D.V. Stroganov1, V.A. Micheev2, V.M. Chernenky3

1 Moscow Automobile and Road State Technical University (MADI) (Moscow, Russia)

2,3 Bauman Moscow State Technical University (Moscow, Russia)

Formulation of the problem. Simulation modeling is often used when there are no analytical methods for solving a certain problem. In this case, the simulation model solves it with a greater or lesser degree of adequacy. In addition, if there is an optimization problem, then there is a problem of including the simulation model in the optimization loop. The article assumes 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. model time, at which the local neighborhood of the current point of the search algorithm is investigated. The choice of the control interval is a rather difficult task. A number of works have shown the feasibility of its reduction. This article considers the limiting case when the duration of the control interval tends to zero. The behavior of such a model and the possibility of solving the optimization problem on it is of theoretical interest.

The aim of the work is a formal approach to the construction of such a model of a controlled imitation process, when the duration of the control interval tends to zero. Of interest is the description of the characteristics of the nonstationary behavior of such a model. As the main result, it is shown that under certain constraints, the controlled imitation process will converge to the diffusion one. In particular cases, the behavior of the model can be represented in the form of the Ornstein-Uhlenbeck process. Also, for a number of cases, an analytical solution has been found for the characteristics of the mathematical expectation and variance of the nonstationary mode.

The results obtained are more theoretical in nature. However, the practical interest lies in the possibility of assessing the position of the extremum of the controlled parameter without analyzing the estimates of the functional, which is set by the simulation model.

Stroganov D.V., Micheev V.A., Chernenky V.M. Analysis of the behavior of search engine optimization algorithms on transient modes of non-stationary simulation processes. Dynamics of complex systems. 2021. T. 15. № 4. Р. 21−28. DOI: 10.18127/j19997493-202104-03 (In Russian)

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