Devising a universal optimization method under conditions of fuzzy initial data
Лев Григорьевич Раскин, Оксана Сіра, Larysa Sukhomlyn, Viacheslav Karpenko, Vitalii Vlasenko · Eastern-European Journal of Enterprise Technologies · 2025
The object of this study is an optimization method under conditions when the initial data (parameters of the system or the environment in which the system operates) are not precisely defined. The problem that arises in this case is related to the lack of universal mathematical methods that solve optimization problems under conditions of uncertainty of the initial data. To solve these problems, approaches are proposed based on the transformation of the initial fuzzy problems into clear problems of mathematical programming. In this case, either a solution to the optimization problem "on average" or solutions obtained for extreme values of inaccurately specified parameters of the problem are proposed as the desired result. The error of the resulting solution is unpredictable. This paper proposes an alternative approach to solving optimization problems under conditions of fuzzy initial data. The method is based on the use of a multiplicative convolution of the objective function of the problem and a set of membership functions of fuzzy parameters. A feature of the method is that it is stable with respect to the possible variety of analytical descriptions of the objective function of the problem and ensures an adequate solution that takes into account the real uncertainty of the initial data. The fundamental feature of the method: the technique of its construction and the computational scheme of its implementation do not depend in any way on the type, nature, and complexity of the analytical description of the objective function of the original problem. At the same time, to implement the proposed optimization procedure, it is sufficient to have the ability to calculate the value of the objective function on any set of its variables. It is shown that in all cases the original problem with fuzzy initial data is transformed into a conventional deterministic optimization problem solved by known methods. An example of an analytical solution to the problem is given