INVESTIGATION OF ACCURACY AND SPEED OF CONVERGENCE OF ALGORITHMS OF STOCHASTIC OPTIMIZATION OF FUNCTIONS ON A MULTIDIMENSIONAL SPACE

Abstract

The purpose of this paper is to analyze the accuracy of calculations and the amount of time spent on finding optimal values for functions of several variables using the algorithmic stochastic optimization algorithms based on the annealing simulation method. To conduct research by the staff of the Department of General Mechanics of the Lipetsk State Technical University, software has been created that implements algorithms for finding extremal values for functions of several variables. The functional purpose of the software is intellectual support for decision-making in the formation of chemical compositions of cast iron alloys. Optimization is performed on a specific and fixed search area, which is a hyperparallelepiped, the boundaries of the variation in the percentage content of a chemical element in the alloy. In the program, ten modifications of the annealing simulation algorithm are realized, allowing a finite number of steps to make an estimate of the optimal value of the input elements of the function under study on a multidimensional space. In particular, modification of A, B and С algorithm schemes using the Boltzmann and Cauchy distribution functions, as well as the superfast annealing algorithm and the Xin Yao algorithm are implemented. The results of the computational experiment for three different functions are presented: from six, eight and nine variables, a comparative analysis of the proximity of the results to the optimal values for each modification of the algorithm is carried out. The obtained data made it possible to draw conclusions about the advantages and disadvantages of each of the modifications of the stochastic search algorithm. Based on the results of computational experiments, the regularities between the time costs of algorithms and their numerical parameters are determined. With the help of linear regression, analytical dependencies are obtained, which allow estimating the time of the algorithms operation depending on the values of their numerical parameters. The paper contains a number of conclusions about the applicability of stochastic optimization modifications for solving applied problems, the shortcomings of modifications and their dignity are highlighted.