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Cybernetics And Systems Analysis
International Theoretical Science Journal
UDC 519.85
Kovalenko A.A., Romanova T.E., Stetsyuk P.I.

THE PROBLEM OF BALANCE LAYOUT OF 3D-OBJECTS: MATHEMATICAL MODEL AND SOLUTION METHODS

Abstract. The paper introduces a general mathematical model of the optimal layout of 3D-objects (spheres, straight circular cylinders, straight regular prisms, and straight rectangular parallelepipeds) into a container (straight circular cylinder, paraboloid of revolution, truncated circular cone) with circular shelves. The model takes into account the minimum and maximum allowable distances between objects as well as the behavior constraints of the mechanical system (equilibrium, moments of inertia, and stability constraints). We propose solution methods based on Shor’s r-algorithm, multistart algorithm, and accelerated search of terminal nodes of the solution tree.

Keywords: balance layout problem, phi-function, quasi phi-function, admissible distances, behavior constraints, nonlinear programming, Shor’s r-algorithm.



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Коваленко Анна Андреевна,
аспирантка Института проблем машиностроения им. А.Н. Подгорного НАН Украины, Харьков,
e-mail: ladyann09@mail.ru.

Романова Татьяна Евгеньевна,
доктор техн. наук, ведущий научный сотрудник Института проблем машиностроения им. А.Н. Подгорного НАН Украины, Харьков, e-mail: sherom@kharkov.ua.

Стецюк Петр Иванович,
доктор физ.-мат. наук, заведующий отделом Института кибернетики им. В.М. Глушкова НАН Украины, Киев, e-mail: stetsyukp@gmail.com.

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