that is considered to be the most relevant in a given situation.