We study NP-hard placement optimization problems, which cover a wide spectrum of industrial applications, including space engineering. The review paper considers phi-functions as an analytical tool for describing placement constraints, including containment, non-overlapping, allowable distances, prohibited areas, object translations and rotations. A mathematical model of a basic placement problem is presented as a non-smooth optimization problem. We consider two solution algorithms for optimization placement problems. The reader will get acquainted with two subsequent problems of the basic placement problem encountered in space engineering.