Packing circles within ellipses

作者: Ernesto G. Birgin , Luis Henrique Bustamante , Hector Flores Callisaya , Jose Mario Martínez

DOI: 10.1111/ITOR.12006

关键词:

摘要: The problem of packing circles within ellipses is considered in the present paper. A new ellipse-based system coordinates introduced by means which a closed formula to compute distance an arbitrary point boundary ellipse exists. Nonlinear programming models for some variants 2D and 3D problems involving circular items elliptical objects are given. resulting medium-sized highly challenging nonlinear global solution sought. For this purpose, multistart strategies carefully thoroughly explored. Numerical experiments exhibited.

参考文章(22)
Ernesto G. Birgin, José Mario Martínez, Large-Scale Active-Set Box-Constrained Optimization Method with Spectral Projected Gradients Computational Optimization and Applications. ,vol. 23, pp. 101- 125 ,(2002) , 10.1023/A:1019928808826
A. V. Levy, A. Montalvo, The Tunneling Algorithm for the Global Minimization of Functions SIAM Journal on Scientific and Statistical Computing. ,vol. 6, pp. 15- 29 ,(1985) , 10.1137/0906002
C. Barrón, S. Gómez, D. Romero, Archimedean polyhedron structure yields a lower energy atomic cluster Applied Mathematics Letters. ,vol. 9, pp. 75- 78 ,(1996) , 10.1016/0893-9659(96)00076-6
Mekapati Srinivas, G.P. Rangaiah, Implementation and evaluation of random tunneling algorithm for chemical engineering applications Computers & Chemical Engineering. ,vol. 30, pp. 1400- 1415 ,(2006) , 10.1016/J.COMPCHEMENG.2006.04.005
E.G. Birgin, J.M. Martı́nez, D.P. Ronconi, Optimizing the packing of cylinders into a rectangular container: A nonlinear approach European Journal of Operational Research. ,vol. 160, pp. 19- 33 ,(2005) , 10.1016/J.EJOR.2003.06.018
R. Andreani, E. G. Birgin, J. M. Martínez, M. L. Schuverdt, On Augmented Lagrangian Methods with General Lower-Level Constraints Siam Journal on Optimization. ,vol. 18, pp. 1286- 1309 ,(2007) , 10.1137/060654797
Ernesto G Birgin, Jan M Gentil, None, New and improved results for packing identical unitary radius circles within triangles, rectangles and strips Computers & Operations Research. ,vol. 37, pp. 1318- 1327 ,(2010) , 10.1016/J.COR.2009.09.017
L. Martínez, R. Andrade, E. G. Birgin, J. M. Martínez, PACKMOL: a package for building initial configurations for molecular dynamics simulations. Journal of Computational Chemistry. ,vol. 30, pp. 2157- 2164 ,(2009) , 10.1002/JCC.21224
Dan Vladimir Nichita, Susana Gomez, Efficient location of multiple global minima for the phase stability problem Chemical Engineering Journal. ,vol. 152, pp. 251- 263 ,(2009) , 10.1016/J.CEJ.2009.05.011
Ignacio Castillo, Frank J. Kampas, János D. Pintér, Solving circle packing problems by global optimization: Numerical results and industrial applications European Journal of Operational Research. ,vol. 191, pp. 786- 802 ,(2008) , 10.1016/J.EJOR.2007.01.054