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General Ellipse Packings in Optimized Regular Polygons

Frank J. Kampas(frank***at***physicistatlarge.com)
Ignacio Castillo(icastillo***at***wlu.ca)
Janos D. Pinter(Janos.D.Pinter***at***gmail.com)

Abstract: In this paper, we present a model development and numerical solution approach to packing ellipses into an optimized regular polygon. Specifically, our optimization strategy is based on the concept of embedded Lagrange multipliers. In this Lagrangian setting, we aim at optimizing the apothem (thereby the area) of a regular polygon while preventing ellipse overlaps. We proceed simultaneously towards these objectives using the LGO solver system for global-local nonlinear optimization. Our numerical results demonstrate the applicability of the embedded Lagrange multipliers based modeling approach combined with global optimization to tackle a broad class of highly non-convex ellipse packing problems.

Keywords: General Ellipse Packings in Regular Polygons; Model Development Using Embedded Lagrange Multipliers; Global-Local Optimization; LGO Solver Suite; Numerical Results.

Category 1: Global Optimization

Category 2: Optimization Software and Modeling Systems

Category 3: Global Optimization (Applications )

Citation: Research Report, February 2016. Submitted for publication.

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Entry Submitted: 02/22/2016
Entry Accepted: 03/01/2016
Entry Last Modified: 02/22/2016

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