Multi-objectives optimization and convolution fuzzy C-means: control of diabetic population dynamic

Abstract

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.

Genetic algorithm applied to fractional optimal control of a diabetic patient

“…The real beginning of the use of genetic algorithm for dynamic control systems was in 1992 by Krishnakumar and Goldberg [27], who gave a start to GA in a very important discipline of applied mathematics [28], [31], [33]. Among the most recent works of optimal control that have studied the phenomenon with metaheuristic methods is that by El Moutaouakil et al [32], which used artificial intelligence methods for a general study of the phenomenon of diabetes, for more details see [32]. The major objective of this work is to achieve a significant reduction in the number of diabetics.…”

A Multiobjective Diet Planning Model for Diabetic Patients in the Moroccan Health Context Using Particle Swarm Intelligence

“…It is important to note that mathematical programming models of feeding problems do not take into account the variability of nutrients in foods. Recall artificial intelligence techniques [22,23,24,25,26,27] in particular fuzzy logic [28,29,30,31] are being used to deal with the uncertainty associated with the parameters of the diet problem. Our problem was first presented in [20] in which the objectives are robust and presented separately as two singleobjective robust optimization problems.…”

FP-Conv-CM: Fuzzy Probabilistic Convolution C-Means

“…To obtain the probabilistic version of k-means, it is assumed that the observations of the learning set B are the realizations of a random variable whose density function is a mixture of k normal distributions [44,53]:…”

“…We investigated, in [43], a constrained optimization method that de-assigns memberships from centers to reduce the impact of outlier samples. To benefit from the capacity of dynamic systems to memorize prior groupings and the understanding of the features of the data by neural networks, we have introduced, in our previous work [44], an original clustering method that implements fuzzy logic and a recurrent neural network, namely the Recurrent Neural Network Fuzzy C-means. Other recent versions of Fuzzy C-means were introduced.…”