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Space defragmentation for packing problems

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  • Zhu, Wenbin
  • Zhang, Zhaoyi
  • Oon, Wee-Chong
  • Lim, Andrew

Abstract

One of main difficulties of multi-dimensional packing problems is the fragmentation of free space into several unusable small parts after a few items are packed. This study proposes a defragmentation technique to combine the fragmented space into a continuous usable space, which potentially allows the packing of additional items. We illustrate the effectiveness of this technique using the two- and three-dimensional bin packing problem, where the aim is to load all given items (represented by rectangular boxes) into the minimum number of identical bins. Experimental results based on well-known 2D and 3D bin packing data sets show that our defragmentation technique alone is able to produce solutions approaching the quality of considerably more complex meta-heuristic approaches for the problem. In conjunction with a bin shuffling strategy for incremental improvement, our resultant algorithm outperforms all leading meta-heuristic approaches based on the commonly used benchmark data by a significant margin.

Suggested Citation

  • Zhu, Wenbin & Zhang, Zhaoyi & Oon, Wee-Chong & Lim, Andrew, 2012. "Space defragmentation for packing problems," European Journal of Operational Research, Elsevier, vol. 222(3), pages 452-463.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:3:p:452-463
    DOI: 10.1016/j.ejor.2012.05.031
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    1. Sándor P. Fekete & Jörg Schepers, 2004. "A Combinatorial Characterization of Higher-Dimensional Orthogonal Packing," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 353-368, May.
    2. Tobias Fanslau & Andreas Bortfeldt, 2010. "A Tree Search Algorithm for Solving the Container Loading Problem," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 222-235, May.
    3. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    4. Lodi, Andrea & Martello, Silvano & Vigo, Daniele, 2002. "Heuristic algorithms for the three-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 410-420, September.
    5. Michele Monaci & Paolo Toth, 2006. "A Set-Covering-Based Heuristic Approach for Bin-Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 71-85, February.
    6. Andrea Lodi & Silvano Martello & Daniele Vigo, 1999. "Heuristic and Metaheuristic Approaches for a Class of Two-Dimensional Bin Packing Problems," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 345-357, November.
    7. Dyckhoff, Harald, 1990. "A typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 44(2), pages 145-159, January.
    8. Che, Chan Hou & Huang, Weili & Lim, Andrew & Zhu, Wenbin, 2011. "The multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 214(3), pages 501-511, November.
    9. F. Parreño & R. Alvarez-Valdes & J. M. Tamarit & J. F. Oliveira, 2008. "A Maximal-Space Algorithm for the Container Loading Problem," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 412-422, August.
    10. Crainic, Teodor Gabriel & Perboli, Guido & Tadei, Roberto, 2009. "TS2PACK: A two-level tabu search for the three-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 195(3), pages 744-760, June.
    11. F. Parreño & R. Alvarez-Valdes & J. Oliveira & J. Tamarit, 2010. "A hybrid GRASP/VND algorithm for two- and three-dimensional bin packing," Annals of Operations Research, Springer, vol. 179(1), pages 203-220, September.
    12. Teodor Gabriel Crainic & Guido Perboli & Roberto Tadei, 2008. "Extreme Point-Based Heuristics for Three-Dimensional Bin Packing," INFORMS Journal on Computing, INFORMS, vol. 20(3), pages 368-384, August.
    13. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    14. Oluf Faroe & David Pisinger & Martin Zachariasen, 2003. "Guided Local Search for the Three-Dimensional Bin-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 267-283, August.
    15. Silvano Martello & Daniele Vigo, 1998. "Exact Solution of the Two-Dimensional Finite Bin Packing Problem," Management Science, INFORMS, vol. 44(3), pages 388-399, March.
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    Cited by:

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    3. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.
    4. Adamos Daios & Nikolaos Kladovasilakis & Ioannis Kostavelis, 2024. "Mixed Palletizing for Smart Warehouse Environments: Sustainability Review of Existing Methods," Sustainability, MDPI, vol. 16(3), pages 1-15, February.
    5. Gzara, Fatma & Elhedhli, Samir & Yildiz, Burak C., 2020. "The Pallet Loading Problem: Three-dimensional bin packing with practical constraints," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1062-1074.

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