Volume 56, Number 5, September-October 2022
|Page(s)||3245 - 3256|
|Published online||12 September 2022|
Multi-objectives optimization and convolution fuzzy C-means: control of diabetic population dynamic
Engineering Science Laboratory (LSI), Faculty Polydisciplinary of Taza, USMBA, Morocco
2 MorphoSciences Research Laboratory, Faculty of Medicine and Pharmacy, CAU, Morocco
3 Biosciences and Health laboratory, Faculty of Medicine and Pharmacy, CAU, Morocco
* Corresponding author: firstname.lastname@example.org
Accepted: 8 August 2022
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.
Mathematics Subject Classification: 90C20 / 90C29 / 90C90 / 93E20
Key words: Diabetes / optimal control / multi-objectives optimization / Non-dominated Sorting Genetic Algorithm II (NSGA-II) / fuzzy C-means / kernel convolution
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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