Denys Medynskyi, Iryna Borets


The ways to find the ways of solving the problem of optimal service for unmanned aerial vehicles in the conditions of vehicle shortage are explored.

In the study of theory of optimal control and discrete optimization insufficiently explored the problem of optimal graph coverage by the chains of a fixed pattern with the help of a description system of ordinary differential equations.

With the help of the graph theory investigated the optimization problem of the «Upper Cover» for unmanned aerial vehicles service in the conditions of vehicle shortage has been solved.

Study of the problem relates to the mathematical dependence of transport systems. It can be used for determination of the optimal ratio between the amount of Unmanned Aerial Vehicles and fuel (electricity) reserves used by the Unmanned Aerial Vehicles. The method of solving the problem of determining the weight of the arcs of the graph and the problem of constructing a chain is based on that dependence. Part of the problem is the task of docking. The combinatorial task of choosing a set of stations for servicing points of the initial unmanned aerial vehicles dislocation is based on the dependence mentioned. Effective method for solving the problem of optimal coverage of a graph for supply chains with constraints is developed on the bases of the dependence.

The proposed research methods can significantly reduce the cost of delivery of urgent goods using unmanned aerial vehicles.

The proposed research methods can significantly reduce the cost of delivery of urgent goods using unmanned aerial vehicles. Perspective of further researches is studying of mathematical model of optimal servicing the delivery areas in the conditions of the lack of UAV. The constraints for practical purposes must have a group-theoretical approach to solving optimization problems and be reduced for the constructing an optimal cost matrix analysis. Algebraic approach is used, when there is a need in solving a large set of similar types of optimization problems with different constraints in the right hand side only.

It is possible to apply a heuristic algorithm for solving the problem of optimal UAV service. The problem means optimal coverage of a special graph with chains with restriction on the chain length


unmanned aerial vehicle; graph; drone; optimality criterion; algorithm solving method; phase coordinates; functions; supply chains

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