On the Solution of the Traveling Salesman Problem by a Modification of the Hungarian Method

Introduction. The traveling salesman problem is becoming an important object of research in various fields of science, economics and technology. Construction of efficient algorithms with an optimality criterion for the obtained solution is a relevant task. The traveling salesman problem is a transport-type problem and a natural approach to its solution can be methods for solving transport problems, in particular, variants of the Hungarian method. Purpose. Development of a modification of the Hungarian method for solving the traveling salesman problem. Expanding the capabilities of exact methods for solving transport-type problems. Results. The possibility of solving the traveling salesman problem by modifying the Hungarian method for solving the assignment problem is shown. The concepts of a set of cyclically independent elements and a cyclically independent zero of a given matrix are introduced. The idea of the modification and one of its implementations are presented in these new terms. Computational experiments were conducted. The results are reflected by three indicators: the average number of iterations and the processor time for a set of problems of a given dimension. Conclusions. The need to develop effective exact methods for solving the traveling salesman problem leads to the emergence of new ideas and approaches. In this sense, it is useful to use a natural approach based on the application of methods for solving transport-type problems, since the traveling salesman problem is a transport-type problem. It is shown that based on the modification of the Hungarian method, it is possible to build an effective method for obtaining an exact or approximate one depending on the specific situation. Keywords: traveling salesman problem, cyclically independent elements, modified Hungarian method.