Kovalenko A. Balance layout problem for 3D-objects: mathematical models and solution methods

The subject of the research is the optimal balance layout process for 3D-objects taking into account behavior constraints and arrangement constraints including minimal and maximal allowable distances. The objective of the research is improving of the efficiency of solutions of optimization balance layout problems by developing of constructive tools of mathematical modeling, new mathematical models and efficient optimization algorithms. The research methods employ analytical geometry, function analysis, mathematical analysis, theoretical mechanics, geometric design methods, methods of nonlinear programming and nonsmooth optimization. The theoretical and practical results of the thesis for optimal balance layout problems (BLP) for 3D-objects allow us to consider behavior constraints and to search for local-optimal solutions which are better in comparison with the known published results. Scientific novelty: the tools of mathematical modeling and computer simulation are developed in the form of new adjusted phi-functions and adjusted quasi-phi-functions taking into account features of the problem BLP, the behavior constraints are formalized in the form of inequality system with differentiable functions, the new mathematical models of the problems BLP are derived in the form of nonlinear programming problems, the strategy and the algorithms are developed for solving problems BLP, employing methods of nonlinear programming, nonsmooth optimization and NLP-solvers. The results are used in the educational process of technical universities. Developed software products are implemented and provided with appropriate references and certificates. They also can be used in logistics, machinery, in particular, in space engineering for rocketry design.