Sphere Packing Problem

Chen, Danny Z.

doi:10.1007/978-0-387-30162-4_391

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…In problems ( 10)-( 14), constraints ( 11)-( 12) define the minimal allowable distances between objects as well as between each object and the boundary of the container, (13) presents the composition condition, while ( 14) is a balance condition. The latter guarantees that the gravity center of the system of spheres S i (ξ i ), i ∈ I coincides with the center of the container S 0 .…”

Section: Generalized Balance Packing Problems (Gbpp)mentioning

confidence: 99%

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A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

Litvinchev,

Fischer,

Romanova

et al. 2024

Mathematics

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Packing irregular objects composed by generalized spheres is considered. A generalized sphere is defined by an arbitrary norm. For three classes of packing problems, balance, homothetic and sparse packing, the corresponding new (generalized) models are formulated. Non-overlapping and containment conditions for irregular objects composed by generalized spheres are presented. It is demonstrated that these formulations can be stated for any norm. Different geometrical shapes can be treated in the same way by simply selecting a suitable norm. The approach is applied to generalized spheres defined by Lp norms and their compositions. Numerical solutions of small problem instances obtained by the global solver BARON are provided for two-dimensional objects composed by spheres defined in Lp norms to demonstrate the potential of the approach for a wide range of engineering optimization problems.

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Section: Generalized Balance Packing Problems (Gbpp)mentioning

confidence: 99%

“…Applications range from planning radio-surgical treatment of tumors [3,4] to studying structure of nanomaterials [5][6][7]; from spherical packing in coding theory [8,9] to modeling power bed fusion in additive manufacturing [10,11]. See also [12][13][14][15][16][17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

Litvinchev,

Fischer,

Romanova

et al. 2024

Mathematics

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The Expanding Space Method in Sphere Packing Problem

Yakovlev

2020

Advances in Intelligent Systems and Computing

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Packing spheres with quasi-containment conditions

Fischer,

Litvinchev,

Romanova

et al. 2024

J Glob Optim

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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.

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Sphere Packing Problem

Cited by 4 publications

References 12 publications

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

A New Class of Irregular Packing Problems Reducible to Sphere Packing in Arbitrary Norms

The Expanding Space Method in Sphere Packing Problem

Packing spheres with quasi-containment conditions

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