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

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 rac...

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Bibliographic Details
Published in:Cybernetics and systems analysis 2015-07, Vol.51 (4), p.556-565
Main Authors: Kovalenko, A. A., Romanova, T. E., Stetsyuk, P. I.
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Circular cylinders
Circularity
Constraint modelling
Control
Cybernetics
Decision trees
Equilibrium
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Mechanical systems
Methods
Nonlinear programming
Optimization
Processor Architectures
Satellites
Searching
Software Engineering/Programming and Operating Systems
Spheres
Studies
Symmetry
Systems Theory
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Summary: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.
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-015-9746-5