ОПТИМІЗАЦІЯ РОЗМІЩЕННЯ ДЖЕРЕЛ ФІЗИЧНОГО ПОЛЯ НА ФІКСОВАНІ МІСЦЯ

• Datum: 2020
• Hauptverfasser: Lyashko, S.I., Yaremchuk, S.I., Lyashko, N.I., Shupikov, A.A., Bondar, E.S.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: оптимізація; лінійний оператор; функція мети
• Online Zugang: https://jais.net.ua/index.php/files/article/view/475
• Назва журналу: Problems of Control and Informatics

The problems of finding such placement of physical field sources at fixed landing places are considered, at which the maximum of the resulting field values at the measurement points is the smallest. The paper presents a mathematical model of this problem, which was previously developed by the authors, which is minimax linear programming problem with Boolean variables and method «P-algorithm» which resolves it. The new mathematical model which is partly an integer linear programming problem with Boolean variables was built. Classic optimization methods such as the Land and Doig method can be used to solve this problem. Obtained modification of this method significantly increased the speed of solving this problem. An example of how to solve a practical problem by using a Land and Doig method modification is an illustration of how to use the proposed methods. In this paper, it is analytically substantiated and verified by numerical experimentation, which showed that applying the Land and Doig method modification significantly speeds up the solution of the task compared to the classic professional libraries. The use of parallel computations in modifications of the Land and Doig method increased its speed by almost 60 %. The correctness of the boundary-value problems given in the work follows from the a priori estimates obtained by the authors in negative norms. The results of the work easily apply to systems with point or impulse action.