THE USE OF DIJKSTRA'S ALGORITHM IN THE COMPUTER SEARCH OF THE OPTIMAL PATH OF AN UNDIRECTED GRAPH TAKING INTO ACCOUNT THE INFLUENCE OF RADIAL COVERAGE ON THE WEIGHT FUNCTIONS OF THE EDGES - SHCHERBAN, VOLODYMYR; GOLDBERG, MARJANA; MELNIK, GENADIJ; KIRICHENKO, ANTON; SHCHERBAN, YURYJ (Herald of Khmelnytskyi National University. Technical sciences, 2024)
Taking into account the influence of radial coverage, the weight functions of the edges of an undirected graph during the computer search for the optimal path are determined. Algorithms and computer programs were used to find the optimal path of the graph using the Dijkstra algorithm, which made it possible to determine the tension and changes in the relative tension in the filling zones of knitted and textile machines, taking into account the specifics of the design of the thread feeding system. This leads to a decrease in thread breakage. The development of mathematical models for determining the reduced coefficient of friction during the interaction of the thread with the ring and tubular thread guides of knitting machines allows the use of algorithms and computer programs to find the optimal path of the graph, using Dijkstra's algorithm, in which the tension of the thread at the exit point will be minimal. This makes it possible to determine the tension and change of relative tension in the filling zones of knitted and textile machines, taking into account the specifics of the design of the thread feeding system, taking into account the effect of radial coverage. Searching for the optimal path of the graph allows you to reduce thread breakage and optimize thread tension in the working area of ​​the initial product formation. Determining the weight functions of edges, taking into account the influence of radial coverage, unoriented graph during the computer search for the optimal path is an important component of the optimization of thread tension in the working zone of the formation of the output product. Tension optimization is carried out on the basis of its minimization, which allows to reduce the probability of a break in the working area.Optimization of the geometric parameters of the thread feeding system on the technological equipment, namely the construction of such a broken form of the thread, in which the total angle of coverage of the constructive structural elements of the technological equipment in the form of guides of a cylindrical shape and in the form of a torus, elements of tensioning devices, devices for monitoring breakage will have a minimum value. This will reduce the amount of friction force between the thread and the guide surfaces and obtain minimum tension in the working area. Taking into account the large number of structural elements of the thread feeding system on technological machines, their location in the plane and space, there is a need to use modern information technologies.
Keywords: Dijkstra's algorithm; computer search; optimal path; undirected graph; radial coverage; weight functions of edges