IDEAS home Printed from https://ideas.repec.org/a/eee/proeco/v145y2013i2p500-510.html
   My bibliography  Save this article

A biased random key genetic algorithm for 2D and 3D bin packing problems

Author

Listed:
  • Gonçalves, José Fernando
  • Resende, Mauricio G.C.

Abstract

In this paper we present a novel biased random-key genetic algorithm (BRKGA) for 2D and 3D bin packing problems. The approach uses a maximal-space representation to manage the free spaces in the bins. The proposed algorithm hybridizes a novel placement procedure with a genetic algorithm based on random keys. The BRKGA is used to evolve the order in which the boxes are packed into the bins and the parameters used by the placement procedure. Two new placement heuristics are used to determine the bin and the free maximal space where each box is placed. A novel fitness function that improves significantly the solution quality is also developed. The new approach is extensively tested on 858 problem instances and compared with other approaches published in the literature. The computational experiment results demonstrate that the new approach consistently equals or outperforms the other approaches and the statistical analysis confirms that the approach is significantly better than all the other approaches.

Suggested Citation

  • Gonçalves, José Fernando & Resende, Mauricio G.C., 2013. "A biased random key genetic algorithm for 2D and 3D bin packing problems," International Journal of Production Economics, Elsevier, vol. 145(2), pages 500-510.
    • Handle: RePEc:eee:proeco:v:145:y:2013:i:2:p:500-510
    DOI: 10.1016/j.ijpe.2013.04.019
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0925527313001837
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ijpe.2013.04.019?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. Nicos Christofides & Charles Whitlock, 1977. "An Algorithm for Two-Dimensional Cutting Problems," Operations Research, INFORMS, vol. 25(1), pages 30-44, February.
    2. 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.
    3. Lodi, Andrea & Martello, Silvano & Vigo, Daniele, 1999. "Approximation algorithms for the oriented two-dimensional bin packing problem," European Journal of Operational Research, Elsevier, vol. 112(1), pages 158-166, January.
    4. J. E. Beasley, 1985. "An Exact Two-Dimensional Non-Guillotine Cutting Tree Search Procedure," Operations Research, INFORMS, vol. 33(1), pages 49-64, February.
    5. 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.
    6. Silvano Martello & David Pisinger & Daniele Vigo, 2000. "The Three-Dimensional Bin Packing Problem," Operations Research, INFORMS, vol. 48(2), pages 256-267, April.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Andrea Lodi & Silvano Martello & Daniele Vigo, 2004. "TSpack: A Unified Tabu Search Code for Multi-Dimensional Bin Packing Problems," Annals of Operations Research, Springer, vol. 131(1), pages 203-213, October.
    12. Liu, Dequan & Teng, Hongfei, 1999. "An improved BL-algorithm for genetic algorithm of the orthogonal packing of rectangles," European Journal of Operational Research, Elsevier, vol. 112(2), pages 413-420, January.
    13. 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.
    14. Goncalves, Jose Fernando & de Magalhaes Mendes, Jorge Jose & Resende, Mauricio G. C., 2005. "A hybrid genetic algorithm for the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 167(1), pages 77-95, November.
    15. Daniel Mack & Andreas Bortfeldt, 2012. "A heuristic for solving large bin packing problems in two and three dimensions," 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. 20(2), pages 337-354, June.
    16. 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.
    17. James C. Bean, 1994. "Genetic Algorithms and Random Keys for Sequencing and Optimization," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 154-160, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Bernardo F. Almeida & Isabel Correia & Francisco Saldanha-da-Gama, 2018. "A biased random-key genetic algorithm for the project scheduling problem with flexible resources," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 283-308, July.
    3. Bayliss, Christopher & Currie, Christine S.M. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2021. "Queue-constrained packing: A vehicle ferry case study," European Journal of Operational Research, Elsevier, vol. 289(2), pages 727-741.
    4. Li, Xueping & Zhang, Kaike, 2018. "Single batch processing machine scheduling with two-dimensional bin packing constraints," International Journal of Production Economics, Elsevier, vol. 196(C), pages 113-121.
    5. Kurpel, Deidson Vitorio & Scarpin, Cassius Tadeu & Pécora Junior, José Eduardo & Schenekemberg, Cleder Marcos & Coelho, Leandro C., 2020. "The exact solutions of several types of container loading problems," European Journal of Operational Research, Elsevier, vol. 284(1), pages 87-107.
    6. Jonatas B. C. Chagas & Julian Blank & Markus Wagner & Marcone J. F. Souza & Kalyanmoy Deb, 2021. "A non-dominated sorting based customized random-key genetic algorithm for the bi-objective traveling thief problem," Journal of Heuristics, Springer, vol. 27(3), pages 267-301, June.
    7. Gonçalves, José Fernando & Resende, Mauricio G.C., 2015. "A biased random-key genetic algorithm for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 246(1), pages 86-107.
    8. Bayliss, Christopher & Currie, Christine S.M. & Bennell, Julia A. & Martinez-Sykora, Antonio, 2019. "Dynamic pricing for vehicle ferries: Using packing and simulation to optimize revenues," European Journal of Operational Research, Elsevier, vol. 273(1), pages 288-304.
    9. R. M. A. Silva & M. G. C. Resende & P. M. Pardalos, 2015. "A Python/C++ library for bound-constrained global optimization using a biased random-key genetic algorithm," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 710-728, October.
    10. Gonçalves, José Fernando & Wäscher, Gerhard, 2020. "A MIP model and a biased random-key genetic algorithm based approach for a two-dimensional cutting problem with defects," European Journal of Operational Research, Elsevier, vol. 286(3), pages 867-882.
    11. Galrão Ramos, A. & Oliveira, José F. & Gonçalves, José F. & Lopes, Manuel P., 2016. "A container loading algorithm with static mechanical equilibrium stability constraints," Transportation Research Part B: Methodological, Elsevier, vol. 91(C), pages 565-581.
    12. Nestor M Cid-Garcia & Yasmin A Rios-Solis, 2020. "Positions and covering: A two-stage methodology to obtain optimal solutions for the 2d-bin packing problem," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-22, April.

    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. 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.
    2. Nestor M Cid-Garcia & Yasmin A Rios-Solis, 2020. "Positions and covering: A two-stage methodology to obtain optimal solutions for the 2d-bin packing problem," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-22, April.
    3. 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.
    4. 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.
    5. Bortfeldt, Andreas & Wäscher, Gerhard, 2013. "Constraints in container loading – A state-of-the-art review," European Journal of Operational Research, Elsevier, vol. 229(1), pages 1-20.
    6. 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.
    7. Jean-François Côté & Mohamed Haouari & Manuel Iori, 2021. "Combinatorial Benders Decomposition for the Two-Dimensional Bin Packing Problem," INFORMS Journal on Computing, INFORMS, vol. 33(3), pages 963-978, July.
    8. Daniel Mack & Andreas Bortfeldt, 2012. "A heuristic for solving large bin packing problems in two and three dimensions," 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. 20(2), pages 337-354, June.
    9. Schmid, Verena & Doerner, Karl F. & Laporte, Gilbert, 2013. "Rich routing problems arising in supply chain management," European Journal of Operational Research, Elsevier, vol. 224(3), pages 435-448.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Wei, Lijun & Zhu, Wenbin & Lim, Andrew, 2015. "A goal-driven prototype column generation strategy for the multiple container loading cost minimization problem," European Journal of Operational Research, Elsevier, vol. 241(1), pages 39-49.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. Nikolaus Furian & Siegfried Vössner, 2014. "A hybrid algorithm for constrained order packing," 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(1), pages 157-186, March.
    20. 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.

    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:eee:proeco:v:145:y:2013:i:2:p:500-510. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ijpe .

    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.