The optimal regime models implement parameters presented by nominal values, intervals, fuzzy models, intuitionistic models. Unfortunately, these models are restrictive and ignore a significant portion of the knowledge contained in the specifications. To overcome this problem, we propose an optimal system that implements deep learning artificial neural networks and fuzzy genetic algorithms for the first time in the literature. The deep neural network extracts the information, the neural network units memorize this information, genetic algorithms select the best architecture of the auto-encoder basing on new regulation function, and fuzzy logic allows some flexibility for our system. First, we collect the expert's nutrients recommendations from different expert research papers. These recommendations are, then, represented in terms of trapezoidal numbers by adopting appropriate rules that encourage the consumption of the favorable nutrients and limit consumption of the unfavorable nutrients in daily diets. Then, we generate large data sets basing on the trapezoidal representation. To transform the expert's recommendations into significant crisp values, we call the auto-encoder neural network, and we propose an original regulation term that controls all the auto-encoder units. To select the best auto-encoder architecture, we use the fuzzy genetic algorithm basing on a simple fuzzy rule to determine the crossover percent, the mutation percent, and the population size at each iteration. Compared to the random systems, the proposed method has shown a great capacity to generalize its experience to unseen recommendations. In a clinical setting, our system can be used by a dietician to accurately determine the daily nutrient requirements of a given individual.
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.
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