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Packing Ovals In Optimized Regular Polygons

F.J. Kampas(frank***at***physicistatlarge.com)
J.D. Pintér(jdp416***at***lehigh.edu)
I. Castillo(icastillo***at***wlu.ca)

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 R". 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.

Keywords: Object Packings ∙ Generalized Ellipses (Ovals, Eggs) ∙ Regular Polygon Containers ∙ Model Development Using Embedded Lagrange Multipliers ∙ Global-Local Nonlinear Optimization ∙ Numerical Test Results

Category 1: Global Optimization

Category 2: Optimization Software and Modeling Systems

Category 3: Global Optimization (Applications )

Citation: Research Report, November 2018. Submitted for publication.

Download: [PDF]

Entry Submitted: 11/27/2018
Entry Accepted: 11/27/2018
Entry Last Modified: 11/27/2018

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