TO THE PROBLEM OF GLOBAL PARAMETER OPTIMIZATION RELIABILITY AND SECURITY OF COMPLEX DYNAMIC SYSTEMS USING THE INVERSE METHOD
Background . Complex dynamic systems are characterized by many parameters that change during the design and operation, which can lead to a loss of reliability and security of the system, additional costs for maintaining their performance. In the design process, it is necessary to solve the optimization problem in order to determine the best values of the system parameters or its structure. One has to deal with multi-extreme objective functions and equations of large dimension. The search for effective methods for finding a global minimum or maximum in a certain area of a finite-dimensional vector space of possible design solutions is an urgent task. The aim of the work is to develop an effective method of global optimization in the tasks of constructing complex dynamic systems. Materials and methods . The work uses the theory of statistical synthesis of complex systems, search engine optimization methods and mathematical statistics, as well as the method of generating inverse functions. Results. A fundamentally new method has been developed for solving global optimization problems in which no special restrictions are imposed on the objective function. The inverse method consists in representing variable parameters in the form of approximating inverse functions, the argument of which is the value of the objective function, which changes according to certain rules, forming partly a relaxation sequence. Conclusions. Representation of the inverse approximating functions made it possible to avoid viewing the criterial surface on the entire admissible set, since surface sensing is carried out only in the direction of improving the optimality criterion. Since the approximating functions are determined by a limited number of free parameters, the dimensionality of the problems to be solved is seriously reduced and the restrictions on the form and features of the objective functions are removed. The developed method is proposed to be used in the process of constructing and evaluating the reliability and safety of complex dynamic systems with variable structure and parameters.