Zlotnik M. A mathematical model and method for solving packing optimization problem of non-oriented poligons and circles

The problem of arranging non-oriented 2D geometric objects on a strip is investigated. The objective of the study is mathematical modelling and developing methods for solving the optimisation problem of arranging non-oriented polygons and circles on a strip. The following methods are used: geometric design, the Ф-functions method, the method of consecutive-single arrangement based on object approximation, the modified method of converging neighbourhoods and the modified method of feasible directions. A computer is used for numerical simulation. A full class of Ф-functions and normalised Ф-functions for non-oriented base objects and nonconvex polygons was first built. Also, an Ф-function was built for a pair of geometric objects, one of which is a convex polygon and the second one is the result of intersection of two circular biconnected objects. The mathematical model of the problem of arranging non-oriented polygons and circles was first built and investigated. The approach to solving optimisation arrangement problems, which consists in combining methods of local and global optimisation for non-oriented objects has been advanced. The results of dissertation studies are used at the Expert and Technological Centre Diagnostics during appraisal of plans of liquidating emergencies at high-hazard objects to evaluate options of layout of buildings, structures and technological equipment at an industrial site with account of the zone of action of affecting factors of possible accidents. The results are also used in the instruction process at the Kharkiv National University of Internal Affairs. The programs can also be used in CAD of various technical systems and devices during cutting of materials in the light and heavy industry, etc.