The study aims to develop a system of models and a method for optimizing the operating modes of a catalytic reforming unit using fuzzy information, which makes it possible to effectively control the reforming process of the object under study. The object of study of this work is a catalytic reforming unit that has been operating for more than half a century and is characterized by the lack of clarity of some part of the initial information. The research methods are methods of system analysis, mathematical modeling, multicriteria optimization, and expert assessments, as well as methods of theories of fuzzy set theories, which allows formalizing and using fuzzy information, as well as experimental-statistical methods. As a result of the conducted research, the following main results were obtained. Based on a systematic approach, an effective methodology has been developed for developing a system of models of interconnected plant units using various types of available information, including fuzzy information. Using the proposed method, hybrid models have been developed to determine the volume of the produced catalyzate and its quality indicators. A scheme has been constructed for combining the developed models of the main units of the catalytic reforming unit into a single package of models. The built system of models makes it possible to systematically simulate the operation of the plant under study and improve the efficiency of the facility by increasing the volume of target products produced and improving its quality indicators. A statement of the problem of multicriteria optimization is obtained, taking into account the partial fuzziness of the initial information, and a heuristic method for its solution is developed, which is based on the use of knowledge, experience, and intuition of the decision-maker. The results of modeling and optimization show the effectiveness of the proposed fuzzy approach.

The current expansion of national colleges and universities or the increase in the number of enrolments requires teaching management to ensure the quality of teaching. The problem of scheduling is a very complicated prob-lem in teaching management, and there are many restrictions. If the number of courses scheduled is large, it will be necessary to repeat the experiment and make adjustments. This kind of work is difficult to accomplish accu-rately by manpower. Moreover, for a comprehensive university, there are many subjects, many professional settings, limited classroom resources, limited multimedia classroom resources, and other factors that limit and constrain the results of class scheduling. Such a large data volume and com-plicated workforce are difficult to complete accurately. Therefore, manpow-er scheduling cannot meet the needs of the educational administration of colleges and universities. Today, computer technology is highly developed. It is very economical to use software technology to design a course schedul-ing system and let the computer complete this demanding and rigorous work. Common course scheduling systems mainly include hill climbing al-gorithms, tabu search algorithms, ant colony algorithms, and simulated an-nealing algorithms. These algorithms have certain shortcomings. In this re-search, we investigated the mutation genetic algorithm and applied the algo-rithm to the student’s scheduling system. Finally, we tested the running speed and accuracy of the system. We found that the algorithm worked well in the course scheduling system and provided strong support for solving the tedious scheduling work of the educational administration staff.

This study developed models to solve problems of optimisation, production, and consumption in waste management based on methods of system analysis. Mathematical models of the problems of optimisation and sustainable waste management in deterministic conditions and in a fuzzy environment were formulated. The income from production was maximised considering environmental standards that apply to the field of macroeconomics and microeconomics. The proposed approach used MANAGER software to formalise and solve the problem of revenue optimisation with production waste management to optimise the production of oil products with waste management at a specific technological facility of the Atyrau oil refinery in Kazakhstan. Based on the combined application of the principles of maximin and Pareto optimality, a formulation of the problem of production optimisation with waste management was obtained and a heuristic algorithm for solving the formulated fuzzy optimisation problem with waste management was developed.

The features of using the acoustic method for accurately determining the concentration of components in two-component composite materials by measuring the speed of sound of long waves are described in this paper. Furthermore, explicit expressions for the volume concentrations of the matrix material and reinforcing particles or fibers of composite materials obtained by acoustic measurements are found. In addition, the advantages, features, and limits of the application of acoustic quality control of composite materials of various compositions and purposes are described. It is established that the methods for determining the concentration of components are valid for all types of composite materials, which are conveniently considered as phonon crystals. These results make it possible to more accurately determine or select a measuring cell for the experimental determination of the speed of sound. The mathematical problem to be solved is a purely exact inverse problem.

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