Intelligent optimal control of nonlinear diabetic population dynamics system using a genetic algorithm




optimal control, differential equation, diabetes, genetic algorithms, artificial intelligence, intelligent local search


Diabetes is a chronic disease affecting millions of people worldwide. Several studies have been carried out to control the diabetes problem, involving both linear and non-linear models. However, the complexity of linear models makes it impossible to describe the diabetic population dynamic in depth. To capture more detail about this dynamic, non-linear terms were introduced into the mathematical models, resulting in more complicated models strongly consistent with reality (capable of re-producing observable data). The most commonly used methods for control estimation are Pantryagain’s maximum principle and Gumel’s numerical method. However, these methods lead to a costly strategy regarding material and human resources; in addition, diabetologists cannot use the formulas implemented by the proposed controls. In this paper, the authors propose a straightforward and well-performing strategy based on non-linear models and genetic algorithms (GA) that consists of three steps: 1) discretization of the considered non-linear model using classical numerical methods (trapezoidal rule and Euler–Cauchy algorithm); 2) estimation of the optimal control, in several points, based on GA with appropriate fitness function and suitable genetic operators (mutation, crossover, and selection); 3) construction of the optimal control using an interpolation model (splines). The results show that the use of the GA for non-linear models was successfully solved, resulting in a control approach that shows a significant decrease in the number of diabetes cases and diabetics with complications. Remarkably, this result is achieved using less than 70% of available resources.

Author Biographies

Abdellatif El Ouissari, Sidi Mohamed Ben Abdellah University; Higher School of Engineering in Applied Sciences, Fes

Engineering Science Laboratory (LSI), Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, Fes, Morocco; ESISA Analytica Laboratory, Higher School of Engineering in Applied Sciences, Fes, Morocco.

Karim El Moutaouakil, Sidi Mohamed Ben Abdellah University, Fez

Professor, Engineering Science Laboratory (LSI), Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, Fez, Morocco.


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Mathematical methods, models, problems and technologies for complex systems research