Multiple circle coverings of an equilateral triangle, square, and circle

We study $k$-fold coverings of an equilateral triangle, square, and circle with $n$ congruent circles of the minimum possible radius $r^*_{n,k}$. We describe mathematical models for these problems and algorithms for their solving. We also prove optimality of the constructed coverings for certain $n$ and $k$, $1<k\le n$. For $n\le15$ and $1<k\le n$, we present the best found (possibly, improvable) values of circles radii ensuring the $k$-fold covering of the equilateral triangle, square or a circle. Ill. 4, tab. 3, bibliogr. 39.