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The article is devoted to circle covering problem for a bounded set in a two-dimensional metric space with a given amount of circles. Here we focus on a more complex problem of constructing reserve and multiple coverings. Besides that, we consider the case, where covering set is a multiply-connected domain. The numerical algorithms based on fundamental physical principles due to Fermat and Huygens is suggested and implemented. It allows us to solve the problems for the cases of non-convex sets and non-Euclidean metrics. Preliminary results of numerical experiments are presented and discussed. Calculations show the applicability of the proposed approach.

On reserve and double covering problems for the sets with non-Euclidean metrics