Quasi-packing different spheres with ratio conditions in a spherical container
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Contributors
Abstract
This paper considers the optimized packing of different spheres into a given spherical container under non-standard placement conditions. A sphere is considered placed in the container if at least a certain part of the sphere is in the container. Spheres are allowed to overlap with each other according to predefined parameters. Ratio conditions are introduced to establish correspondence between the number of packed spheres of different radii. The packing aims to maximize the total number of packed spheres subject to ratio, partial overlapping and quasi-containment conditions. A nonlinear mixed-integer optimization model is proposed for this ratio quasi-packing problem. A heuristic algorithm is developed that reduces the original problem to a sequence of continuous open dimension problems for quasi-packing scaled spheres. Computational results for finding global solutions for small instances and good feasible solutions for large instances are provided.
Details
Original language | English |
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Article number | 2033 |
Number of pages | 19 |
Journal | Mathematics |
Volume | 11 |
Issue number | 9 |
Publication status | Published - May 2023 |
Peer-reviewed | Yes |
External IDs
Scopus | 85159210770 |
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WOS | 000986944000001 |
Mendeley | d8a41461-8caa-3975-8dec-51158209b7d6 |
Keywords
Research priority areas of TU Dresden
DFG Classification of Subject Areas according to Review Boards
Subject groups, research areas, subject areas according to Destatis
Sustainable Development Goals
ASJC Scopus subject areas
Keywords
- Optimization, Partial overlapping, Quasi-containment, Ratio condition, Sphere packing, Spherical container, spherical container, optimization, partial overlapping, quasi-containment, ratio condition, sphere packing