Packing ovals in optimized regular polygons

Frank J. Kampas, János D. Pintér and Ignacio Castillo ()
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Frank J. Kampas: Physicist at Large Consulting LLC
János D. Pintér: Lehigh University
Ignacio Castillo: Wilfrid Laurier University

Journal of Global Optimization, 2020, vol. 77, issue 1, No 10, 175-196

Abstract: 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, we discuss the problem of packing ovals (egg-shaped objects, defined here as generalized ellipses) into optimized regular polygons in $$ {\mathbb{R}}^{2} $$R2. Our solution strategy is based on the use of embedded Lagrange multipliers, followed by nonlinear optimization. Credible numerical results are attained using randomized starting solutions, refined by a single call to a local optimization solver. We obtain visibly good quality packings for packing 4 to 10 ovals into regular polygons with 3 to 10 sides in all 224 test problems presented here. Our modeling and solution approach can be extended towards handling other 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 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-019-00824-8

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