LP bounds in various constraint programming approaches for orthogonal packing

Computers and Operations Research

Volumn 39, Issue 10, 2012, Pages 2425-2438

  Mesyagutov, M ^a   Scheithauer, G ^a   Belov, G ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Column generation; Constraint programming; Linear programming

Indexed keywords

COLUMN GENERATION; CONSTRAINT PROGRAMMING; CONSTRAINT PROPAGATION; FEASIBILITY PROBLEM; NUMERICAL RESULTS; RECTANGULAR CONTAINERS; SEARCH PROCEDURES; STRIP PACKING PROBLEM;

CONSTRAINT THEORY; LINEAR PROGRAMMING;

COMPUTER PROGRAMMING;

EID: 84856101677     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2011.12.010     Document Type: Article

References (40)

1. K.R. Apt Principles of constraint programming 2003 Cambridge University Press
2. C. Alves, and J.M. Valério de Carvalho A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem Computers & Operations Research 35 4 2008 1315 1328 (Pubitemid 47404772)
3. R. Alvarez-Valdes, F. Parreño, and J. Tamarit A branch and bound algorithm for the strip packing problem OR Spectrum 31 2009 431 459 10.1007/s00291-008-0128-5
4. R. Baldacci, and M. Boschetti A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem European Journal of Operational Research 183 3 2007 1136 1149 (Pubitemid 47030732)
5. N. Beldiceanu, M. Carlsson, S. Demassey, and E. Poder New filtering for the cumulative constraint in the context of non-overlapping rectangles Annals of Operations Research 184 1 2011 27 50
6. N. Beldiceanu, M. Carlsson, and E. Poder New filtering for the cumulative constraint in the context of non-overlapping rectangles Proceedings of the 5th international conference on integration of AI and OR techniques in constraint programming for combinatorial optimization problems, CPAIOR08 2008 Springer-Verlag Berlin, Heidelberg 21 35 (Pubitemid 351777369)
7. J.E. Beasley Bounds for two-dimensional cutting Journal of Operational Research Society 36 1 1985 71 74 (Pubitemid 15460768)
8. G. Belov, V. Kartak, H. Rohling, and G. Scheithauer One-dimensional relaxations and lp bounds for orthogonal packing International Transactions in Operational Research 16 6 2009 745 766
9. Belov G, Kartak V, Rohling H, Scheithauer G. Conservative scales in packing problems. Technical report. Preprint MATH-NM-03-2011. Technische Universität Dresden; 2011.
10. M.A. Boschetti, and A. Mingozzi The two-dimensional finite bin packing problem. Part I. New lower bounds for the oriented case 4OR: A Quarterly Journal of Operations Research 1 2003 27 42 10.1007/s10288-002-0005-z
11. Belov G, Rohling H. A branch-and-price graph-theoretical algorithm for orthogonal-packing feasibility. Technical report. Preprint MATH-NM-10-2009. Technische Universität Dresden; 2009.
12. G. Belov, G. Scheithauer, and E.A. Mukhacheva One-dimensional heuristics adapted for two-dimensional rectangular strip packing Journal of the Operational Research Society 59 10 2008 823 832 (Pubitemid 351641215)
13. F. Clautiaux, C. Alves, and J. Valério de Carvalho A survey of dual-feasible and superadditive functions Annals of Operations Research 179 2010 317 342
14. F. Clautiaux, C. Alves, and J. Valério de Carvalho A survey of dual-feasible and superadditive functions Annals of Operations Research 179 2010 317 342 10.1007/s10479-008-0453-8
15. J. Carlier, F. Clautiaux, and A. Moukrim New reduction procedures and lower bounds for the two-dimensional bin packing problem with fixed orientation Computers & Operations Research 34 8 2007 2223 2250 (Pubitemid 46073419)
16. F. Clautiaux, A. Jouglet, J. Carlier, and A. Moukrim A new constraint programming approach for the orthogonal packing problem Computers & Operations Research 35 3 2008 944 959 (Pubitemid 47368856)
17. F. Clautiaux, A. Jouglet, and A. Moukrim A new graph-theoretical model for k-dimensional guillotine-cutting problems Proceedings of the 7th international conference on experimental algorithms, WEA08 2008 Springer-Verlag Berlin, Heidelberg 43 54
18. S.P. Fekete, and J. Schepers New classes of fast lower bounds for bin packing problems Mathematical Programming 91 2001 11 31 10.1007/s101070100243 (Pubitemid 33758904)
19. S.P. Fekete, and J. Schepers A combinatorial characterization of higher-dimensional orthogonal packing Mathematics of Operations Research 29 2 2004 353 368
20. S.P. Fekete, and J. Schepers A general framework for bounds for higher-dimensional orthogonal packing problems Mathematical Methods of Operations Research 60 2 2004 311 329
21. P.C. Gilmore, and R.E. Gomory A linear programming approach to the cutting-stock problem (Part I) Operations Research 9 1961 849 859
22. M. Hifi Exact algorithms for the guillotine strip cutting/packing problem Computers & Operations Research 25 11 1998 925 940
23. Hopper E. Two-dimensional packing utilising evolutionary algorithms and other meta-heuristic methods. PhD thesis. Cardiff University; 2000.
24. E. Hopper, and B.C.H. Turton An empirical investigation of metaheuristic and heuristic algorithms for a 2D packing problem European Journal of Operational Research 128 2000 34 57
25. M. Kenmochi, T. Imamichi, K. Nonobe, M. Yagiura, and H. Nagamochi Exact algorithms for the two-dimensional strip packing problem with and without rotations European Journal of Operational Research 198 1 2009 73 83
26. R. Korf, M. Moffitt, and M. Pollack Optimal rectangle packing Annals of Operations Research 179 2010 261 295 10.1007/s10479-008-0463-6
27. Kantorovich LV, Zalgaller VF. Calculation of rational cutting of stock (in Russian). Leningrad: Lenizdat; 1951.
28. Lueker GS. Bin packing with items uniformly distributed over intervals [a,b]. In: FOCS83; 1983. p. 28997.
29. R. Macedo, C. Alves, and J.M. Valério de Carvalho Arc-flow model for the two-dimensional guillotine cutting stock problem Computers & Operations Research 37 June 2010 991 1001
30. M. Mesyagutov, E. Mukhacheva, G. Belov, and G. Scheithauer Packing of one-dimensional bins with contiguous selection of identical items: an exact method of optimal solution Automation and Remote Control 72 2011 141 159 10.1134/S0005117911010127
31. S. Martello, M. Monaci, and D. Vigo An exact approach to the strip packing problem INFORMS Journal on Computing 15 3 2003 310 319 (Pubitemid 39042723)
32. S. Martello, D. Pisinger, and P. Toth Dynamic programming and strong bounds for the 01 knapsack problem Management Science 45 1999 414 423
33. Mesyagutov M, Scheithauer G, Belov G. LP bounds in constraint programming approaches for orthogonal packing. Technical report. Preprint MATH-NM-06-2011. Technische Universität Dresden; 2011.
34. M. Padberg Packing small boxes into a big box Mathematical Methods of Operations Research 52 1 2000 1 21
35. D. Pisinger, and M. Sigurd Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem INFORMS Journal on Computing 19 January 2007 36 51
36. G. Scheithauer Equivalence and dominance for problems of optimal packing of rectangles Ricerca Operativa 83 27 1995 3 34
37. G. Scheithauer LP-based bounds for the container and multi-container loading problem International Transactions in Operational Research 6 2 1999 199 213
38. G. Scheithauer Zuschnitt- und Packungsoptimierung: Problemstellungen, Modellierungstechniken, Lösungsmethoden 2008 Teubner Verlag Wiesbaden
39. H. Simonis, and B. OSullivan Search strategies for rectangle packing Proceedings of the 14th international conference on principles and practice of constraint programming, CP08 2008 Springer-Verlag Berlin, Heidelberg 52 66
40. G. Wäscher, H. Hausner, and H. Schumann An improved typology of cutting and packing problems European Journal of Operational Research 183 3 2007 1109 1130 (Pubitemid 47030730)