New and improved results for packing identical unitary radius circles within triangles, rectangles and strips

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Author(s):	Birgin, Ernesto G. ^[1] ; Gentil, Jan M. ^[1] Total Authors: 2
Affiliation:	^[1] Univ Sao Paulo, Inst Math & Stat, Dept Comp Sci, BR-05508090 Sao Paulo - Brazil Total Affiliations: 1
Document type:	Journal article
Source:	Computers & Operations Research; v. 37, n. 7, p. 1318-1327, JUL 2010.
Web of Science Citations:	36
Abstract
The focus of study in this paper is the class of packing problems. More specifically, it deals with the placement of a set of N circular items of unitary radius inside an object with the aim of minimizing its dimensions. Differently shaped containers are considered, namely circles, squares, rectangles, strips and triangles. By means of the resolution of non-linear equations systems through the Newton-Raphson method, the herein presented algorithm succeeds in improving the accuracy of previous results attained by continuous optimization approaches up to numerical machine precision. The computer implementation and the data sets are available at http://www.ime.usp.br/similar to egbirgin/packing/. (C) 2009 Elsevier Ltd, All rights reserved. (AU)

FAPESP's process:	06/53768-0 - Computational methods of optimization
Grantee:	José Mário Martinez Perez
Support Opportunities:	Research Projects - Thematic Grants