A best-first branch-and-bound algorithm for orthogonal rectangular packing problems

International Transactions in Operational Research

Volumn 5, Issue 5, 1998, Pages 345-356

  Hifi, M ^a   Ouafi, R ^b  

^a LABORATOIRE DES SCIENCES DU CLIMAT ET DE L ENVIRONNEMENT   (France)

^b UNIVERSITY OF SCIENCES AND TECHNOLOGY HOUARI BOUMEDIENE   (Algeria)

Author keywords

Branch and bound; Combinatorial optimization; Heuristics; Rectangular packing

Indexed keywords

EID: 85016655736     PISSN: 09696016     EISSN: 14753995     Source Type: Journal    
DOI: 10.1111/j.1475-3995.1998.tb00119.x     Document Type: Article

References (32)

1. Albano, A. (1977) A method to improve two-dimensional layout. Comp. Aid. Des. 9, 48-52.
2. Albano, A. and Sapuppo, G. (1980) Optimal allocation of two-dimensional irregular shapes using heuristic search methods. IEEE Trans. Sys. Man. Cyb. smc-10 (5), 242-248.
3. Baker, B. S., Coffman, E. G. and Rives, R. L. (1980) Orthogonal packings in two dimensions. SIAM Journal of Computing 9 (4), 846-855.
4. Baker, B. S., Brown, D. J. and Katseff, H. P. (1981) A 5/4 algorithm for two-dimensional packing. Journal of Algorithms 2 (4), 348-368.
5. Beasley, J. E. (1985) Algorithms for unconstrained two-dimensional guillotine cutting. Journal of the Operational Research Society 36, 297-306.
6. Christofides, N. and Whitlock, C. (1977) An algorithm for two-dimensional cutting problems. Operations Research 2, 30-44.
7. Coffman, E. G. and Lagarias, J. C. (1989) Algorithms for packing squares: a probabilistic analysis. SIAM Journal of Computing 18 (1), 166-185.
8. Dechter, R. and Pearl, J. (1988) The optimality of A*. Search in Artificial Intelligence, Spinger.
9. Duijvestijn, A. J. W. (1978) Simple perfect squared square of lowest order. Journal of Combinatorial Theory 25 (B), 260-263.
10. Dyckhoff, H. (1990) A typology of cutting and packing problems. Europ. Journal of Operational Research 44, 145-159.
11. Federico, P. J., Bondy, J. A. and Murty, U. S. R. (1979) Squaring rectangles and squares. Graph theory and related topics, Editions Academic Press.
12. Fernandez de la Vega, W. and Lueker, G. S. (1981) Bin packing can be solved within 1 +ε in linear time. Combinatoria 1 (4), 349-355.
13. Gilmore, P. (1979) Cutting stock, linear programming, knapsacking, dynamic programming and integer programming, some interconnections. Annals of Discrete Mathematics 4, 217-235.
14. Herz, J. C. (1972) A recursive computing procedure for two-dimensional stock cutting. IBM Journal of Research and Development 16, 462-469.
15. Hifi, M. (1994) Study of some combinatorial optimization problems: cutting stock, packing and set covering problems, Ph.D. Thesis, Université de Paris 1 Panthéon-Sorbonne (in French).
16. Hifi, M. (1997a) The DH/KD algorithm: a hybrid approach for unconstrained two-dimensional cutting problems. European Journal of Operational Research 97, 41-51.
17. Hifi, M. (1997b) An improvement of Viswanathan and Bagchi's exact algorithm for constrained two-dimensional cutting stock. Computers and Operations Research 24 (8), 727-736.
18. Hifi, M. and Ouafi, R. (1997) Best-first search and dynamic programming methods for cutting problems: the cases of one and more stock plates. Computers and Industrial Engineering 32 (1), 187-205.
19. Hifi, M. and Zissimopoulos, V. (1996) A recursive exact algorithm for weighted two-dimensional cutting. European Journal of Operational Research 91, 553-564.
20. Hinxman, A. I. (1980) The trim-loss and assortment problems: a survey. European Journal of Operational Research 5, 8-18.
21. Jakobs, S. (1996) On genetic algorithms for the packing of polygons. European Journal of Operational Research 88, 165-181.
22. Kantorovich, L. K. (1960) Mathematical methods of organizing and planning production. Management Science 6, 363-422.
23. Kleitman, D. J. and Krieger, M. K. (1975) An optimal bound for two dimensional bin packing. Proceedings of the 16th Annual Symposium on Foundations of Computer Science, pp. 163-168.
24. Kuntz, G. and Uhry, J. P. (1982) Optimisation de pertes de matiere en Industrie textile, Ph.D. Thesis, Laboratoire IMAG, Université de Grenoble (in French).
25. Morabito, R., Arenales, M. and Arcaro, V. (1992) An and-or-graph approach for two-dimensional cutting problems. European Journal of Operational Research 58 (2), 263-271.
26. Sweeney, P. E. and Paternoster, E. R. (1992) Cutting and packing problems: a categorized applications-oriented research bibliography. Journal of the Operational Research Society 43, 691-706.
27. Oliveira, J. F. and Ferreira, J. S. (1990) An improved version of Wang's algorithm for two-dimensional cutting problems. European Journal of Operational Research 44, 256-266.
28. Syslo, M., Deo, N. and Kowalik, J. (1983) Discrete optimization algorithms, Prentice-Hall, New Jersey.
29. Tschöke, S. and Holthöfer, N. (1996) A new parallel approach to the constrained two-dimensional cutting stock problem, Preprint, University of Paderbon, D.C.S. 33095 Paderborn, Germany.
30. Vasko, F. J. (1989) A computational improvement to Wang's two-dimensional cutting stock algorithm. Computers and Industrial Engineering 16, 109-115.
31. Viswanathan, K. V. and Bagchi, A. (1993) Best-first search methods for constrained two-dimensional cutting stock problems. Operations Research 41 (4), 768-776.
32. Wang, P. Y. (1983) Two algorithms for constrained two-dimensional cutting stock problems. Operations Research 31 (3), 573-586.