THE METHOD OF SELECTION OF THE OPTIMAL ROUTE OF MOVEMENT OF COLUMNS OF VEHICLES UNDER NON-STATIONARY ROAD NETWORK

Abstract

Context. Effective solution of a large number of applications requires optimal transportation. Construction of optimal routes on a static in time graph describing a network of roads is a classic and detailed study of tasks. However, in many applications, there is a need to take into account the possible dynamics of the change in time of road conditions, which requires the development of the appropriate scientific and methodical apparatus. Objective. The purpose of the work is to develop a methodology for choosing the optimal route of movement of the equipment column on a non-stationary road network. Method. In the paper a mathematical model of the choice of the optimal route of the movement of the vehicles column along the network is proposed. A graph is used to describe the network of roads. The criterion of optimality when choosing a route is to minimize the time spent on travel. The peculiarity of the model is to take into account the possibility of dynamically changing the weight of the edges of the graph when moving the column of technology on the chosen route. Based on the use of this model, a technique is proposed which ensures the selection of optimal route for discrete-stochastic, discrete-deterministic and continuouslyindefinite cases of changes in the weight of the edges of the graph. Results. In the article the algorithms are chosen and the features of their application are shown, which provide solution of the problem of choosing the optimal route in the conditions of the ribs that are not fixed in time, which describe the network of roads. The description of the algorithmic and programmatic implementation of the proposed methodology is given. With the use of developed software, the research model of the road network with a non-stationary weight of the ribs. The example shows the imperfection of the solutions for optimal route under the non-stationary weight of the edges of the graph obtained using classical methods. Conclusions. Failure to take into account the possible change in the road situation, which manifests itself in the change in the time scale of the edges of the graph, which describes the network of roads, may lead to the non-optimality of the solutions obtained using the classic methods of finding the shortest route in the graph. To get the best routes, taking into account the change in the time of the road situation during the movement of the column, it is possible to use the method proposed in this study. The obtained results extend the possibilities for solving the problems in the field of discrete optimization taking into account the dynamics of the changing situation in the implementation of optimal solutions.