Optimization of a multiple covering of a bounded set with circles

Numerical algorithms for the optimization of multiple covering of a bounded set $G$ in the plane $P$ with equal circles are proposed. The variants in which $G$ is a connected bounded set in $P$ or a finite set in $P$ are considered. The circles may be centered at arbitrary points of $G$ or at points belonging to a given set. Minimization of the radius of the given number of circles and minimization of the number of circles of a given radius are considered. Models and solution algorithms are described, and estimates of the solutions provided by most variants are given. Numerical results are presented.