An Evolutionary Mono-Objective Approach for Solving the Menu Planning Problem

Abstract

This work proposes an evolutionary approach to solve the Menu Planning Problem. Our work uses the Brazilian school context and our principal goal is to create menus that minimize the total cost of these menus. However, those menus must also satisfy requirements of the Brazilian government, such as: (i) student age group, (ii) school category, (iii) school duration time, (iv) school location, (v) variety of preparations, (vi) harmony of preparations, (vii) maximum amount to be paid for each meal and, (viii) lower and upper limits of macronutrients. The results demonstrate that the evolutionary approach is not only able to generate a set of inexpensive and healthy menus but also respect the required set of constraints. A constrained deterministic approach is performed to generate 5-day menu through a greedy-based function taking into account the normalized sum of all macronutrients and the monetary cost of the menu. A comparison between the 5-day menu obtained by the proposed approach and the constrained greedy-based approach menu is carried out. Despite the fact the obtained menu outperforms the greed-based menu taking into account the total cost, this difference is not so expressive. However, all macronutrients were outside the pre-defined range at least in one day of the week. The 5-day menu obtained by the proposed approach is evaluated by a nutritionist. The overall quality of the menu is outstanding and the time spent to generate it is 60 seconds.