In recent years, various methods and directions for solving a system of Boolean algebraic equations have been invented, and now they are being very actively investigated. One of these directions is the method of transforming a system of Boolean algebraic equations, given over a ring of Boolean polynomials, into systems of equations over a field of real numbers, and various optimization methods can be applied to these systems. In this paper, we propose a new transformation method for Solving Systems of Boolean Algebraic Equations (SBAE). The essence of the proposed method is that firstly, SBAE written with logical operations are transformed (approximated) in a system of harmonic-polynomial equations in the unit n-dimensional cube Kn  with the usual operations of addition and multiplication of numbers. Secondly, a transformed (approximated) system in Kn  is solved by using the optimization method. We substantiated the correctness and the right to exist of the proposed method with reliable evidence. Based on this work, plans for further research to improve the proposed method are outlined.

Detecting sugar beetroot crops with mechanical damage using machine learning methods is necessary for fine-tuning beet harvester units. The Agrifac HEXX TRAXX harvester with an installed computer vision system was investigated. A video camera (24 fps) was installed above the turbine, which receives the dug-out beets after the digger and is connected to a single-board computer. At the preprocessing stage, static and insignificant image details were revealed. Canny edge detector and excess green minus excess red (ExGR) method were used. The identified areas were excluded from the image. The remaining areas were glued with similar areas of another image. As a result, the number of images entering the second stage of preprocessing was reduced by half. Then Otsu's binarization was used. The main stage of image processing is divided into two sub-stages: detection and classification. The improved YOLOv4tiny method was chosen for root crop detection using a single-board computer (SBC). This method allows processing up to 14 images of 416 × 416 pixels with 86% precision and 91% recall. To classify root crop damage, we considered two algorithms as candidates: 1. bag of visual words (BoVW) with a support vector machine (SVM) classifier using histogram of oriented gradients (HOG) and scale-invariant feature transform (SIFT) descriptors; 2. convolutional neural networks (CNN). Under normal lighting conditions, CNN showed the best accuracy, which ranged from 97% to 100%, depending on the damage class. The implemented methods were used to detect and classify blurred images of sugar beetroots, which were previously rejected. For improved YOLOv4-tiny precision was 74% and recall was 70%. CNN classification accuracy ranged from 90% to 95% depending on the root crops damage class.

The problem of the effectiveness of teaching can be successfully solved only if the high quality of lessons is supported by well-organized homework of students. The question of homework occupies one of the main places in educational activities since this question is directly related to the health of the child. A competent approach to minimizing the time for completing homework, taking into account the maximum efficiency obtained from the learning process, can preserve the health of students to some extent. The article describes a method for obtaining the most comfortable results of the process of completing homework, which are a Pareto set. This method is implemented using a genetic algorithm and queuing theory, and the selection of homework is carried out on the basis of intellectual analysis of the text of tasks and is a scale of a certain range. The proposed algorithm successfully obtains the solutions of the Pareto set and minimizes the efforts of school students while achieving the maximum efficiency of the educational process to preserve their health. Compared with other known algorithms, the results obtained show that the proposed algorithm demonstrates fairly accurate optimization characteristics presented in the form of a Pareto set. Furthermore, combining a genetic algorithm, queuing theory apparatus, and a neural network makes it possible to model the studied subject area more accurately.

The article discusses the problem of detecting sick or mechanically damaged potatoes using machine learning methods. We proposed an algorithm and developed a system for the rapid detection of damaged tubers. The system can be installed on a conveyor belt in a vegetable store, and it consists of a laptop computer and an action camera, synchronized with a flashlight system. The algorithm consists of two phases. The first phase uses the Viola-Jones algorithm, applied to the filtered action camera image, so it aims to detect separate potato tubers on the conveyor belt. The second phase is the application of a method that we choose based on video capturing conditions. To isolate potatoes infected with certain types of diseases (dry rot, for example), we use the Scale Invariant Feature Transform (SIFT)—Support Vector Machine (SVM) method. In case of inconsistent or weak lighting, the histogram of oriented gradients (HOG)—Bag-of-Visual-Words (BOVW)—neural network (BPNN) method is used. Otherwise, Otsu’s threshold binarization—a convolutional neural network (CNN) method is used. The first phase’s result depends on the conveyor’s speed, the density of tubers on the conveyor, and the accuracy of the video system. With the optimal setting, the result reaches 97%. The second phase’s outcome depends on the method and varies from 80% to 97%. When evaluating the performance of the system, it was found that it allows to detect and classify up to 100 tubers in one second, which significantly exceeds the performance of most similar systems.

This article deals with the multicriteria programming model to optimize the time of completing home assignments by school students in both in-class and online forms of teaching. To develop a solution, we defined 12 criteria influencing the school exercises’ effectiveness. In this amount, five criteria describe exercises themselves and seven others the conditions at which the exercises are completed. We used these criteria to design a neural network, which output influences target function and the search for optimal values with three optimization techniques: backtracking search optimization algorithm (BSA), particle swarm optimization algorithm (PSO), and genetic algorithm (GA). We propose to represent the findings for the optimal time to complete homework as a Pareto set.