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The task of path finding by an agent is one of the basic tasks and is of great practical importance. As a rule, this is an optimization task that is solved in the space of the state graph in order to minimize the length of the path. Such a task becomes more difficult and becomes even more popular if it is solved on the basis of one graph space by several agents. In this case, another practically important optimization parameter appears, which is expressed by the number of conflicts between agents. Such an abstract formulation of the task has numerous variants of formalization and a large number of approaches to its solution. In this paper, the main element of the approach is the application of the classic Dijkstra algorithm, which is executed sequentially by each agent. When finding the shortest route, each agent modifies the graph space in such a way as to reduce the probability of conflicts with subsequent agents. This approach is original and a number of computational experiments were performed to verify it using software developed for this purpose. The experiments that were conducted demonstrate the adequate behavior of the main algorithm. The work analyzes the limitations inherent in the proposed approach within the framework of the abstract formulation of the task. The directions of further development of the basic approach have been determined. [ABSTRACT FROM AUTHOR]