Solving the two-criteria maximum coverage location problem of continuous area monitored by sensor network

The paper investigates the problem of optimizing a sensor network for monitoring a continuous area, considering the bounded coverage areas of sensors. This task is formulated in terms of the maximum coverage location problem. A mathematical model is proposed as a two-criteria optimization problem. The objective functions are the maximum area of the covered part of the region and the minimum total overlapping of sensor coverage areas. This model is transformed into an elastic (quasi-physical quasi-human) model, which differs from the known one in forming the extrusion potential energy function. To solve the problem, an original approach was implemented, combining local and global optimization stages. At the stage of local optimization, the Broyden-Fletcher-Goldfarb-Shanno method was used, in which the gradients were calculated analytically or from first-order differences depending on the shape of sensor coverage areas. At the stage of local optimization, the multistart method was used. The implementation of the approach has been tested for the polygonal shape of the region and elliptical shapes of the sensor coverage areas.