The article is devoted to the consideration of multi-criteria Pareto optimization methods based on genetic algorithms. The NSGA-III and AGE-MOEA-II methods are considered, and their comparative analysis is given. The results obtained are important both for theoretical research in the field of genetic algorithms and for practical application in engineering and other fields where multicriteria optimization plays a key role.

Keywords: multicriteria optimization problem, Pareto front, genetic algorithm, NSGA-III, AGE-MOEA-II

Since 2017, EVRAZ ZSMK JSC has been developing and operating a mathematical model covering all processing stages from ore extraction to final products – SMM Forecast. The model will be used to calculate technical cases, plans, and parity prices for iron ore and coal, and its use brought more than 200 million rubles of economic effect in 2020 alone. The use of a universal mathematical model made it possible in 2023 to begin the development of a module for daily optimization of an agglomeration factory and blast furnace production. The article discusses the experience of EVRAZ ZSMK JSC in the development and implementation of a daily planning system based on the monthly planning model of SMM Forecast, as well as methods for achieving an acceptable speed of multi-period optimization. The SMM Forecast system was originally designed for end-to-end, scenario-based calculation of the main raw materials from ore and coal to finished products in a volumetric monthly planning. The system uses optimization algorithms to search for a global target function to maximize margin income under specified constraints. The mathematical model of redistribution uses the norms and technologies specified in the company's regulatory documents. At the same time, the model is universal and the transfer of algorithms from monthly to daily mode was carried out with minimal modifications. The article also discusses the difficulties encountered and various methods of solving these problems. The first problem faced by the developers was the low speed of optimization of the model in daily dynamics due to the strong complication of the optimization load. The calculation time has increased significantly, and to solve this problem, it took the introduction of a number of optimization cycles aimed at reducing the speed of solving equations, introducing variable boundaries, and determining starting points. As a result, the calculation time for one month was about 40 minutes. The second problem was the need to develop a complex supply management algorithm and optimize stacking at the sinter plant. As a result of solving this problem, a working tool has been developed that brings additional income to the enterprise.

Keywords: metallurgy, modeling, planning, daily planning, sintering plant, blast furnace shop, stacking

A mathematical model for managing a commercial organization that specializes in the production and sale of asphalt and asphalt concrete is presented and analyzed in this paper. The study is based on mathematical modeling principles and management theory. An organized two-tier management system has been proposed, consisting of an asphalt manufacturer and its clients. The problem was considered numerically using various types of input data, and the company "FIRM PROFILE LLC" provided necessary information for calculations. The paper analyzes the results obtained and offers practical recommendations for improving the management of this enterprise.

Keywords: optimal management, mathematical modeling, simulation modeling, enterprise model, hierarchical system

The article deals with multi-criteria mathematical programming problems aimed at optimizing food production. One of the models of one-parameter programming is associated with solving the problem of combining crop production, animal husbandry and product processing. It is proposed to use the time factor as the main parameter, since some production and economic characteristics can be described by significant trends. The second multi-criteria parametric programming model makes it possible to optimize the production of agricultural products and harvesting of wild plants. in relation to the municipality, which is important for territories with developed agriculture and high potential of food forest resources.

Keywords: parametric programming, agricultural production, two-criteria model

The use of simulation analysis requires a large number of models and computational time. Reduce the calculation time in complex complex simulation and statistical modeling, allowing the implementation of parallel programming technologies in the implemented models. This paper sets the task of parallelizing the algorithmization of simulation modeling of the dynamics of a certain indicator (using the example of a model of the dynamics of cargo volume in a storage warehouse). The model is presented in the form of lines for calculating input and output flows, specified as: a moving average autoregressive model with trend components; flows of the described processes, specified according to the principle of limiting the limitation on the volume (size) of the limiting parameter, with strong stationarity of each of them. A parallelization algorithm using OpenMP technology is proposed. The efficiency indicators of the parallel algorithm are estimated: speedup, calculated as the ratio of the execution time of the sequential and parallel algorithm, and efficiency, reflecting the proportion of time that computational threads spend in calculations, and representing the ratio of the speedup to the sequential result of the processors. The dependence of the execution of the sequential and parallel algorithm on the number of simulations has been constructed. The efficiency of the parallel algorithm for the main stages of the simulation implementation was obtained at the level of 73%, the speedup is 4.38 with the number of processors 6. Computational experiments demonstrate a fairly high efficiency of the proposed parallel algorithm.

Keywords: simulation modeling, parallel programming, parallel algorithm efficiency, warehouse loading model, OpenMP technology

The problem of planning the sending of messages in a cellular network to destinations with known needs is considered. It is assumed that the costs of transmitting information on the one hand are proportional to the transmitted volumes and the cost of transmitting a unit of information over the selected communication channels in cases of exceeding the traffic established by the contract with the mobile operator, and on the other hand are associated with a fixed subscription fee for the use of channels, independent of the volume of information transmitted. An indicator of the quality of the plan in this setting is the total cost of sending the entire planned volume of messages. A procedure for reducing the formulated problem to a linear transport problem is proposed. The accuracy of the solution obtained on the basis of the proposed algorithm is estimated.

Keywords: single jump function, transport problem, minimum total cost criterion, computational complexity of the algorithm, confidence interval

In this paper, the problem of an equalizer design for high-speed receiver channel which is designed to compensate for the uneven frequency response of the input differential signal. Using special design methods, as well as modeling tools for frequency and transient characteristics, an equalizer with the ability to digitally adjust the gain was developed. This adjustment also reduces the impact of the spread of process parameters, which is inevitable during the production of the chip.

Keywords: attenuation, transceiver, equalizer, IP block, equalization, gain, amplitude

It is propossed to use foggy calculations to reduce the load on data transmission devices and computing systems in GIS. To improve the accuracy of estimating the efficiency of foggy calculations a non-Markov model of a multichannel system with queues, "warming up" and "cooling" is used. A method for calculating the probalistic-temporal characteristics of a non-Markov system with queues and with Cox distributions of the duration of "warming up" and "cooling" is prorosed. A program has been created to calculate the characteristics of the efficiency of fog calculations. The silution can be used as a software tool for predictive evaluation of the efficiency of access to geographic information systems, taking into account the features of fog computing technology and the costs of ensuring information security.

Keywords: fog computing, model of a multi-channel service system with queues, “warming up”, “cooling down”, geographic information systems, Cox distribution

The paper discusses a method for constructing a nonlinear software reliability efficiency function. The proposed algorithm is based on the use of information about the values ​​of reliability criteria, as well as some expert judgments. This approach differs significantly from previously proposed models for assessing software reliability, which are based on a probabilistic approach. In the proposed method, in addition to objective information, subjective expert assessments are taken into account, which allows for a more flexible assessment of the reliability of software products.

Keywords: software reliability, probabilistic models, statistical models, partial performance criteria, linear programming, vector optimization, decision theory

The article examines the two-dimensional flow around rectangular cylinders with an aspect ratio from 0.1 to 2.0 using the k-Realizable turbulence model with a Reynolds number of 2×E5. Numerical calculations in the ANSYS Fluent program have obtained changes in the coefficients of drag, transverse force and the Struhal number depending on the size of the prism section. The calculations were carried out at the intensity of turbulence of the incoming flow 2% and 4%. According to the results of calculations, it was found that with turbulence 4%, there is a good coincidence of the total aerodynamic characteristics with the available experimental data.

Keywords: flow around a rectangular cylinder, k-e Realizable turbulence model, aerodynamic characteristics of a rectangular cylinder

A two-dimensional coefficient inverse problem of thermal conductivity for a finite functionally graded cylinder is investigated. The thermal conductivity coefficient is considered to be variable along the radial and axial coordinates. The direct problem of finding the temperature distribution at different moments of time with known boundary conditions and the thermal conductivity coefficient is formulated in a weak statement and solved in the FreeFem++ finite element package. The influence of various two-dimensional power laws of the thermal conductivity coefficient on additional information (the temperature of the outer surface of the cylinder) is investigated. A projection-iteration scheme is constructed to solve the inverse problem. The thermal conductivity coefficient is presented as the sum of the initial approximation and the correction function specified as an expansion in a system of polynomials. At each stage of the iteration process, the expansion coefficients are calculated from the solution of the system of algebraic equations obtained by discretizing the operator equation of the first kind. The results of computational experiments on restoring various two-dimensional laws of change in the thermal conductivity coefficient are presented.

Keywords: functionally graded cylinder, finite element package FreeFem++, identification, thermal conductivity coefficient, inverse problem, iterative-projection approach, operator equation

The article is devoted to the development of a new mathematical method for modeling radial plain bearings having a polymer coating with an axial groove on the bearing surface. For the calculation evaluation of technical solutions for wear resistance, the compressibility of a truly viscous lubricant under laminar flow conditions is taken into account. As a result, new mathematical models were obtained that make it possible to estimate the duration of the hydrodynamic flow regime of the lubricant, to prove the stability and possibility of changing lubrication modes from boundary to hydrodynamic, as well as to make a calculated assessment of the effect of compressibility of the lubricant and wear resistance on operational characteristics.

Keywords: modeling, mathematical method development, modified design, compressibility impact assessment

With the development of scientific and technological progress, the use of modern data forecasting methods is becoming an increasingly necessary and important task in analyzing the economic activity of any enterprise, since business operations can generate a very large amount of data. This article is devoted to the study of methods for forecasting financial and trade indicators using neural networks for enterprises of the Krasnodar Territory. The indicators under consideration are the company's revenue for the reporting period, the number of published (available for sale) goods, as well as the number of ordered goods during the day, week and month. In this study, a multilayer perceptron is considered in detail, which can be used in revenue forecasting tasks using neural networks, and neural network predictive models "MLP 21-8-1", "MLP 21-6-1", and "MLP 20-10-1" are built based on data from the online auto chemistry store Profline-23.

Keywords: automated neural networks, marketplaces, forecasting, neural network models, mathematical models, forecasting methods

The development of digital technologies stimulates widespread automation of processes in enterprises. This article discusses the problem of determining the values of the oil indicator of a transformer from the resulting image using computer vision. During the study, the device of the MS-1 and MS-2 oil indicators was studied and the features that must be taken into account when recognizing the device in the image and determining its value were considered. Based on the processed material, a method for recognizing device elements in an image has been developed using the OpenCV library and the Python programming language. The developed method determines instrument readings at different angles of rotation and in different weather conditions, which confirms the effectiveness of the proposed method.

Keywords: technical vision, oil indicator, contour recognition, OpenCV library

This work is devoted to the study of the possibility of determining heart diseases on the basis of 13 categorical and numerical signs. We present a detailed analysis of the dataset, including dividing the data into training and test samples, dividing features into numerical and categorical, applying 4 different classification algorithms, checking the quality of the model using two techniques – delayed sampling and cross-validation. To assess the quality of the model, we pay attention to the value of the recall metric and the error matrix built on the test dataset from the deferred sample or on each test fold when using cross-validation. The results of the study are important both for a deep understanding of the relationship between certain medical indicators and heart disease, and for the development of effective methods for predicting them in the presence of individual symptoms.

Keywords: cardiovascular diseases, classification task, quality metrics, cross-validation, recall, machine learning, random forest

The paper describes a multifactorial nonlinear regression model of revenue dynamics of the mining and metallurgical company Severstal, based on retrospective information for 2009-2021. Production volumes by type were used as independent variables: hot-rolled and cold-rolled sheet, galvanized sheet and sheet with other metal coating, rolled products, large diameter pipes, other pipe products and profiles. The criteria of multiple definition and Fisher, as well as the average absolute approximation error, were used as criteria for the adequacy of the model. A model competition was held to select the best regression dependence. As a result, a model is constructed containing inverse transformations of two independent variables in the right part.

Keywords: regression model, least squares method, adequacy criteria, mining and metallurgical company, revenue, model competition

One of the most important points in increasing the conversion component of a web resource is identifying the most attractive places for the site user. To identify these locations, a site user activity data visualization tool was created that provides a visual representation of each user action on a site page.

Keywords: heat map, site, oculograph, fixation, priority area

Overhead power line wires are affected by various external factors such as wind, ice deposits, variable temperature conditions, excessive humidity. This eventually leads to fatigue failure of the wire. It consists in the origin and slow growth of a fatigue crack. The final stage of destruction is the sudden movement of the crack at high speed. The paper proposes a model of slow crack growth, at the mouth of which there is a grain boundary. Under the influence of external stress, a section of the border is a source of vacancies. The resulting vacancy concentration gradient between the grain boundary and the free surface at the crack mouth leads to a diffusion flow of vacancies into the crack. From the solution of the diffusion problem, the magnitude of the flow and the rate of increase in the crack length are found.

Keywords: crack, grain boundary, vacancy diffusion, fatigue failure, air line, mechanical stress, vacancy flow

Gantry piles have been developed to transfer a large load to the load-bearing foundation when erecting critical structures due to the larger contact area of the piles with the ground compared to vertical piles. The design of gantry pile foundations is the most labour-intensive. The responsibility of making a mistake increases when designing this foundation under seismic conditions. This paper deals with the modelling of the performance of cargo piles under seismic loading conditions in the construction of foundations for bridge piers. The results obtained are part of a larger scientific study on the feasibility of using gantry piles in high-rise construction in earthquakes of 6 to 10 on the Richter scale.

Keywords: gantry piles, deep foundation, seismic effects, overpass, modelling, finite element method, soil mass, stresses, deformations, foundation-soil mass system

The article considers the solution of the urgent problem of calculating the size of the effective focal spot of a microfocus X-ray tube using computer modeling methods. The principle of operation of the calculation method used by the authors is to compare interference images obtained using tested microfocus X-ray tubes with simulated interference patterns formed using the developed software by numerically solving the wave equation. It should be noted that modeling a one-dimensional interference pattern using fast Fourier transform requires a significant amount of RAM and takes considerable time even when using modern computer equipment. The paper presents the results of modeling phase contrast profiles for two types of test objects – nylon fishing line and aluminum wire. The considered method for determining the size of the focal spot is characterized by good sensitivity and allows efficient and high-precision calculations for all types of microfocus X-ray tubes.

Keywords: computer modeling, X-ray tube, microfocus source, focal spot, non-destructive testing

In the work, based on the previously constructed multifactor dynamic regression model of water level in the Iya River (Eastern Siberia), the authors forecast this indicator for June 2023 in three options: pessimistic, optimistic and neutral (base). A comparison of the forecasting results with the actual value of the water level confirmed the high adequacy of the model and good prospects for its future successful use to solve a wide range of applied and practical problems.

Keywords: regression model, river water level, lag time, seasonal variable, forecast, adequacy, criteria

The article solves the problem of diabetes mellitus diagnostics. Diabetes mellitus is characterized by high prevalence and significant costs for treatment and prevention of complications. This disease worsens the quality of patient's life, limiting their daily activities and functioning.To solve it, it is proposed to construct and use a neuro-fuzzy model. To train the model, the search and preparation of initial data for analysis were performed. The data were obtained from the publicly available Kaggle source. The data for analysis was prepared on the basis of the analytical platform Deductor. From the prepared data set, training and testing samples were formed, used to construct the model. Comparison of the obtained results with the known results of other authors allowed us to conclude that the model is adequate and can be used in practice.

Keywords: neuro-fuzzy model, fuzzy neural network, diabetes mellitus, modeling, diagnostics, machine learning

Indentation is a universal and practical method for obtaining material characteristics, especially when it is impossible or difficult to expose the material to other measuring methods. Experimental data on the mechanical properties of various types of materials were obtained using the shock loading unit. A mathematical model based on the finite element method was used to verify the experimental results. The article considers the solution of the problem of classification of neural metals with different mechanical properties. As part of the work, an artificial neural network has been created that allows the distribution of materials into selected groups. It is determined that a significant advantage of using neural networks is the ability to process experimental data and identify complex nonlinear dependencies, which makes them in demand in tasks related to the study of material properties.

Keywords: impact indentation, neural network, task of classification, artificial intelligence, dynamic indentation, non-destructive testing.

This paper analyzes the performance of solving the classification problem using various open-source artificial intelligence and machine learning libraries in the field of marketing and customer relationship management; based on the results of experiments, the best library is selected for the purpose of introducing artificial intelligence into domestic CRM systems based on numerical performance indicators.

Keywords: artificial intelligence, machine learning, big data, classification, marketing, customer relationship management, import substitution, open source

Paper presents an algorithm for analyzing and controlling data and project quality in construction using building information modeling and extensible markup language. The authors, argue that project quality stems from data quality and information quality. The proposed algorithm integrates BIM with extensible markup language, converting data quality and project quality criteria from employer information requirements into an extensible markup language scheme to ensure compliance with established standards. Key criteria for data quality and project quality include classification, identity, hierarchy, information identity, coordination, level of development , association, redundancy, staging, and spatial orientation. The algorithm involves creating a test BIM model, to simulate employer information requirements violations, performing checks using a Model Checker, automation tool in Autodesk Revit, and ensuring all criteria are met. The process includes saving verification checks, combining them, and generating reports in comma separated values format for transparency and further analysis. The authors highlight the importance of applying the algorithm from the early stages of project discussions, involving all participants to ensure the accuracy of data quality and project quality schemes. This approach leverages both international and domestic standards for continuous monitoring and immediate decision-making support throughout the project lifecycle.

Keywords: extensible markup language, information technical requirements, employer information requirements, building information model, information quality, project quality, model checking