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

Computers and Operations Research

Volumn 37, Issue 7, 2010, Pages 1318-1327

  Birgin, Ernesto G ^a   Gentil, Jan M ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Newton's method; Non linear equations system; Non linear programming; Packing

Indexed keywords

COMPUTER IMPLEMENTATIONS; CONTINUOUS OPTIMIZATION; DATA SETS; MACHINE PRECISION; NEWTON'S METHODS; PACKING PROBLEMS;

DYNAMIC PROGRAMMING; LINEAR EQUATIONS; LINEARIZATION; OPTIMIZATION;

NEWTON-RAPHSON METHOD;

EID: 70849122690     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2009.09.017     Document Type: Article

References (22)

1. Andreani R., Birgin E.G., Martínez J.M., and Schuverdt M.L. Augmented Lagrangian methods under the constant positive linear dependence constraint qualification. Mathematical Programming 111 (2008) 5-32
2. Andreani R., Birgin E.G., Martínez J.M., and Schuverdt M.L. On augmented Lagrangian methods with general lower-level constraints. SIAM Journal on Optimization 18 (2007) 1286-1309
3. Birgin E.G., Castillo R., and Martínez J.M. Numerical comparison of augmented Lagrangian algorithms for nonconvex problems. Computational Optimization and Applications 31 (2005) 31-56
4. Birgin E.G., and Martínez J.M. Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization. Computational Optimization and Applications 39 (2008) 1-16
5. Birgin E.G., Martínez J.M., Mascarenhas W.F., and Ronconi D.P. Method of sentinels for packing items within arbitrary convex regions. Journal of the Operational Research Society 57 (2006) 735-746
6. Birgin E.G., Martínez J.M., Nishihara F.H., and Ronconi D.P. Orthogonal packing of rectangular items within arbitrary convex regions by nonlinear optimization. Computers & Operations Research 33 (2006) 3535-3548
7. Birgin E.G., Martínez J.M., and Ronconi D.P. Optimizing the packing of cylinders into a rectangular container: a nonlinear approach. European Journal of Operational Research 160 (2005) 19-33
8. Birgin E.G., and Sobral F.N.C. Minimizing the object dimensions in circle and sphere packing problems. Computers & Operations Research 35 (2008) 2357-2375
9. Bondy J.A., and Murty U.S.R. Graph theory. Graduate texts in mathematics Vol. 244 (2008), Springer, New York
10. Dennis Jr. J.E., and Schnabel R.B. Numerical methods for unconstrained optimization and nonlinear equations. Classics in applied mathematics (1996), SIAM Publications, Philadelphia
11. Golub G.H., and Van Loan C.F. Matrix computations (1996), The Johns Hopkins University Press, Baltimore
12. Locatelli M., and Raber U. Packing equal circles in a square: a deterministic global optimization approach. Discrete Applied Mathematics 122 (2002) 139-166
13. Maranas C.D., Floudas C.A., and Pardalos P.M. New results in the packing of equal circles in a square. Discrete Mathematics 142 (1995) 287-293
14. Mladenović N., Plastria F., and Urošević D. Reformulation descent applied to circle packing problems. Computers & Operations Research 32 (2005) 2419-2434
15. Nurmela K.J., and Östergård P.R. Packing up to 50 equal circles in a square. Discrete & Computational Geometry 18 (1997) 111-120
16. Specht E. Packomania (January 20, 2009), available at 〈http://www.packomania.com〉.
17. Stoyan YG. Mathematical methods for geometric design. In: Ellis TMR, Semenkoc OJ, editors, Advances in CAD/CAM. Proceedings of PROLAMAT 82, Leningrad and Amsterdam; 1983. p. 67-86.
18. Stoyan Y.G., and Yas'kov G.N. Mathematical model and solution method of optimization problem of placement of rectangles and circles taking into account special constraints. International Transactions in Operational Research 5 (1998) 45-57
19. Stoyan Y.G., and Yas'kov G.N. A mathematical model and a solution method for the problem of placing various-sized circles into a strip. European Journal of Operational Research 156 (2004) 590-600
20. Stoyan YG, Yas'kov GN, Scheithauer G. Packing spheres of various radii into a parallelepiped. Technical report MATH-NM-15-2001, TU, Dresden, 2001.
21. Zhang D., and Deng A. An effective hybrid algorithm for the problem of packing circles into a larger containing circle. Computers & Operations Research 32 (2005) 1941-1951
22. Zhang D., and Huang W. A simulated annealing algorithm for the circles packing problem. Computational science-ICCS 2004, Lecture Notes in Computer Science vol. 3036 (2004), Springer, Berlin and Heidelberg 206-214