Optimizing sensor cover energy for directional sensors

The Directional Sensors Continuous Coverage Problem (DSCCP) aims at covering a given set of targets in a plane by means of a set of directional sensors. The location of these sensors is known in advance and they are characterized by a discrete set of possible radii and aperture angles. Decisions to be made are about orientation (which in our approach can vary continuously), radius and aperture angle of each sensor. The objective is to get a minimum cost coverage of all targets, if any. We introduce a MINLP formulation of the problem and define a Lagrangian heuristics based on a dual ascent procedure operating on one multiplier at a time. Finally we report the results of the implementation of the method on a set of test problems.