Ugryumova K. Mathematical Models and Solution Searching Methods of Improvement of Systems with a Multiechelon Hierarchy Problem.

The mathematical models, methods and computer tools of solutions searching of nonlinear multi-criteria modification problems for the systems with a multiechelon hierarchy are offered. It is suggested to carry out the rational solutions searching on the basis of multilevel hierarchy scheme of solution synthesis taking into account the level matching of local objective functions with global objective functions in accordance with conception of the equilibrium by J. F. Nash. The methods of systems models construction on the basis of artificial neuron networks, teaching of which was carried out by the method of stochastic approximation with application of regularization adaptive algorithm of solutions synthesis with the lazy correction, are developed. The method of quasi-solutions construction of nonlinear modification problems by the regularization search of smoothed functional minimum with the usage of the method by A. N. Tihonov is developed. The evolutional method of solution of these problems with adaptation of its parameters in the process of solutions searching is offered. The main results of given thesis have found their industrial application for system improvement of aviation technique objects.