Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/315320 
Year of Publication: 
2024
Citation: 
[Journal:] Journal of Global Optimization [ISSN:] 1573-2916 [Volume:] 90 [Issue:] 3 [Publisher:] Springer US [Place:] New York [Year:] 2024 [Pages:] 671-689
Publisher: 
Springer US, New York
Abstract: 
Abstract A novel sphere packing problem is introduced. A maximum number of spheres of different radii should be placed such that the spheres do not overlap and their centers fulfill a quasi-containment condition. The latter allows the spheres to lie partially outside the given cuboidal container. Moreover, specified ratios between the placed spheres of different radii must be satisfied. A corresponding mixed-integer nonlinear programming model is formulated. It enables the exact solution of small instances. For larger instances, a heuristic strategy is proposed, which relies on techniques for the generation of feasible points and the decomposition of open dimension problems. Numerical results are presented to demonstrate the viability of the approach.
Subjects: 
Packing spheres
Nonstandard packing
Quasi-containment
Ratio condition
Mixed-integer nonlinear programming
Heuristic
Open dimension problem
Decomposition technique
Nonlinear programming
Persistent Identifier of the first edition: 
Creative Commons License: 
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Document Type: 
Article
Document Version: 
Published Version
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