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

: pp. 338–350
Received: January 11, 2023
Accepted: March 10, 2023

Mathematical Modeling and Computing, Vol. 10, No. 2, pp. 338–350 (2023)

Engineering science laboratory, FPT of Taza, USMBA of Fez, Morocco
Engineering science laboratory, FPT of Taza, USMBA of Fez, Morocco
Morphoscience laboratory, FMP, CAU of Marrakech, Morocco
Health science laboratory, FMP, CAU of Marrakech, Morocco
Morphoscience laboratory, FMP, CAU of Marrakech, Morocco
Morphoscience laboratory, FMP, CAU of Marrakech, Morocco
Biosciences and Health Research Laboratory, Diabetes and Metabolic Diseases Endocrinology Service, Avicenne Military Hospital, FMP, UCA of Marrakech, Morocco

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.

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