The Concept of Modeling Packing and Covering Problems Using Modern Computational Geometry Software

A class of geometric packing and covering problems is considered. A new concept of their mathematical modeling using a special class of functions is proposed. To solve the problems, special computational geometry software libraries are used. They do not require an analytical form of the functions that describe the packing and covering conditions but allow their verification. The reduction of the computing cost is substantiated, which expands the possibilities of the efficient application of local and global optimization methods. The results of solving the test problems of the maximum coverage of a rectangular area with a set of ellipses of given sizes and the problem of packing ellipses in a rectangle of minimum area are provided.