Recent Advances in Multi-dimensional Packing Problems (original) (raw)

Abstract

sparkles

AI

The chapter delves into Multi-Dimensional Packing problems, emphasizing their applications in transportation and supply chains. It identifies the need for a cohesive methodological framework to efficiently tackle various packing problem variants. The focus is on orthogonal packings, with a twofold aim: to survey item representation approaches and to analyze solution methods concerning performance, limitations, and practical implementations.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (59)

  1. Alvarez-Valdes, R., Parreno, F. & Tamarit, J.-M. (2007). A tabu search algorithm for a two-dimensional non-guillotine cutting problem, European Journal of Operational Research 183: 1167-1182.
  2. Baldacci, R. & Boschetti, M. A. (2007). A cutting plane approach for the two-dimensional orthogonal non guillotine cutting stock problem, European Journal of Operational Research 183: 1136-1149.
  3. Baldi, M., Perboli, G. & Tadei, R. (2011). The three-dimensional knapsack problem with balancing constraints, Publication CIRRELT-2011-51, Centre Interuniversitaire de Recherche sur les Réseaux d'Entreprise, la Logistique et le Transport, Université de Montréal, Montréal, Canada.
  4. Beasley, J. E. (1990). Or-library: distributing test problems by electronic mail, Journal of the Operational Research Society 41: 1069-1072.
  5. Beasley, J. E. (1985a). Algorithms for two-dimensional unconstrained guillotine cutting, Journal of the Operational Research Society 36: 297-306.
  6. Beasley, J. E. (1985b). An exact two-dimensional non-guillotine cutting stock tree search procedure, Operations Research 33: 49-64.
  7. Beasley, J. E. (2004). A population heuristic for constrained two-dimensional non-guillotine cutting, European Journal of Operational Research 156: 601-627.
  8. Berkey, J. O. & Wang, P. Y. (1987). Two dimensional finite bin packing algorithms, Journal of the Operational Research Society 38: 423-429.
  9. Bischoff, E. E. & Marriot, M. D. (1990). A comparative evaluation of heuristics for container loading, European Journal of Operational Research 44: 267-276.
  10. Bischoff, E. E. & Ratcliff, M. S. W. (1995). Issues in the development of approaches to container loading, Omega 23: 377-390.
  11. Bortfeldt, A. & Gehring, H. (1998). A tabu search algorithm for weakly heterogeneous container loading problems, OR Spectrum 20: 237-250.
  12. Bortfeldt, A. & Gehring, H. (2001). A hybrid genetic algorithm for the container loading problem, European Journal of Operational Research 131: 143-161.
  13. Bortfeldt, A. & Winter, T. (2009). A genetic algorithm for the two-dimensional knapsack problem with rectangular pieces, International Transactions in Operational Research 16: 685-713.
  14. Boschetti, M. A., Hadjiconstantinou, E. & Mingozzi, A. (2002). New upper bounds for the twodimensional orthogonal cutting stock problem, IMA Journal of Management Mathematics 13: 95-119.
  15. Caprara, A. & Monaci, M. (2004). On the 2-dimensional knapsack problem, Operations Research Letters 32: 5-14.
  16. Christofides, N. & Whitlock, C. (1977). An algorithm for two-dimensional cutting problems, Operations Research 25: 30-44.
  17. Chung, F. K. R., Garey, M. R. & Johnson, D. S. (1982). On packing two-dimensional bins, SIAM -Journal of Algebraic and Discrete Methods 3(1): 66-76.
  18. Cordeau, J.-F., Gendreau, M., Laporte, G., Potvin, J.-Y. & Semet, F. (2002). A guide to vehicle routing heuristics, Journal of the Operational Research Society 53(5): 512-522.
  19. Crainic, T., Perboli, G. & Tadei, R. (2008). Extreme point-based heuristics for three-dimensional bin packing, INFORMS Journal on Computing 20: 368-384.
  20. Crainic, T., Perboli, G. & Tadei, R. (2009). TS2PACK: A two-level tabu search for the three-dimensional bin packing problem, European Journal of Operational Research 195: 744-760.
  21. den Boef, E., Korst, J., Martello, S., Pisinger, D. & Vigo, D. (2005). Erratum to "the three-dimensional bin packing problem": Robot-packable and orthogonal variants of packing problems, Operations Research 53(4): 735-736.
  22. Egeblad, J. & Pisinger, D. (2009). Heuristic approaches for the two-and three-dimensional knapsack packing problem, Computers & Operations Research 36: 1026-1049.
  23. Faroe, O., Pisinger, D. & Zachariasen, M. (2003). Guided local search for the three-dimensional bin packing problem, INFORMS Journal on Computing 15(3): 267-283.
  24. Fekete, S. P. & Schepers, J. (1997). A new exact algorithm for general orthogonal d-dimensional knapsack problems, ESA '97, Springer Lecture Notes in Computer Science 1284: 144-156.
  25. Fekete, S. P. & Schepers, J. (2004a). A combinatorial characterization of higher-dimensional orthogonal packing, Mathematics of Operations Research 29(2): 353-368.
  26. Fekete, S. P. & Schepers, J. (2004b). A general framework for bounds for higher-dimensional orthogonal packing problems, Mathematical Methods of Operations Research 60(2): 311-329.
  27. Gehring, H. & Bortfeldt, A. (1997). A genetic algorithm for solving the container loading problem, International Transactions in Operational Research 4: 401-418.
  28. George, J. A. & Robinson, D. F. (1980). A heuristic for packing boxes into a container, Computers & Operations Research 7(3): 147-156.
  29. Gilmore, P. C. & Gomory, R. E. (1965). Multistage cutting problems of two and more dimensions, Operations Research 13: 94-119.
  30. Hadjiconstantinou, E. & Christofides, N. (1995). An exact algorithm for general, orthogonal, two-dimensional knapsack problems, European Journal of Operational Research 83(1): 39-56.
  31. Hadjiconstantinou, E. & Iori, M. (2007). A hybrid genetic algorithm for the two-dimensional single large object placement problem, European Journal of Operational Research 183: 1150-1166.
  32. Imahori, S., M.Yagiura & Ibaraki, T. (2003). Local search algorithms for the rectangle packing problem with general spatial costs, Mathematical Programming, Series B 97: 543-569.
  33. Joncour, C., Pêcher, A. & Valicov, P. (2010). MPQ-trees for orthogonal packing problem, Electronic Notes on Discrete Mathematics 36: 423-429.
  34. Korte, N. & Möhring, R. (1989). An incremental linear-time algorithm for recognizing interval graphs, SIAM J. Comput. 18: 68-81.
  35. Lai, K. K. & Chan, J. W. M. (1997a). Developing a simulated annealing algorithm for the cutting stock problem, Computers & Industrial Engineering 32: 115-127.
  36. Lai, K. K. & Chan, J. W. M. (1997b). An evolutionary algorithm for the rectangular cutting stock problem, International Journal of Industrial Engineering 4: 130-139.
  37. Leung, T. W., Yung, C. H. & Troutt, M. D. (2001). Applications of genetic search and simulated annealing to the two-dimensional non-guillotine cutting stock problem, Computers & Industrial Engineering 40: 201-214.
  38. Liu, D. & Teng, H. (1999). An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles, European Journal of Operational Research 112: 413-420.
  39. Lodi, A., Martello, S. & Monaci, M. (2002). Two-dimensional packing problems: a survey, European Journal of Operational Research 141: 241-252.
  40. Lodi, A., Martello, S. & Vigo, D. (1999). Heuristic and metaheuristic approaches for a class of two-dimensional bin packing problems, INFORMS Journal on Computing 11: 345-357.
  41. Lodi, A., Martello, S. & Vigo, D. (2004a). Models and bounds for two-dimensional level packing problems, Journal of Combinatorial Optimization 8: 363-379.
  42. Lodi, A., Martello, S. & Vigo, D. (2004b). Tspack: A unified tabu search code for multi-dimensional bin packing problems, Annals of Operations Research 131: 203-213.
  43. Mack, D., Bortfeldt, A. & Gehring, H. (2004). A parallel hybrid local search algorithm for the container loading problem, International Transactions in Operational Research 11: 511-533.
  44. Martello, S., Pisinger, D. & Vigo, D. (2000). The three-dimensional bin packing problem, Operations Research 48(2): 256-267.
  45. Martello, S., Pisinger, D., Vigo, D., den Boef, E. & Korst, J. (2007). Algorithm 864: General and robot-packable variants of the three-dimensional bin packing problem, ACM Transactions on Mathematical Software 33, Article No 7: 1-12.
  46. Martello, S. & Toth, P. (1990). Knapsack Problems -Algorithms and computer implementations, John Wiley & Sons, Chichester, UK.
  47. Martello, S. & Vigo, D. (1998). Exact solution of the finite two dimensional bin packing problem, Management Science 44(44): 388-399.
  48. Moura, A. & Oliveira, J. F. (2005). A grasp approach to the container loading problem, IEEE Intelligent Systems 20: 50-57.
  49. Murata, H., Fujiyoshi, K., Nakatake, S. & Kajitani, Y. (1996). Vlsi module placement based on rectangle-packing by the sequence-pair, IEEE Trans. Comput. Aided Des. 15: 1518-1524.
  50. Parreño, F., Alvarez-Valdes, R. & Oliveira, J. F. (2008). A maximal-space algorithm for the container loading problem, INFORMS Journal on Computing 20(3): 412-422.
  51. Parreño, F., Alvarez-Valdes, R. & Oliveira, J. F. (2010). Neighborhood structures for the container loading problem: a VNS implementation, Journal of Heuristics 16: 1-22.
  52. Perboli, G. (2002). Bounds and heuristics for the Packing Problems, PhD thesis, Politecnico di Torino, Turin, Italy.
  53. Perboli, G. (2011). An efficient metaheuristic for multi-dimensional knapsack problems, DAUIN Tech. Rep., Department of Control and Computer Engineering, Politecnico di Torino, Turin, Italy.
  54. Perboli, G., Crainic, T. G. & Tadei, R. (2011). An efficient metaheuristic for multi-dimensional multi-container packing, Proceedings of seventh annual IEEE Conference on Automation Science and Engineering (IEEE CASE 2011), pp. 1-6.
  55. Pisinger, D. (2002). Heuristics for the container loading problem, European Journal of Operational Research 141: 382-392.
  56. Pisinger, D. & Sigurd, M. M. (2007). Using decomposition techniques and constraint programming for solving the two-dimensional bin packing problem, INFORMS Journal on Computing 19: 36-51.
  57. SPEC (2006). SPEC CPU2006 benchmarks. http://www.spec.org/cpu2006/results/. URL: http://www.spec.org/cpu2006/results/
  58. Wang, P. Y. (1983). Two algorithms for constrained two-dimensional cutting stock problems, Operations Research 31: 573-586.
  59. Wäscher, G., Haussner, H. & Schumann, H. (2007). An improved typology of cutting and packing problems, European Journal of Operational Research 183: 1109-1130.