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A fast implementation for the 2D/3D box placement problem

Author

Listed:
  • Wenbin Zhu
  • Zhixing Luo
  • Andrew Lim
  • Wee-Chong Oon

Abstract

The box placement problem involves finding a location to place a rectangular box into a container given n rectangular boxes that have already been placed. It commonly arises as a subproblem in many algorithms for cutting stock problems as well as 2D/3D packing problems. We show that the box placement problem is closely related to some well-studied problems in computational geometry, such as the maximum depth problem and Klee’s measure problem. This allows us to leverage on existing techniques for these problems to develop new algorithms for the box placement problem that are not only conceptually simpler but also asymptotically fastest for 2D and faster than existing approaches for 3D. Our implementations rely on augmenting the standard segment tree for 2D or quadtree for 3D, and can be directly incorporated as subroutines into many algorithms for cutting and packing problems. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Wenbin Zhu & Zhixing Luo & Andrew Lim & Wee-Chong Oon, 2016. "A fast implementation for the 2D/3D box placement problem," Computational Optimization and Applications, Springer, vol. 63(2), pages 585-612, March.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:2:p:585-612
    DOI: 10.1007/s10589-015-9780-2
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    References listed on IDEAS

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    1. Zhu, Wenbin & Lim, Andrew, 2012. "A new iterative-doubling Greedy–Lookahead algorithm for the single container loading problem," European Journal of Operational Research, Elsevier, vol. 222(3), pages 408-417.
    2. Michel Gendreau & Manuel Iori & Gilbert Laporte & Silvano Martello, 2006. "A Tabu Search Algorithm for a Routing and Container Loading Problem," Transportation Science, INFORMS, vol. 40(3), pages 342-350, August.
    3. Hopper, E. & Turton, B. C. H., 2001. "An empirical investigation of meta-heuristic and heuristic algorithms for a 2D packing problem," European Journal of Operational Research, Elsevier, vol. 128(1), pages 34-57, January.
    4. Jakobs, Stefan, 1996. "On genetic algorithms for the packing of polygons," European Journal of Operational Research, Elsevier, vol. 88(1), pages 165-181, January.
    5. E. K. Burke & R. S. R. Hellier & G. Kendall & G. Whitwell, 2010. "Irregular Packing Using the Line and Arc No-Fit Polygon," Operations Research, INFORMS, vol. 58(4-part-1), pages 948-970, August.
    6. Wu, Yu-Liang & Huang, Wenqi & Lau, Siu-chung & Wong, C. K. & Young, Gilbert H., 2002. "An effective quasi-human based heuristic for solving the rectangle packing problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 341-358, September.
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    Cited by:

    1. Zhu, Wenbin & Fu, Ying & Zhou, You, 2024. "3D dynamic heterogeneous robotic palletization problem," European Journal of Operational Research, Elsevier, vol. 316(2), pages 584-596.

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