Solving circle packing problems by global optimization: Numerical results and industrial applications

Castillo, Ignacio; Kampas, F. J.; Pintér, János D.

doi:10.1016/j.ejor.2007.01.054

Cited by 197 publications

(118 citation statements)

References 32 publications

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“…By Proposition 4.3, there exist positive constants ij such that constraints (13) and (15) are equivalent to constraints (19) and µ ij ≥ ij for all i, j ∈ I such that i < j. By Proposition 4.3, we can take…”

Section: Preliminariesmentioning

confidence: 99%

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Packing ellipsoids by nonlinear optimization

2015

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In this paper, continuous and differentiable nonlinear programming models and algorithms for packing ellipsoids in the n-dimensional space are introduced. Two different models for the non-overlapping and models for the inclusion of ellipsoids within half-spaces and ellipsoids are presented. By applying a simple multi-start strategy combined with a clever choice of starting guesses and a nonlinear programming local solver, illustrative numerical experiments are presented.

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Section: Preliminariesmentioning

confidence: 99%

“…In particular, many works have tackled the problem with optimization tools. See, for example, [7,9,17,18,19,23,37,50,51,52,53] and the references therein. On the other hand, the problem of packing ellipsoids has received more attention only in the past few years.…”

Section: Introductionmentioning

confidence: 99%

Packing ellipsoids by nonlinear optimization

2015

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“…The height variables z i are subject to the constraint 0 ≤ z i ≤ z max (13) and the objective of the problem is to…”

Section: Balls In a Cylindrical Containermentioning

confidence: 99%

“…MINLP models for cutting circles and convex polygons from rectangles with minimum area were introduced in [19]. A review of NLP models for solving several classes of circle packing problems was presented in [13], where several applications are surveyed and the relevance of nonlinear global optimization techniques for solving circle packing problems is highlighted.…”

Section: Introductionmentioning

confidence: 99%

Packing circles within ellipses

Birgin

Bustamante

Callisaya

et al. 2013

Int Trans Operational Res

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. AbstractThe problem of packing circles within ellipses is considered in the present paper. A new ellipse-based system of coordinates is introduced by means of which a closed formula to compute the distance of an arbitrary point to the boundary of an ellipse exists. Nonlinear programming models for some variants of 2D and 3D packing problems involving circular items and elliptical objects are given. The resulting models are medium-sized highly nonlinear challenging nonlinear programming problems for which a global solution is sought. For this purpose, multistart strategies are carefully and thoroughly explored. Numerical experiments are exhibited.

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“…Most studies were carried out for the packing of uniform and arbitrary sized spheres [1], considering the problem of optimal packing [2][3][4][5], (and its dual, the sphere cutting problem [6,7]) or space-filling [8][9][10][11][12][13][14].…”

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confidence: 99%

A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

Ilin

Bernacki

2016

MATEC Web Conf.

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Abstract.A new constructive ellipse packing algorithm is presented. It allows to respect the imposed area, shape and spatial orientation distribution (i.e. the inertia tensor) and achieve high packing densities. The packing density decreases with increasing particles aspect ratio what is in agreement with results reported in the literature. The generated packings with complex imposed area, shape and spatial orientation distributions with densities in the range of 0.74 and 0.8 are presented. The efficiency of the algorithm is demonstrated by comparison with the Optimized Dropping and Rolling method for disk packing. Moreover, the proposed packing strategy enables to generate very easily non-equiaxed polygonal structures by using Laguerre-Voronoï tessellation of the generated disk-based ellipse packing.

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Solving circle packing problems by global optimization: Numerical results and industrial applications

Cited by 197 publications

References 32 publications

Packing ellipsoids by nonlinear optimization

Packing ellipsoids by nonlinear optimization

Packing circles within ellipses

A new algorithm for dense ellipse packing and polygonal structures generation in context of FEM or DEM

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