**1. Introduction**

For healthy individuals, balanced diets reduce the likelihood of developing chronic diseases; whereas for individuals with chronic diseases, balanced diets reduce the likelihood of entering dangerous stages, especially for diabetics, cardiovascular disease, obesity and cancer [1–6]. It is a matter of satisfying the body's demands in an optimal manner.

The earliest optimization model, relating to the diet issue, was suggested in [7] with the regime cost as an objective function. Within [8], the target function was minimization of weighted meal compositions, implicating case- and rule-based reasoning; in which any new daily vegan menu consisted of breakfast, lunch, dinner, a snack, and, in additional, a fruit serving. Further suggestions [9] involve minimizing the difference between the real and advised consumption whilst satisfying the nutritional needs. In studies [10], the authors suggest supplemental plans (children under the age of 2 years) and dietary plans (school age group 13–18 years) at the lowest total cost. To further investigate more features, various multi-objective driven schemes were suggested. While generating food meals, the authors of [11] tackled the economical and aesthetical aspects (taste, flavor, color… ). When forming the objective functions of their

mathematical optimization model, the authors of the article [12] included the price of regime, and other aspects like carbon dioxide emissions, land, and water consumption, etc. V. Mierlo have considered nearly the identical case by substitution of the regime cost and the fossil fuel depletion minimization [13]. At [14], the authors suggest a multiobjective programming framework which delivers a nutritional program plan and minimizes glycemic load and cholesterol consumption, seen as the major causes of childhood overweight.

Recently, we have proposed an original mathematical optimization model for the optimal diet problem. In this paper, we compare three well-known swarm algorithms on optimal regime based on our mathematical optimization model introduced recently [5]. Different parameters of this latter are estimated based on 176 foods who's the nutrients values are calculated for 100 g. The daily nutrients needs are estimated based on the expert's knowledge [6].

The remainder of the material is structured as follows: the second section concerns the mathematical model of the diet problem. The third section is about the three swarm optimization methods: SFS, FA, and PSO. In the fourth section, several experimental results are presented and analyzed. At the end, some conclusions and future propositions are discussed.
