Chugay A. A mathematical model and method for solving packing optimization problem of cylinders and parallelepipeds into a prism with account of special restrictions

A problem of packing of three-dimensional geometrical objects into a prism with account of technological restrictions on admissible distances and prohibited areas is investigated. The purpose of the thesis is mathematical modeling and development of methods of solving an optimization packing problem of cylinders and parallelepipeds into the prism with account admissible distances and prohibited areas. Utilized are a method of Ф-functions, method of consecutive-single packing based on approximations of objects, modified method of decremental neighborhood and modified method of possible directions. To realize computational modeling a computer is used. For the first time a mathematical model of the packing optimization problem of cylinders and parallelepipeds into the prism with account restrictions on admissible distances and prohibited areas and a mathematical model of the problem of packing of identical cylinders into the prism with account prohibited areas are built. A special decision tree is constructed. Modification of a decremental neighborhood method are developed. A new integrated approach for solving problems is offered. This approach consists in a combination of a method of searching for initial approximations of local extremums, modified method of decremental neighborhood and modified method of possible directions. Outcome of the thesis was introduced into the State research-and-production enterprise "Meridian" and "Potential" as a complex of the computer programs. The software developed allows in part automate designing. It may be also applied in systems of automated designing of various technical systems and devices in mechanical engineering, in tasks of cargoes transportation, in tasks of stocks storage on warehouses etc.