A heuristic for the circle packing problem with a variety of containers

European Journal of Operational Research

Volumn 214, Issue 3, 2011, Pages 512-525

  Lopez C O ^a   Beasley, J E ^a  

^a BRUNEL UNIVERSITY   (United Kingdom)

Author keywords

Circle packing; Formulation space search; Metaheuristic

Indexed keywords

CONTAINERS; HEURISTIC ALGORITHMS; NONLINEAR PROGRAMMING; OPTIMIZATION;

CIRCLE PACKING; CIRCLE PACKING PROBLEM; METAHEURISTIC; NON-LINEAR OPTIMIZATION; NON-LINEAR OPTIMIZATION PROBLEMS; POLAR COORDINATE SYSTEMS; SPACE SEARCH; TWO-DIMENSIONAL CONTAINERS;

HEURISTIC METHODS;

EID: 84861198052     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2011.04.024     Document Type: Article

References (23)

1. E.G. Birgin, J.M. Gentil, New and improved results for packing identical unitary radius circles within triangles, rectangles and strips, Computer & Operations Research 37 (7) (2010) 1318-1327.
2. E.G. Birgin, F.N.C. Sobral, Minimizing the object dimensions in circle and sphere packing problems, Computer & Operations Research 35 (7) (2008) 2357-2375. (Pubitemid 350167494)
3. I. Castillo, F.J. Kampas, J.D. Pinter, Solving circle packing problems by global optimization: Numerical results and industrial applications, European Journal of Operational Research 191 (3) (2008) 786-802. (Pubitemid 351778615)
4. Gill, P.E., Murray, W., Saunders, M.A., 2008. User's Guide for SNOPT Version 7: Software for Large-Scale Nonlinear Programming. Available at .
5. A. Grosso, A.R.M.J.U. Jamali, M. Locatelli, F. Schoen, Solving the problem of packing equal and unequal circles in a circular container, Journal of Global Optimization 47 (1) (2010) 63-81.
6. A. Grosso, M. Locatelli, F. Schoen, A population-based approach for hard global optimization problems based on dissimilarity measures, Mathematical Programming Series A 110 (2) (2007) 373-404. (Pubitemid 46496753)
7. Hansen, P., Mladenović , N., Brimberg, J., Perez, J.A.M., 2010. Variable neighborhood search. In: Gendreau, M., Potvin, J.-Y. (Eds.), Handbook of Metaheuristics, Springer. International Series in Operations Research & Management Science, vol. 146, pp. 61-86.
8. U.H.E. Hansmann, L.T. Wille, Global optimization by energy landscape paving, Physical Review Letters 88 (6) (2002) (Article 068105).
9. A. Hertz, M. Plumettaz, N. Zufferey, Variable space search for graph coloring, Discrete Applied Mathematics 156 (13) (2008) 2551-2560.
10. A. Hertz, M. Plumettaz, N. Zufferey, Corrigendum to variable space search for graph coloring [Discrete Appl. Math. 156 (2008) 2551-2560], Discrete Applied Mathematics 157 (7) (2009) 1335-1336.
11. M. Hifi, R. M'Hallah, A literature review on circle and sphere packing problems: Models and methodologies, Advances in Operations Research (2009). Article ID 150624 .
12. Holmström, K., Göran, A.O., Edvall, M.M., 2008. User's Guide for TOMLAB/SNOPT. Available at .
13. Y. Kochetov, P. Kononova, M. Paschenko, Formulation space search approach for the teacher/class timetabling problem, Yugoslav Journal of Operations Research 18 (1) (2008) 1-11.
14. R.H. Leary, Global optimization on funneling landscapes, Journal of Global Optimization 18 (4) (2000) 367-383.
15. Liu, J., Wang, Y., Pan, J., 2009. Efficiently packing circles into a larger containing circle. In: Zhang, W., Chen, Z., Douglas, C.C., Tong, W. (Eds.), High Performance Computing and Applications", Revised Selected Papers from the Second International Conference, HPCA 2009, Shanghai, China, August 10-12. Lecture Notes in Computer Science, vol. 5938, pp. 250-256.
16. J. Liu, S. Xue, Z. Liu, D. Xu, An improved energy landscape paving algorithm for the problem of packing circles into a larger containing circle, Computers & Industrial Engineering 57 (3) (2009) 1144-1149.
17. Liu, J., Yao, Y., Zheng, Y., Geng, H., Zhou, G., 2009. An effective hybrid algorithm for the circles and spheres packing problems. In: Proceedings of the Third International Conference on Combinatorial Optimization and its Applications, COCOA 2009, Huangshan, China, June 10-12. Lecture Notes in Computer Science, vol. 5573, pp. 135-144.
18. N. Mladenović , F. Plastria, D. Urošević , Reformulation descent applied to circle packing problems, Computer & Operations Research 32 (9) (2005) 2419-2434. (Pubitemid 40118819)
19. Mladenović , N., Plastria, F., Urošević , D., 2007. Formulation space search for circle packing problems. In: Proceedings of the International Workshop on Engineering Stochastic Local Search Algorithms. Designing, Implementing and Analyzing Effective Heuristics, SLS 2007, Brussels, Belgium, September 6-8, 2007. Lecture Notes in Computer Science, vol. 4638, pp. 212-216.
20. J.D. Pintér, Nonlinear optimization with GAMS/LGO, Journal of Global Optimization 38 (1) (2007) 79-101.
21. Specht, E., 2010. Packomania. Available at .
22. P.G. Szabó, M.C. Markót, T. Csendes, E. Specht, L.G. Casado, I. Garcia, New approaches to circle packing in a square: With program codes, Springer Optimization and its Applications 6 (2007).
23. D.J. Wales, J.P.K. Doye, Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms, The Journal of Physical Chemistry A 101 (28) (1997) 5111-5116. (Pubitemid 127578169)