Packing Unequal Spheres into Various Containers

Yu. G. Stoyan1, Guntram Scheithauer2, Georgiy Yaskov1
1A. N. Podgorny Institute for in Mechanical Engineering Problems, National Academy of Sciences of Ukraine, Kharkiv, Ukraine
2Institute of Numerical Mathematics, Dresden University of Technology, Dresden, Germany

Tóm tắt

Từ khóa


Tài liệu tham khảo

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices, and Groups, Springer-Verlag, New York (1999).

A. Sutou and Y. Day, “Global optimization approach to unequal sphere packing problems in 3D,” J. Optimiz. Theory and Appl., 114, No. 3, 671–694 (2002).

Yu. Stoyan, G. Yaskov, and G. Scheithauer, “Packing of various solid spheres into a parallelepiped,” Central European J. Oper. Research, 11, No. 4, 389–407 (2003).

E. G. Birgin and F. N. C. Sobral, “Minimizing the object dimensions in circle and sphere packing problems,” Computers & Oper. Research, 35, 2357–2375 (2008).

T. Kubach, A. Bortfeldt, T. Tilli, and H. Gehring, “Parallel greedy algorithms for packing unequal spheres into a cuboidal strip or a cuboid,” Technical Report, Diskussionsbeitrag Nr. 440, Fakultät für Wirtschaftswissenschaft, FernUniversität in Hagen (2009).

T. Kubach, A. Bortfeldt, T. Tilli, and H. Gehring, “Greedy algorithms for packing unequal spheres into a cuboidal strip or a cuboid,” Asia Pac. J. Oper. Res., 28, No. 6, 739–753 (2011).

W. Q. Huang, Y. Li, H. Akeb, and C. M. Li, “Greedy algorithms for packing unequal circles into a rectangular container,” J. Oper. Research Society, 56, No. 5, 539–548 (2005).

M. Hifi and L. Yousef, “Width beam and hill-climbing strategies for the three-dimensional sphere packing problem,” in: Proc. 2014 Federated Conf. on Computer Science and Information Systems, ACSIS, 2 (2014), pp. 421–428.

J. Liu, Y. Yao, Yu. Zheng, H. Geng, and G. Zhou, “An effective hybrid algorithm for the circles and spheres packing problems,” in: Combinatorial Optimization and Applications. Lecture Notes in Computer Science, 5573 (2009), pp. 135–144.

Z. Z. Zeng, W. Q. Huang, R. C. Xu, and Z. H. Fu, “An algorithm to packing unequal spheres in a larger sphere,” Advanced Materials Research, 546–547, 1464–1469 (2012).

M. Hifi and R. M’Hallah, “A literature review on circle and sphere packing problems: Models and methodologies,” Advances in Operations Research (2009).

Yu. Stoyan and G. Yaskov, “Packing unequal circles into a strip of minimal length with a jump algorithm,” Optimization Letters, 8, No. 3, 949–970 (2014).

Yu. G. Stoyan and G. N. Yaskov, “A mathematical model and a solution method for the problem of placing various-sized circles into a strip,” Europ. J. Oper. Research, 156, 590–600 (2004).

A. Wächter and L. T. Biegler, “On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming,” Mathem. Programming, 106, No. 1, 25–57 (2006).

Yu. G. Stoyan and G. N. Yaskov, “Packing identical spheres into a cylinder,” Intern. Trans. in Oper. Research, 17, No. 1, 51–70 (2010).