Optimal Packing of General Ellipses in a Circle

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

doi:10.1007/978-3-319-66616-7_2

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Eggs: General Definition and Some Special Cases1

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2019

2022

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Cited by 3 publications

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“…Our modeling and solution approach is based on extending the use of embedded Lagrange multipliers to the case of egg objects studied here. Embedded Lagrange multipliers were introduced to pack ellipses inside optimized circular containers in Kampas et al (2017), and to pack ellipses inside optimized regular polygons in Kampas et al (2018).…”

Section: Eggs: General Definition and Some Special Casesmentioning

confidence: 99%

Packing ovals in optimized regular polygons

2019

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We present a model development framework and numerical solution approach to the general problem-class of packing convex objects into optimized convex containers. Specifically, here we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in ℝ 2 . Our solution strategy is based on the use of embedded Lagrange multipliers, followed by nonlinear (global-local) optimization. The numerical results are attained using randomized starting solutions refined by a single call to a local optimization solver. We obtain credible, tight packings for packing 4 to 10 ovals into regular polygons with 3 to 10 sides in all (224) test problems presented here, and for other similarly difficult packing problems.

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Section: Eggs: General Definition and Some Special Casesmentioning

confidence: 99%