Cybernetics and Systems Analysis

, Volume 51, Issue 4, pp 556–565 | Cite as

Balance Layout Problem for 3D-Objects: Mathematical Model and Solution Methods

  • A. A. KovalenkoEmail author
  • T. E. Romanova
  • P. I. Stetsyuk


The paper introduces a general mathematical model of the optimal layout of 3D-objects (full-spheres, right circular cylinders, right regular prisms, and right rectangular parallelepipeds) in a container (straight circular cylinder, paraboloid of revolution, truncated circular cone) with circular racks. The model takes into account the minimum and maximum admissible 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 vertices of the decision tree.


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


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. A. Kovalenko
    • 1
    Email author
  • T. E. Romanova
    • 1
  • P. I. Stetsyuk
    • 2
  1. 1.A. N. Podgorny Institute for Mechanical Engineering ProblemsNational Academy of Sciences of UkraineKharkovUkraine
  2. 2.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKharkovUkraine

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