Hybrid firefly genetic algorithm and integral fuzzy quadratic programming to an optimal Moroccan diet

In this paper, we solve the Moroccan daily diet problem based on 6 optimization programming $(P)$ taking into account dietary guidelines of US department of health, human services, and department of agriculture.  The objective function controls the fuzzy glycemic load, the favorable nutrients gap, and unfavorable nutrient excess.  To transform the proposed program into a line equation, we use the integral fuzzy ranking function.  To solve the obtained model, we use the Hybrid Firefly Genetic Algorithm (HFGA) that combines some advantages of the Firefly Algorithm (FA) and the Genetic Algorithm (GA).  The proposed model produces the best and generic diets with reasonable glycemic loads and acceptable core nutrient deficiencies.  In addition, the proposed model showed remarkable consistency with the uniform distribution of glycemic load of different foods.

optimal Moroccan diet
fuzzy quadratic programming
triangular fuzzy numbers
integral ranking most function
генетичний алгоритм
firefly algorithm
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