A hybrid genetic algorithm for the two-dimensional single large object placement problem

European Journal of Operational Research

Volumn 183, Issue 3, 2007, Pages 1150-1166

  Hadjiconstantinou, Eleni ^a   Iori, Manuel ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Genetic algorithms; Single large object placement problem; Two dimensional cutting and packing

Indexed keywords

BENCHMARKING; COMPUTATIONAL METHODS; GENETIC ALGORITHMS; HEURISTIC ALGORITHMS; HEURISTIC METHODS; PROBLEM SOLVING;

SINGLE LARGE OBJECT PLACEMENT PROBLEMS; TWO-DIMENSIONAL CUTTING; TWO-DIMENSIONAL PACKING;

OPERATIONS RESEARCH;

EID: 34447106778     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2005.11.061     Document Type: Article

References (53)

1. A. Amaral, A.N. Letchford, An improved upper bound for the two-dimensional non-guillotine cutting problem, Technical report, Lancaster University, UK, 2001. Available from: .
2. Arenales M., and Morabito R. An and/or-graph approach to the solution of two-dimensional guillotine cutting problems. European Journal of Operational Research 84 (1995) 599-617
3. Beasley J.E. Algorithms for unconstrained two-dimensional guillotine cutting. Journal of the Operational Research Society 36 (1985) 297-306
4. Beasley J.E. An exact two-dimensional non-guillotine cutting tree search procedure. Operations Research 33 (1985) 49-64
5. Beasley J.E. Or-library: Distributing test problems by electronic mail. Journal of the Operational Research Society 41 (1990) 1069-1072
6. Beasley J.E. A population heuristic for constrained two-dimensional non-guillotine cutting. European Journal of Operational Research 156 (2004) 601-627
7. Boschetti M.A., Hadjiconstantinou E., and Mingozzi A. New upper bounds for the two-dimensional orthogonal non guillotine cutting stock problem. IMA Journal of Management Mathematics 13 (2002) 95-119
8. Burke E.K., Kendall G., and Whitwell G. A new placement heuristic for the orthogonal stock-cutting problem. Operations Research 52 (2004) 655-671
9. Caprara A., and Monaci M. On the 2-dimensional knapsack problem. Operations Research Letters 32 (2004) 5-14
10. Christofides N., and Hadjiconstantinou E. An exact algorithm for the orthogonal, 2-d cutting problems using guillotine cuts. European Journal of Operational Research 83 (1995) 21-38
11. Christofides N., and Whitlock C. An algorithm for two-dimensional cutting problems. Operations Research 25 (1977) 30-44
12. L. Davis, Applying adaptive algorithms to epistatic domains, in: Proceedings of the International Joint Conference on Artificial Intelligence, 1985, Morgan Kaufmann, pp. 162-164.
13. Davis L. A Handbook of Genetic Algorithms (1991), Van Nostrand Reinhold, New York
14. K.A. De Jong, An analysis of the behavior of a class of genetic adaptive systems, PhD thesis, University of Michigan, 1975.
15. J.J. Dongarra, Performance of various computers using standard linear equations software, Working paper, Computer Science Department, University of Tennesse, 2003.
16. Dowsland K.A., and Dowsland W.B. Packing problems. European Journal of Operational Research 56 (1992) 2-14
17. Dyckhoff H. A typology of cutting and packing problems. European Journal of Operational Research 44 (1990) 145-159
18. Fekete S.P., and Schepers J. A new exact algorithm for general orthogonal d-dimensional knapsack problems. Algorithms - ESA '97. Springer Lecture Notes in Computer Science 1284 (1997) 144-156
19. S.P. Fekete, J. Schepers, On more-dimensional packing II: Bounds, Technical Report ZPR97-289, Mathematisches Institut, Universität zu Köln, 1997.
20. Fekete S.P., and Schepers J. A combinatorial characterization of higher-dimensional orthogonal packing. Mathematics of Operations Research 29 (2004) 353-368
21. S.P. Fekete, J. Schepers, J.C. Van der Veen, An exact algorithm for higher-dimensional orthogonal packing, Operations Research, in press.
22. Gardner M. Mathematical games: The problem of Mrs. Perkin's quilt and answers to the last month's puzzles. Scientific American 215 (1966) 264-272
23. Gardner M. The problem of Mrs. Perkin's quilt and other square-packing problems. In: Knopf A.A. (Ed). Mathematical Carnival (1975), Vintage, New York 139-149
24. Gilmore P.C., and Gomory R.E. Multistage cutting problems of two and more dimensions. Operations Research 13 (1965) 94-119
25. Goldberg D.E., and Lingle R.L. Alleles, loci and the traveling salesman problem. Proceedings of the 1st International Conference on Genetic Algorithms and their Applications (1985), Erlbaum, Hillsdale, NJ 154-159
26. Gomez A., and De La Fuente D. Resolution of strip-packing problems with genetic algorithms. Journal of the Operational Research Society 51 (2000) 1289-1295
27. Hadjiconstantinou E., and Christofides N. An exact algorithm for general, orthogonal, two-dimensional knapsack problems. European Journal of Operational Research 83 (1995) 39-56
28. Haessler R.W., and Sweeney P.E. Cutting stock problems and solution procedures. European Journal of Operational Research 54 (1991) 141-150
29. Healy P., Creavin M., and Kuusik A. An optimal algorithm for rectangle placement. Operations Research Letters 24 (1999) 73-80
30. Hertz J.C. A recursive computational procedure for two-dimensional stock cutting. IBM Journal of Research and Development 16 (1972) 462-469
31. Holland J. Adaptation in Natural and Artificial Systems (1975), Michigan Press, Ann Arbor, IL
32. Hopper E., and Turton B.C.H. An empirical investigation of meta-heuristic and heuristic algorithms for a 2d packing problem. European Journal of Operational Research 128 (2001) 34-57
33. Iori M., Martello S., and Monaci M. Metaheuristic algorithms for the strip packing problem. In: Pardalos P., and Korotkich V. (Eds). Optimization and Industry: New Frontiers (2003), Kluwer, Boston 159-179
34. Jakobs S. On genetic algorithms for the packing of polygons. European Journal of Operational Research 88 (1996) 165-181
35. R. Korf, 2003. Optimal rectangle packing: Initial results, in: Proceedings of the International Conference on Automated Planning and Scheduling (ICAPS03), Trento, Italy, 2003, pp. 287-295.
36. Korf R. Optimal rectangle packing: New results. Proceedings of the International Conference on Automated Planning and Scheduling (ICAPS04) (2004), spring, British Columbia 142-149
37. Lai K.K., and Chan J.W.M. Developing a simulated annealing algorithm for the cutting stock problem. Computers and Industrial Engineering 32 (1997) 115-127
38. Lai K.K., and Chan J.W.M. An evolutionary algorithm for the rectangular cutting stock problem. International Journal of Industrial Engineering 4 (1997) 130-139
39. Leung T.W., Yung C.H., and Troutt M.D. Applications of genetic search and simulated annealing to the two-dimensional non-guillotine cutting stock problem. Computers and Industrial Engineering 40 (2001) 201-214
40. Liu D., and Teng H. An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles. European Journal of Operational Research 112 (1999) 413-420
41. Lodi A., Martello S., and Monaci M. Two-dimensional packing problems: A survey. European Journal of Operational Research 141 (2002) 241-252
42. Lodi A., Martello S., and Vigo D. Approximation algorithms for the oriented two-dimensional bin packing problem. European Journal of Operational Research 112 (1999) 158-166
43. Lodi A., Martello S., and Vigo D. Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems. INFORMS Journal on Computing 11 (1999) 345-357
44. Martello S., and Toth P. Knapsack Problems: Algorithms and Computer Implementations (1990), John Wiley & Sons, Chichester
45. Martello S., and Vigo D. Exact solution of the two-dimensional finite bin packing problem. Management Science 44 (1998) 388-399
46. Poon P.W., and Carter J.N. Genetic algorithm crossover operators for ordering applications. Computers and Operations Research 22 (1995) 135-147
47. Reeves C. Hybrid genetic algorithms for the bin-packing and related problems. Annals of Operations Research 63 (1996) 371-396
48. Reeves C.R. Modern Heuristic Techniques for Combinatorial Problems (1993), Blackwell Scientific Publications, Oxford
49. Scheithauer G. Equivalence and dominance for problems of optimal packing of rectangles. Ricerca Operativa 83 (1997) 3-34
50. Scheithauer G., and Terno J. Modeling of packing problems. Optimization 28 (1993) 63-84
51. Sweeney P.E., and Paternoster E.R. Cutting and packing problems: A categorized, application-orientated research bibliography. Journal of the Operational Research Society 43 (1992) 691-706
52. G. Wäscher, H. Haussner, H. Schumann, An improved typology of cutting and packing problems, European Journal of Operational Research, this issue, doi:10.1016/j.ejor.2005.12.047.
53. Wang P.Y. Two algorithms for constrained two-dimensional cutting stock problems. Operations Research 31 (1983) 573-586