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Volume 57 >>> № 6 NOVEMBER — DECEMBER 2021
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UDC 519.85
Y.G. Stoyan1, T.E. Romanova2, O.V. Pankratov3,
P.I. Stetsyuk4, S.V. Maximov5


1 A. Pidgorny Institute of Mechanical Engineering
Problems of the National Academy of Sciences
of Ukraine, Kharkiv, Ukraine

 yustoyan19@gmail.com

2 A. Pidgorny Institute of Mechanical Engineering
Problems of the National Academy of Sciences
of Ukraine, Kharkiv, Ukraine

 tarom27@yahoo.com

3 A. Pidgorny Institute of Mechanical Engineering
Problems of the National Academy of Sciences
of Ukraine, Kharkiv, Ukraine

 pankratov2001@yahoo.com

4 V.M. Glushkov Institute of Cybernetics,
National Academy of Sciences of Ukraine, Kyiv, Ukraine

 stetsyukp@gmail.com

5 A. Pidgorny Institute of Mechanical Engineering
Problems of the National Academy of Sciences
of Ukraine, Kharkiv, Ukraine

 maksimovsergey08@gmail.com

SPARSE BALANCED LAYOUT OF ELLIPSOIDS

Abstract. The authors consider the problem of generating spheroidal voids in a three- dimensional domain of complex geometry, taking into account the constraints on the “sparseness” of the placement of voids subject to the system balance. The problem is reduced to the optimized layout of ellipsoids of revolution in a convex container (cylinder or cuboid), taking into account the prohibited zones, constraints on the allowable distances between objects, and the balancing condition. The problem is aimed to maximize the minimum distance between each pair of ellipsoids and each ellipsoid and the boundary of the container. Adjusted quasi-phi-functions for analytical description of the placement constraints are defined. A mathematical model is constructed in the form of a nonlinear programming problem. A solution method is proposed that uses the multistart strategy in combination with smart algorithms to search for feasible and locally optimal solutions. The results of computational experiments are presented.

Keywords: sparse layout, ellipsoids of revolution, phi-function, nonlinear programming, r-algorithm.


FULL TEXT

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