Alexander Petrovich Mikhailov is a member of the editorial board of our journal, a major Russian scientist, a well-known specialist in mathematical modeling, Doctor of Physical and Mathematical Sciences and professor died on May 24, 2022.

The result obtained in the course of solving optimization problems is relevant for use in industrial and laboratory processes. Multi-criteria optimization involves optimizing two or more conflicting objective functions.

Materials and methods. On the basis of the kinetic model of the catalytic reaction of the synthesis of benzylalkyl esters, the task of multi-criteria optimization is set taking into account the variable parameters: temperature, molar ratio of reagents and the time of carrying out, which have limitations. The use of the methods of «ideal» point and lexicographic ordering is justified.

Results. An algorithm for solving the multi-criteria optimization problem has been developed. Using the kinetic model of the synthesis of benzylalkyl esters, the problem of MKO of the conditions of conducting was solved and optimal values of the variable parameters of the system were obtained, at which the output of the target product was maximized and the by-products of the chemical process were minimized.

Discussion and conclusions. Multi-criteria optimization of this process will make it possible to give technological recommendations for the industrial implementation of the process with maximum output of target products and minimum content of by-products. The paper presents two methods for solving the problem, since in order to apply the results obtained in practice, the recommendations of the decision-maker must be taken into account.

The paper considers the application of various modern technologies of high-performance computing to accelerate the numerical solution of the problems of propagation of dynamic wave disturbances using the grid-characteristic method. Technologies are considered both for central processing units (CPUs) and for graphic processors (GPUs). Comparative results of applying MPI, OpenMP, CUDA technologies are presented. As examples of the work of the developed software package, a number of examples of calculating the problems of seismic and geophysics are given. Separately, the issue of parallelizing problems with the presence of contacts of many grids and the topography of the day surface using curvilinear grids is considered.

An important role in the management of water resources is played by inland freshwater reservoirs, the main uses of which are: meeting the needs of the population in fresh water, irrigation, hydroenergy, shipping, fish farming, etc. At the same time, undesirable and inevitable disturbances of the natural environment and the natural balance of the ecosystem are increasingly observed. water bodies. A serious problem is a significant change in the bottom relief, the destruction of the shores, the accumulation of bottom sediments. The results presented in this article are aimed at creating a modern basis for forecasting trends in the development of inland freshwater reservoirs in the South of Russia, based on calculations of the hydrophysical characteristics of the wave regime. Mathematical models of three-dimensional wave hydrodynamics have been constructed and adapted to natural and climatic conditions and geographical features on the example of the Tsimlyansk reservoir. Based on the developed experimental set of programs, prognostic calculations were performed for its coast, the nearby village of Sarkel, named after the historical Khazar fortress city of Sarkel (flooded by a reservoir). For the selected local site, studies of the hydrodynamic characteristics of the wave impact on the coastal recreational zone, including wave profiles and velocity vector fields at different values of wind speed, were carried out.

Modeling allows to get a description of the object being modeled, in particular complications, which improves and clarifies its understanding and presents an organization of information that makes it easier to get the necessary information. Modeling of chemical kinetics problems is the solution of systems of ordinary nonlinear differential equations with determination of kinetic parameters. The inverse problem refers to incorrectly set tasks and does not have a single solution. The development of modern methods of evolutionary optimization, including the genetic algorithm, makes it possible to obtain a solution to such a high-dimensional problem in an acceptable time.

Materials and methods. The object of research is the catalytic reaction of dimethyl carbonate (DMC) with alcohols in the presence of hexacarbonyl tungsten. The solution of the direct problem is the solution of a system of ordinary nonlinear differential equations with initial data and given kinetic parameters. The solution of the inverse problem consists in determining the kinetic parameters corresponding to the minimum deviation of the calculated values of substance concentrations from the experimental data.

Results. The inverse problem of chemical kinetics is solved, which consists in calculating kinetic parameters with minimizing the functional deviation of the calculated values of component concentrations from experimental data. In the language of Python, program has been developed that implements the genetic algorithm. Numerical experiments with different numbers of iterations are performed and their impact on the accuracy of the solution, as well as the corresponding time costs, is estimated.

Discussion and conclusions. The calculated values of the component concentrations based on the kinetic parameters found correspond to the values of the experimental data.

Numerical experiments with different numbers of iterations are performed. Based on experiments, it was concluded that with an increase in the number of iterations, the accuracy of the solution increases. An increase in the number of iterations, in turn, leads to an increase in the time required for performing calculations. The time dependence on the number of iterations is analyzed.