Проблема оцінки та оптимізації обʼєкта за кількома критеріями

• Дата: 2023
• Автори: Voronin, Albert, Savchenko, Alina
• Формат: Стаття
• Мова: English
• Опубліковано: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2023
• Теми: багатокритеріальність; функція корисності; скалярна згортка; формалізація; ситуація; нелінійна схема компромісів; шкала Харрінгтона
• Онлайн доступ: https://jais.net.ua/index.php/files/article/view/195
• Назва журналу: Problems of Control and Informatics

The problems of estimation and optimization of an object pursuing several goals are considered. In the estimation problem, the evaluation function is calculated with known parameters that determine the state of the object. In the optimization problem, there are optimization arguments that deliver the extremum of the objective function. Both the evaluation and objective functions are built on the basis of the concept of a nonlinear trade-off scheme, for which the principle «away from restrictions» is fulfilled. Both tasks are solved in a formalized manner, without the direct participation of the decision maker (DM). Model examples are given. The object O is considered, the state of which is determined by the set of values x1, x2,…,xn, that make up the vector x={xj}ni=1 ϵ X   The object pursues several goals, the degree of achievement of each of them is expressed by the corresponding criterion yk(x), k ϵ [1,…,s]. The criteria form a vector y={yk(x)}sk=1 ϵ M. Restrictions are imposed on the criteria  yk min(x)≤yk(x)≤ yk max(x). The problem of estimating the quality of the functio­ning of an object O is to determine the value of a certain function Y[y(x)]  with known parameters x1, x2,…,xn. The function Y[y(x)]  in this case is called the evaluation function. The optimization problem is to determine the values x1, x2,…,xn by extremizing the function Y[y(x)]  In this case, the function Y[y(x)]  is the objective, and the parameters are called optimization arguments. Both tasks require the function Y[y(x)]. In fact, this function is a scalar convolution of the criteria vector y(x)  which reflects the utility function of the decision maker (DM) in solving a specific estimation or optimization problem. Scalar convolution is an act of composing criteria. The criterion yk(x) is a measure of the quality of the object O functioning in relation to the achievement of the k-th goal. If «more» means «better», then such a criterion should be maximized to improve the quality. Otherwise, the criterion is minimized. For definiteness, we consider the optimization problem under minimized performance criteria.