Інтелектуальне оптимальне керування нелінійною системою популяційної динаміки хворих на діабет із використанням генетичного алгоритму
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....
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute"
2024
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| Subjects: | |
| Online Access: | http://journal.iasa.kpi.ua/article/view/304622 |
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| Journal Title: | System research and information technologies |
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System research and information technologies| Summary: | 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. |
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