Proving the Existence of Solutions to the Problems of Minimizing the Energy Consumption of Sensor Networks

Sensors and sensor networks have become widespread in today’s technological world. As with any technical system, sensors and sensor networks face certain challenges, one of which is the problem of energy efficiency, the solution of which allows for increasing the autonomy of sensors and making the network more cost-effective. This problem is relevant, and there are many studies devoted to its solution. In some of the proposed solutions, this problem is formulated as an optimization problem. However, in most cases, there is no proof of the existence of a solution to the presented optimization problem, which in turn calls into question the correctness of the proposed approaches. The article presents proof of the existence of a solution to the problem of minimizing the energy consumption of a sensor network by adjusting the sensor coverage radii. The work also proves the existence of a solution to a multi-criteria optimization problem, the criteria of which are the minimization of the network cost and the maximization of the area of the covered territory. An analysis of the energy efficiency of the network was carried out in cases of different values of the intersection of coverage zones and different values of the level of the intersection of coverage zones. Using the described approaches, the energy consumption of a specific sensor network was reduced by 7%, which confirms the effectiveness of the presented methods.