The article discusses the solution of the spatial traveling salesman problem (TSP 3D variation) using Ant Colony Optimization (ACO). The traveling salesman problem considers n bridges and a matrix of pairwise distances between them. It is necessary to find such an order of visiting cities so that the total distance traveled was minimal, each city was visited exactly once and the salesman returned to the city from which he began his route. In the TSP 3D variation problem, each “city” has 3 coordinates x, y, z. The analysis of the main methods of solving, in particular, the metaheuristic algorithms to which ACO belongs, is performed. At each iteration of these methods, a new solution of the problem is built, which is based not on one, but several solutions of the population. The ACO uses an idea that is based on collecting statistical information about the best solutions. The program code is implemented in MATLAB. During computational experiments, various network topologies were randomly generated, and the number of iterations at which the optimal cycle was achieved was recorded. The execution time of the code for the TSP 3D task is almost the same as the execution time of TSP 2D. The results can be used for spatial tasks of the salesman (TSP 3D-variation), which arise in the process of 3D printing, planning UAV trajectories (UAV) in mountain conditions or multi-story urban development, road planning in multi-story buildings.

In the process of self-assessment and accreditation examination, assessment is carried out according to a scale that covers four levels of compliance with the quality criteria of the educational program and educational activities. Assessing the quality of education is complicated by the fact that the value of quality criteria is due to a large number of factors, possibly with an unknown nature of influence, as well as the fact that when conducting pedagogical measurements it is necessary to work with non-numerical information. To solve these problems, the authors proposed a method for assessing the quality of educational programs and educational activities based on the adaptive neuro-fuzzy input system (ANFIS), implemented in the package Fuzzy Logic Toolbox system MATLAB and artificial neural network direct propagation with one output and multiple inputs. As input variables of the system ANFIS used criteria for evaluating the educational program. The initial variable of the system formed a total indicator of the quality of the curriculum and educational activities according to a certain criterion or group of criteria. The article considers a neural network that can provide a forecast for assessing the quality of educational programs and educational activities by experts. The training of the artificial neural network was carried out based on survey data of students and graduates of higher education institutions. Before the accreditation examination, students were offered questionnaires with a proposal to assess the quality of the educational program and educational activities of the specialty on an assessment scale covering four levels. Student assessments were used to form the vector of artificial neural network inputs. It was assumed that if the assessments of students and graduates are sorted by increasing the rating based on determining the average grade point average, the artificial neural network, which was taught based on this organized data set, can provide effective forecasts of accreditation examinations. As a result of comparing the initial data of the neural network with the estimates of experts, it was found that the neural network does make predictions quite close to reality.

The rapid development of information technology, robotics, nanotechnology, and biotechnology requires modern education to train highly qualified specialists who can support it, preparing students and students for producing creative work. The need to reform education to modern challenges is an urgent problem today. It is predicted that the most popular professions soon will be programmers, engineers, roboticists, nanotechnologists, biotechnologists, IT specialists, etc. STEM education can combine these areas into a complex, which can be implemented in different age groups. One example of the use of STEM technologies is the development and implementation of scientific and technical projects using the Arduino hardware and software complex. With the help of STEM technologies, a method for calibrating an NTC thermistor in the operating temperature range is proposed and a working model of an electronic thermometer is presented using the example of an NTC thermistor and an Arduino microcontroller.

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The article raises the issue of teaching seventh-grade children a systematic course “Geometry”. It is proposed to create reference notes in the form of creolized texts, which are already penetrating into modern education. Their main components are the verbal part (inscription) and the iconic part (figure). This concept and three ways of their formation are revealed: verbal text + image, image + verbal text, verbal text = image. Given the peculiarities of the new generation, in the educational process, we propose to use more the second method of creolized texts formation. This approach to the study of geometry is justified by the need to take into account the peculiarity of the modern generation – clip thinking. The article reveals the concept of “clip thinking”. This concept was introduced in the '90s and means a person's perception of the world around him as a sequence of unrelated phenomena. Such thinking has positive aspects, among which it is important to quickly perceive information, mainly by reading the image-picture. And the negative aspects that negatively affect the ability of the younger generation to learn, analyze, generalize, and find cause-and-effect relationships. These negative aspects need to be overcome in every geometry lesson, teaching children to analyze both when solving problems and when creating reference summaries of theoretical material in the form of creolized texts. In the article, the author gives a schematic summary of all the basic geometric material, which children study in the seventh grade (according to the textbook of O. Ister). It is the creation of such a syllabus in the seventh grade and its continuation in the next grades (and this is a mandatory part of the teaching methodology) that promotes the better mastering by students of a systematic course in geometry. This synopsis will be their guide in preparation for the state final certification in the ninth grade.