Analysis of the behavior of search engine optimization algorithms on transient modes of non-stationary simulation processes

Abstract

The article deals with the analysis of the behavior of controlled simulation models for solving the choice of extreme values of the functional, which it determines on the basis of the average integral estimate. It is assumed that the search engine optimization algorithm is directly included in the model. Of interest is the problem of estimating the duration of the control interval, i.e. system simulation time with different parameters to select the search direction. The smaller the control interval, the lower the accuracy of the estimates of the functional and, accordingly, the lower the probability of choosing the correct search direction. However, with a general limitation on the simulation time, the search algorithm performs a larger number of steps, which increases the rate of convergence to the extreme value. Thus, the choice of the duration of the control interval raises a question. The aim of the work is to build a model of a controlled process, i.e. the process of changing the controlled parameters, to estimate the rate of convergence of the optimization algorithm depending on the duration of the control interval. The analysis of the convergence of the optimization process directly on the simulation model is practically impossible due to the nonstationary nature of all ongoing processes. In this regard, the article introduces a class of conditionally non-stationary Gaussian processes, on which the efficiency of a controlled simulation model is evaluated. It is assumed that a symmetric design is used to choose the direction, and all realizations of the nonstationary process at the current point have the same initial state. As a result of the analysis of such a model, analytical expressions were obtained for estimating the accuracy of the position of the extremum depending on the duration of the control interval. The results obtained make it possible, with a general limitation of the time for conducting experiments with a simulation model, to construct a sequential analysis plan, which improves the accuracy of solving the optimization problem.