Packing Spheres into a Minimum-Height Parabolic Container

Sphere packing consists of placing several spheres in a container without mutual overlapping. While packing into regular-shape containers is well explored, less attention is focused on containers with nonlinear boundaries, such as ellipsoids or paraboloids. Packing n-dimensional spheres into a minim...

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Bibliographic Details
Published in:Axioms 2024-06, Vol.13 (6), p.396
Main Authors: Stoyan, Yuriy, Yaskov, Georgiy, Romanova, Tetyana, Litvinchev, Igor, Velarde Cantú, José Manuel, Mauricio López Acosta
Format: Article
Language:English
Subjects:
Algorithms
Containers
Ellipsoids
Euclidean space
Knapsack problem
Mathematical models
multidimensional spheres
nonlinear optimization
Nonlinear programming
Optimization techniques
packing
Packing problem
paraboloid
Spheres
Φ-function
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Summary:Sphere packing consists of placing several spheres in a container without mutual overlapping. While packing into regular-shape containers is well explored, less attention is focused on containers with nonlinear boundaries, such as ellipsoids or paraboloids. Packing n-dimensional spheres into a minimum-height container bounded by a parabolic surface is formulated. The minimum allowable distances between spheres as well as between spheres and the container boundary are considered. A normalized Φ-function is used for analytical description of the containment constraints. A nonlinear programming model for the packing problem is provided. A solution algorithm based on the feasible directions approach and a decomposition technique is proposed. The computational results for problem instances with various space dimensions, different numbers of spheres and their radii, the minimal allowable distances and the parameters of the parabolic container are presented to demonstrate the efficiency of the proposed approach.
ISSN:2075-1680
DOI:10.3390/axioms13060396