Configuration Spaces of Geometric Objects with Their Applications in Packing, Layout and Covering Problems

The concept of spatial configuration is introduced as a mapping of a finite set of geometric objects into a partially ordered set of a certain structure subject to a given constraints. Depending on the choice of generalized variables, various classes of spatial configurations are investigated. New approaches have been proposed for an analytical description of the main constraints in the packing, layout and covering optimization problems. This approach is based on the use of a special class of functions defined on a set of generalized variables of the configuration space.