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Sparse Balanced Layout of Spherical Voids in Three-Dimensional Domains

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Cybernetics and Systems Analysis Aims and scope

Abstract

The authors consider the optimization problem of layout of spherical voids in three-dimensional domains bounded by cylindrical and spherical surfaces and planes. The problem is reduced to arranging spherical objects in a composite container, with regard for the constraints on their “sparseness” and balance conditions (location of the gravity center of the system). A mathematical model in the form of a nonlinear programming problem is constructed. A method of fast search for feasible solutions based on the balanced homothetic transformations of 3D objects and methods of finding locally optimal solutions using the decomposition algorithm and r-algorithm are proposed. The results of numerical experiments are provided.

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Authors and Affiliations

  1. A. Pidhornyi Institute of Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Y. G. Stoyan, T. E. Romanova, O. V. Pankratov & Y. E. Stoian

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

    P. I. Stetsyuk

Authors
  1. Y. G. Stoyan
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  2. T. E. Romanova
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  3. O. V. Pankratov
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  4. P. I. Stetsyuk
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  5. Y. E. Stoian
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Corresponding author

Correspondence to Y. G. Stoyan.

Additional information

The study was financially supported by the National Research Foundation of Ukraine (Grant # 2020.02/0128, Y. G. Stoyan, T. E. Romanova, Y. E. Stoian) and Volkswagen Foundation (Grant 97775, T. E. Romanova, P. I. Stetsyuk).

Translated from Kibernetyka ta Systemnyi Analiz, No. 4, July–August, 2021, pp. 44–55.

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Stoyan, Y.G., Romanova, T.E., Pankratov, O.V. et al. Sparse Balanced Layout of Spherical Voids in Three-Dimensional Domains. Cybern Syst Anal 57, 542–551 (2021). https://doi.org/10.1007/s10559-021-00379-1

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  • DOI: https://doi.org/10.1007/s10559-021-00379-1

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