IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v63y2016i2p585-612.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9780-2
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9780-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Felix Prause & Kai Hoppmann-Baum & Boris Defourny & Thorsten Koch, 2021. "The maximum diversity assortment selection problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 521-554, June.
    2. 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, Elsevier, vol. 183(3), pages 1167-1182, December.
    3. Igor Kierkosz & Maciej Luczak, 2014. "A hybrid evolutionary algorithm for the two-dimensional packing problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 22(4), pages 729-753, December.
    4. Beasley, J. E., 2004. "A population heuristic for constrained two-dimensional non-guillotine cutting," European Journal of Operational Research, Elsevier, vol. 156(3), pages 601-627, August.
    5. José Fernando Gonçalves & Mauricio G. C. Resende, 2011. "A parallel multi-population genetic algorithm for a constrained two-dimensional orthogonal packing problem," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 180-201, August.
    6. Wei, Lijun & Oon, Wee-Chong & Zhu, Wenbin & Lim, Andrew, 2011. "A skyline heuristic for the 2D rectangular packing and strip packing problems," European Journal of Operational Research, Elsevier, vol. 215(2), pages 337-346, December.
    7. Imahori, S. & Yagiura, M. & Ibaraki, T., 2005. "Improved local search algorithms for the rectangle packing problem with general spatial costs," European Journal of Operational Research, Elsevier, vol. 167(1), pages 48-67, November.
    8. Henriette Koch & Andreas Bortfeldt & Gerhard Wäscher, 2017. "A hybrid solution approach for the 3L-VRP with simultaneous delivery and pickups," FEMM Working Papers 170005, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    9. Wei, Lijun & Tian, Tian & Zhu, Wenbin & Lim, Andrew, 2014. "A block-based layer building approach for the 2D guillotine strip packing problem," European Journal of Operational Research, Elsevier, vol. 239(1), pages 58-69.
    10. Binkley, Kevin J. & Hagiwara, Masafumi, 2007. "Applying self-adaptive evolutionary algorithms to two-dimensional packing problems using a four corners' heuristic," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1230-1248, December.
    11. Edmund K. Burke & Graham Kendall & Glenn Whitwell, 2009. "A Simulated Annealing Enhancement of the Best-Fit Heuristic for the Orthogonal Stock-Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 505-516, August.
    12. Leung, Stephen C.H. & Zhang, Defu & Sim, Kwang Mong, 2011. "A two-stage intelligent search algorithm for the two-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 57-69, November.
    13. Önder Aşık & Ender Özcan, 2009. "Bidirectional best-fit heuristic for orthogonal rectangular strip packing," Annals of Operations Research, Springer, vol. 172(1), pages 405-427, November.
    14. Hadjiconstantinou, Eleni & Iori, Manuel, 2007. "A hybrid genetic algorithm for the two-dimensional single large object placement problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1150-1166, December.
    15. Chehrazad, Sahar & Roose, Dirk & Wauters, Tony, 2022. "A fast and scalable bottom-left-fill algorithm to solve nesting problems using a semi-discrete representation," European Journal of Operational Research, Elsevier, vol. 300(3), pages 809-826.
    16. R Alvarez-Valdes & F Parreño & J M Tamarit, 2005. "A GRASP algorithm for constrained two-dimensional non-guillotine cutting problems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(4), pages 414-425, April.
    17. Defu Zhang & Lijun Wei & Stephen C. H. Leung & Qingshan Chen, 2013. "A Binary Search Heuristic Algorithm Based on Randomized Local Search for the Rectangular Strip-Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 25(2), pages 332-345, May.
    18. Kenmochi, Mitsutoshi & Imamichi, Takashi & Nonobe, Koji & Yagiura, Mutsunori & Nagamochi, Hiroshi, 2009. "Exact algorithms for the two-dimensional strip packing problem with and without rotations," European Journal of Operational Research, Elsevier, vol. 198(1), pages 73-83, October.
    19. Marco Antonio Boschetti & Lorenza Montaletti, 2010. "An Exact Algorithm for the Two-Dimensional Strip-Packing Problem," Operations Research, INFORMS, vol. 58(6), pages 1774-1791, December.
    20. Iori, Manuel & de Lima, Vinícius L. & Martello, Silvano & Miyazawa, Flávio K. & Monaci, Michele, 2021. "Exact solution techniques for two-dimensional cutting and packing," European Journal of Operational Research, Elsevier, vol. 289(2), pages 399-415.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:63:y:2016:i:2:p:585-612. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.