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The optimal control models proposed in the literature to control a population of diabetics are all single-objective which limits the identification of alternatives and potential opportunities for different reasons: the minimization of the total does not necessarily imply the minimization of different terms and two patients from two different compartments may not support the same intensity of exercise or the same severity of regime. In this work, we propose a multi-objectives optimal control model to control a population of diabetics taking into account the specificity of each compartment such that each objective function involves a single compartment and a single control. In addition, the Pontryagin's maximum principle results in expansive control that devours all resources because of max-min operators and the control formula is very complex and difficult to assimilate by the diabetologists. In our case, we use a multi-objectives heuristic method, NSGA-II, to estimate the optimal control based on our model. Since the objective functions are conflicting, we obtain the Pareto optimal front formed by the non-dominated solutions and we use fuzzy C-means to determine the important main strategies based on a typical characterization. To limit human intervention, during the control period, we use the convolution operator to reduce hyper-fluctuations using kernels with different size.  Several experiments were conducted and the proposed system highlights four feasible control strategies capable of mitigating socio-economic damages for a reasonable budget.

Solving the optimal diet problem necessarily involves estimating the daily requirements in positive and negative nutrients. Most approaches proposed in the literature are based on standard nominal estimates, which may cause shortages in some nutrients and overdoses in others. The approach proposed in this paper consists in personalizing these needs based on an intelligent system. In the beginning, we present the needs derived from the recommendations of experts in the field of nutrition in trapezoidal numbers. Based on this model, we generate a vast database. The latter is used to educate a deep learning neural network, the architecture of which we optimize by the fuzzy genetic algorithm method in the way of adopting a customized regulation term. Our system estimates nutrient requirements based only on gender and age. These estimations are integrated into a mathematical model obtained in our previous work. Then we again use the fuzzy genetic algorithm to draw up personalized diets. The proposed system has demonstrated a very high capacity to predict the needs of different individuals and has allowed the drawing up of very high-quality diets.

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