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arXiv · 1901.07056

Packing Ovals in Optimized Regular Polygons

Frank J. Kampas·Janos D. Pinter·Ignacio Castillo
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Abstract

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 $\mathbb{R}^2$. 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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Frank J. Kampas, Janos D. Pinter, Ignacio Castillo. 2019-01-21. Packing Ovals in Optimized Regular Polygons. https://arxiv.org/abs/1901.07056

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