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The Control Parametrization Enhancing Technique for Multi-Objective Optimal Control of HIV Dynamic | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 1، دوره 1، شماره 2، دی 2016، صفحه 1-21 اصل مقاله (706.95 K) | ||
| نوع مقاله: Research Article | ||
| نویسنده | ||
| Hassan Zarei* | ||
| Department of Mathematic, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| In this paper, a computational approach is adopted for solving a multi-objective optimal control problem (MOOCP) formulation of optimal drug scheduling in human immunodeficiency (HIV) virus infected by individuals. The MOOCP, which uses a mathematical model of HIV infection, has some incompatible objectives. The objectives are maximizing the survival time of patients, the level of D4+ T-cells and the level of cytotoxic T-lymphocytes (CTLs), and minimizing the viral load and the drug costs. In this approach the fuzzy goals described by the linear membership functions, are incorporated for the objectives and the optimal solution is investigated by maximizing the degree of attainment of the aggregated fuzzy goals resulting a fuzzy goal optimal control problem (FGOCP). Using the minimum operator for aggregation of fuzzy goals, the FGOCP is converted into a constrained optimal control problem (OCP) in canonical form. The control parametrization enhancing technique (CPET) is used for approximating the OCP by an optimal parameter selection problem, with the final goal of implementing continuous and interrupted (structured treatment interruptions, STI) combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies. Efficiency of the proposed method is confirmed by numerical simulations. | ||
| کلیدواژه‌ها | ||
| Multi-objective problem؛ Optimal control؛ Fuzzy goal programming؛ Therapy optimization | ||
| عنوان مقاله [English] | ||
| کنترل بهینه چندهدفه دینامیک HIV به کمک تکنیک پارامتری کردن کنترل | ||
| چکیده [English] | ||
| دراین مقاله یک ایده محاسباتی برای حل یک مسئله فرمول‌بندی کنترل بهینه چندهدفه زمان‌بندی درمان بهینه در افراد آلوده به ویروس نقص ایمنی انسانی (HIV) مطرح می‌شود. مسئله کنترل بهینه چندهدفه که از یک مدل ریاضی عفونت HIV استفاده می‌کند، دارای چند هدف غیرهمسو است. مانند طول عمر بیمار، سطح سلول‌های CD4+ و سطح CTL که باید بیشینه گردند، سطح ویروس و هزینه‌های دارو که باید کمینه گردند. دراین ایده آرمان‌های فازی توصیف شده توسط توابع عضویت خطی، به اهداف اضافه شده و جواب بهینه با بیشینه‌سازی درجه حصول آرمان‌های فازی انباشته شده، مورد جستجو قرار گرفته و یک مسئله کنترل بهینه آرمانی فازی نتیجه می‌شود. با استفاده از عملگر کمینه برای انبوهش آرمان‌های فازی، مسئله کنترل بهینه آرمانی فازی تبدیل به یک مسئله کنترل بهینه محدود در فرم کانونی می‌شود. روش پارامتری کردن کنترل برای تقریب مسئله کنترل بهینه با یک مسئله انتخاب پارامتر بهینه با هدف نهایی پیاده‌سازی ترکیبات پیوسته و منقطع (STI) کارایی داروهای دسته PI و RTI به کارمی‌رود. کارایی ایده بیان شده توسط شبیه‌سازی‌های عددی مورد تایید قرار می‌گیرد. | ||
| کلیدواژه‌ها [English] | ||
| مسئله چندهدفه, کنترل بهینه, برنامه‌ریزی آرمانی فازی, بهینه‌سازی درمان | ||
| مراجع | ||
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