Application of Projection Algorithms for Geometric Modeling and Optimization of Socio-Economic Processes

Abstract

The article proposes an approach to systematization, modeling and optimization of multidimensional statistical data based on the use of projection algorithms for computer modeling. The proposed approach is presented on the example of computer modeling and optimization of socio-economic data, but it can also be effectively used to systematize and analyze other experimental statistical data. It consists the fact that the original multidimensional data are presented in the form of projections on the Radishchev’s complex drawing in the form of curved lines system. Then, on the indicator curve, the optimal value of the socio-economic indicator is selected (as a rule, this is one of the extrema of the function) and the value of the time at which it was reached is fixed. Here, the indicator curve is understood as the curve corresponding to the response function, and the factor curve is the curves corresponding to the factors influencing the response function. Further, a scientific hypothesis is put forward that the joint interaction of factors recorded at a given moment in time ensures the optimal value of the socio-economic indicator. Thus, we obtain the optimal values of the factors influencing the response function, which in this case is the socio-economic indicator. The interaction between the indicator curve and the factor curves is carried out through the line of interprojection connection. The proposed scientific hypothesis is fully justified, provided that all possible factors affecting the behavior of the socio-economic indicator are taken into account. The implementation of the proposed approach was carried out using the Radishchev’s complex drawing, which displays both the values of the factors and the socio-economic indicator. At the same time, on the Radishchev’s complex drawing, the most favorable conditions for the socio-economic indicator are selected by methods of mathematical analysis. Further, with the help of the line of inter-projection communication, by means of standardization, the desired weight coefficients are determined, corresponding to the most favorable conditions for the socio-economic indicator. This approach is completely independent of the subjective opinion of experts and based solely on the initial statistical information.