Yas'kov G. A mathematical model and methods of solving a placement problem of rectangles with account of admissible distances

A problem of placement of geometric objects with account of technological restrictions on admissible distances is investigated. The purpose of the thesis is development of effective methods of solving an optimization placement problem of rectangles and circles taking into account admissible distances. Utilized are Ф-functions, structures of inequalities, branch-and-bound algorithm, reduced gradient method, strategy of active inequalities, Newton method. To realize computational modelling computer is used. A set of extreme points are investigated. Developed are the following methods: 1) modification of branch-and-bound algorithm; 2) method for local optimization; 3) method of sorting the local minima (for problem of circle placement). Problem-oriented model and software of a problem of layout of plant stock in mineral processing plants and a problem of recycling of wastes in man-caused zone of alienation of Chernobyl's nuclear power plant are developed. Outcome of the thesis was introduced into manufact uring in opened cooperative association "Pivdendiproshakht" in the form of an experimental software. The software developed allows in part automate designing. It may be also applied in building (when making out development plans), in industry (when solving problem of rational placement of equipment and communications).