Mathematical models of functions of partial criteria in tasks of vectorial optimization of complex technical systems

Abstract

The article is devoted to different approaches in constructing regression models of functions of partial criteria in vector optimization problems, basic requirements for models, problems that arise in the subsequent application of models and methods of their solution.

Multifactor regression models for the synthesis of complex technical systems are created on the basis of experimental procedures. Models are created for each individual criterion based on the relevant experimental data. The obtained models allow to determine numerical values of partial criteria in given ranges of conceptual parameters of a complex technical system, which are used in the subsequent stages of solving the problem of vector optimization. The necessity to perform these procedures is caused by the fact that when solving an optimization task in relation to complex systems, the analytical dependencies of criteria on optimization arguments are unknown. The polynomial form of regression models is used as approximating polynomials. To ensure good conditionality of the experimental data matrix, standard transformations are performed. The polynomials of Chebyshev of the first and second order are used for this purpose. Unknown polynomial coefficients are calculated using the least squares method. In order to obtain regression models, a complex evaluation of statistical characteristics based on regression analysis results is performed. Then it is decided whether the models can be used to synthesize many alternatives of a complex technical system optimization criterion. The choice of instrumental and methodical devices for scientific and applied researches, engineering works is one problem during the solution of vector optimization problems. In the article it has been stated that nowadays there is a great number of methods and software products which provide wide opportunities for solving vector optimization problems and carrying out different types of data analysis. For example, SPSS, PS PRIAM, STATISTICA, ProSto are the most acceptable and effective, as well as the use of a large number of existing and new modules based on the integrated package of Microsoft Office. This helps to solve a wide range of problems, starting with the procedure of building a regression model of some criteria based on the data from the experiments, the calculation acceptable variants of system and ending with the choice of the residual compromise optimal solution.