Алгоритми оптимального вибору варіантів для одного спеціального класу задач

• Дата: 2024
• Автори: Stetsyuk, Petro, Vakulenko, Dmytro, Semykopna, Tetyana
• Формат: Стаття
• Мова: Ukrainian
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2024
• Теми: задача цілочислового нелінійного (лінійного; квадратичного) програмування; BARON; Gurobi; реабілітаційна програма пацієнта; мультидисциплінарна команда
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/409
• Назва журналу: Problems of Control and Informatics

Three problems of mathematical programming for finding optimal cost (linear criterion) and weighting (quadratic criterion) resultative rehabilitation programs are formulated and substantiated. Effectiveness of the program is determined by transition from larger initial values of the patient state parameters to smaller final values of the patient state parameters due to effect of the selected program implementation options. The first problem is designed to find minimal in terms of total cost number of options for implementing the program. It is formulated as an integer nonlinear programming problem and its equivalent integer linear programming problem. The second problem is designed to find minimal weighted number of options and is formulated as an integer quadratic programming problem. The third problem is formulated as an integer quadratic programming problem and is designed to find minimal weighted program, whose cost does not exceed the given cost of the program. Algorithmic properties of the problems constructed are illustrated on the example of the problem of finding optimal number of interventions in rehabilitation programs performed by specialists of a multidisciplinary team. Calculations are presented for a model example, where the patient’s rehabilitation program is performed by four specialists of a multidisciplinary team and three codes of the International Classification of Functioning, Disability and Health (ICF).