Paper Info
Title
Packing ellipses in an optimized convex polygon
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).
Year
DOI
Venue
2019
10.1007/s10898-019-00777-y
Journal of Global Optimization
Keywords
Field
DocType
Packing, Ellipses, Continuous rotations, Convex polygon, Phi-function technique, Nonlinear optimization
Applied mathematics,Polygon,Homothetic transformation,Mathematical optimization,Packing problems,Nonlinear programming,Convex polygon,Regular polygon,Ellipse,Scaling,Mathematics
Journal
Volume
Issue
ISSN
75
2
0925-5001
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Aleksandr Pankratov1172.46
T. Romanova2657.04
Igor S. Litvinchev33310.71