Packing convex polygons in minimum-perimeter convex hulls

Josef Kallrath (), Tatiana Romanova (), Alexander Pankratov, Igor Litvinchev () and Luis Infante
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Josef Kallrath: University of Florida
Tatiana Romanova: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
Alexander Pankratov: Institute for Mechanical Engineering Problems of the National Academy of Sciences of Ukraine
Igor Litvinchev: Graduate Program in Systems Engineering, Nuevo Leon State University (UANL)
Luis Infante: Graduate Program in Systems Engineering, Nuevo Leon State University (UANL)

Journal of Global Optimization, 2023, vol. 85, issue 1, No 3, 39-59

Abstract: Abstract The problem of packing a given set of freely translated and rotated convex polygons in a minimum-perimeter convex polygon (in particular the minimum-perimeter convex hull) is introduced. A mathematical model of the problem using the phi-function technique is provided. Problem instances with up to 6 convex polygons are solved by the global NLP solver BARON to get a minimum-perimeter convex hull. Numerical experiments for larger instances are reported using the local NLP solver IPOPT.

Keywords: Global optimization; Non-convex nonlinear programming; Polygon packing problem; Convex hull; Perimeter minimization; Non-overlap constraints; Computational geometry (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-022-01194-4

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