Packing ellipses in an optimized convex polygon

A. Pankratov, T. Romanova () and I. Litvinchev
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A. Pankratov: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
T. Romanova: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
I. Litvinchev: Nuevo Leon State University (UANL)

Journal of Global Optimization, 2019, vol. 75, issue 2, No 9, 495-522

Abstract: Abstract Packing ellipses with arbitrary orientation into a convex polygonal container which has a given shape is considered. The objective is to find a minimum scaling (homothetic) coefficient for the polygon still containing a given collection of ellipses. New phi-functions and quasi phi-functions to describe non-overlapping and containment constraints are introduced. The packing problem is then stated as a continuous nonlinear programming problem. A solution approach is proposed combining a new starting point algorithm and a new modification of the LOFRT procedure (J Glob Optim 65(2):283–307, 2016) to search for locally optimal solutions. Computational results are provided to demonstrate the efficiency of our approach. The computational results are presented for new problem instances, as well as for instances presented in the recent paper ( http://www.optimization-online.org/DB_FILE/2016/03/5348.pdf , 2016).

Keywords: Packing; Ellipses; Continuous rotations; Convex polygon; Phi-function technique; Nonlinear optimization (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-019-00777-y

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