МЕТОД ВИРІШЕННЯ ЗАДАЧІ УМОВНОЇ ОПТИМІЗАЦІЇ НА КОМБІНАТОРНІЙ МНОЖИНІ РОЗМІЩЕНЬ

• Datum: 2025
• Hauptverfasser: Kolechkina, L.N., Nagornaya, A.N., Semenov, V.V.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2025
• Schlagworte: задача умовної оптимізації; комбінаторна множина розміщень; екстремум функції; матриця нормалізації
• Online Zugang: https://jais.net.ua/index.php/files/article/view/668
• Назва журналу: Problems of Control and Informatics

Defining a problem of optimization on a combinatorial set of arrangements is considered and presenting the method of its solution, taking into account satisfaction of the conditions imposed on gains of restrictions and objective function is proposed. Themethod consists of three steps where at the initial stage matrixes of normalization and compliance are built, which provide elements arrangement set transformation to a necessary form for criterion function and the defined restrictions. The second step consists in finding the first basic solution, taking into account property of arrangement set. It should be noted that for finding the first basic solution it is enough to calculate gains of restrictions. If the allowable solution satisfies presented inequalities, then initial data is fixed, which will be the verification conditions for the following improved solution. The value of the goal function is determined at theexpense of calculating the increments of the target function, without the need to calculate the entire previous function. The third step of a method provides finding of an optimal solution at direct improvement of the found basic solution. On this step sufficient and necessary conditions for search of an optimal solution are formulated. Numerical examples of search functions's extrems on a set of arrangements are considered and also the numerical experiment for the case |А3К|is presented, at increase of sample units quantity of an arrangements set ( k ). Also it should be noted that the finding steps quantity of an optimal solution considerablydoes not increase, at sharp increase of elements quantity in a set of arrangements. Analyzing an indicator of percentage correlation of the considered points quantity when finding an optimal solution to quantity of elements on an arrangements set, it should be noted its considerable reduction that gives evidence about efficiency of the offered method. So, this method allows to find a function extremum on a set of arrangements during a finite number of steps.