Інтелектуальне оптимальне керування нелінійною системою популяційної динаміки хворих на діабет із використанням генетичного алгоритму

• Дата: 2024
• Автори: El Ouissari, Abdellatif, El Moutaouakil, Karim
• Формат: Стаття
• Мова: English
• Опубліковано: The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2024
• Теми: оптимальне керування; диференціальне рівняння; діабет; генетичні алгоритми; штучний інтелект; інтелектуальний локальний пошук; optimal control; differential equation; diabetes; genetic algorithms; artificial intelligence; intelligent local search
• Онлайн доступ: http://journal.iasa.kpi.ua/article/view/304622
• Назва журналу: System research and information technologies

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.