Girenko E. Mathematical model and solution method for a placement problem of non-oriented composed geometric 2D objects

Process placement problem of a composed geometric objects, taking into account rotations. Mathematical and computer modeling of a placement problem of the non-oriented composed objects taking into prohibited areas. Theory of sets, functional analysis, analytical geometry, the geometric design methods, optimization method by a group of variables, modified method of narrowing environs, method of internal point, modified method of possible directions. The complete class of Ф-functions for an extended class of non-oriented primary objects and class of Ф-functions for a family of the non-oriented composed objects are constructed. A mathematical model is presented as a constrained non linear optimization problem. A solution tree for each Ф-inequality of a pair of objects from the family of non-oriented composed objects is constructed. Computer programs "Packing of circles, rotating circular segments and polygons", "Packing of non-oriented composed objects" have been developed. The results of dissertation researches is used on the science- production enterprise of CLL "ELKOR complete SET", on a production base in KDBM the name of A.A. Morozova and in the instruction process at the Kharkiv National University of Radio Electronics and Kharkiv National University of Internal Affairs. The programs may be used for solving irregular packing and cutting problems in metal, textile, paper, wood, sheet, plastics and glass industries.