Skip to main content
SpringerLink
Log in

Handling Lower Bound and Hill-Climbing Strategies for Sphere Packing Problems

  • Chapter
  • First Online:
Recent Advances in Computational Optimization

Part of the book series: Studies in Computational Intelligence ((SCI,volume 610))

Abstract

In this paper the 3-dimensional sphere packing problem is solved by using an iterative tree search-based heuristic. The goal of the problem is to determine a minimum length of the container that contains all available spheres/items without overlapping. Such a length is searched by applying a tree search that combines hill-climbing and bounding strategies. All branches of the tree are created following eligible positions associated to successive items to pack and the bounds are computed by applying a greedy procedure. Because the number of positions is large, the hill-climbing strategy is introduced in order to filter the search by choosing some best paths. The proposed algorithm is evaluated on benchmark instances taken from the literature and on new benchmark instances: the provided results are compared to those reached by recent methods available in the literature. The proposed method remains competitive and it yields new results.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. H. Akeb, A look-forward heuristic for packing spheres into a three-dimensional bin, in Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, ed. by M. Ganzha, L. Maciaszek, M. Paprzycki, ACSIS, vol. 2, pp. 397–404 (2014). doi:10.15439/2014F145

  2. E.G. Birgin, F.N.C. Sobral, Minimizing the object dimensions in circle and sphere packing problems. Comput. Oper. Res. 35, 2357–2375 (2008). doi:10.1016/j.cor.2006.11.002

    Article  MathSciNet  MATH  Google Scholar 

  3. R.S. Farr, Random close packing fractions of log-normal distributions of hard spheres. Powder Technol. 245, 28–34 (2013). doi:10.1016/j.powtec.2013.04.009

    Article  Google Scholar 

  4. M. Hifi, R. M’Hallah, A literature review on circle and sphere packing problems: models and methodologies. Adv. Oper. Res., Article ID 150624, 22 p. (2009). doi:10.1155/2009/150624

    Google Scholar 

  5. M. Hifi, R. M’Hallah, Beam search and non-linear programming tools for the circular packing problem. Int. J. Math. Oper. Res. 1, 476–503 (2009). doi:10.1504/IJMOR.2009.026278

    Article  MATH  Google Scholar 

  6. M. Hifi, T. Saadi, A cooperative algorithm for constrained two-staged two-dimensional cutting problems. Int. J. Math. Oper. Res. 9, 104–124 (2010). doi:10.1504/IJOR.2010.034363

    Article  MATH  Google Scholar 

  7. M. Hifi, L. Yousef, A dichotomous search-based heuristic for the three-dimensional sphere packing problem. Cogent Eng. (Taylor and Francis Group). (To appear)

    Google Scholar 

  8. M. Hifi, L. Yousef, Width beam and hill-climbing strategies for the three-dimensional sphere packing problem, in Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, ed. by M. Ganzha, L. Maciaszek, M. Paprzycki, ACSIS, vol. 2, pp. 397–404 (2014). doi:10.15439/2014F284

  9. T. Kubach, A. Bortfeldt, T. Tilli, H. Gehring, Parallel greedy algorithms for packing unequal spheres into a cuboidal strip or a cuboid. Working Paper, Department of Management Science, University of Magdeburg, (Diskussionsbeitrag der Fakultät für Wirtschaftswissenschaft der FernUniversität in Hagen). No 440, Hagen (2009)

    Google Scholar 

  10. T. Kubach, A. Bortfeldt, T. Tilli, H. Gehring, Greedy algorithms for packing unequal sphere into a cuboidal strip or a cuboid. Asia-Pac. J. Oper. Res. 28(06), 739–753 (2011). doi:10.1142/S0217595911003326

    Article  MathSciNet  MATH  Google Scholar 

  11. Y. Li, W. Ji, Stability and convergence analysis of a dynamics-based collective method for random sphere packing. J. Comput. Phys. 250, 373–387 (2013). doi:10.1016/j.jcp.2013.05.023

    Article  MathSciNet  Google Scholar 

  12. K. Lochmann, L. Oger, D. Stoyan, Statistical analysis of random sphere packings with variable radius distribution. Solid State Sci. 8(12), 1397–1413 (2006). doi:10.1016/j.solidstatesciences.2006.07.01

    Article  MATH  Google Scholar 

  13. R. M’Hallah, A. Alkandari, N. Mladenović, Packing unit spheres into the smallest sphere using VNS and NLP. Comput. Oper. Res. 40(2), 603–615 (2013). doi:10.1016/j.cor.2012.08.019

    Article  MathSciNet  Google Scholar 

  14. R. M’Hallah, A. Alkandari, Packing unit spheres into a cube using VNS. Electron. Notes Discret. Math. 39(1), 201–208 (2012)

    Article  MathSciNet  Google Scholar 

  15. K. Soontrapa, Y. Chen, Mono-sized sphere packing algorithm development using optimized Monte Carlo technique. Adv. Powder Technol. 24(6), 955–961 (2013). doi:10.1016/j.apt.2013.01.007

    Article  Google Scholar 

  16. Y. Stoyan, G. Yaskow, G. Scheithauer, Packing of various radii solid spheres into a parallelepiped. Cent. Eur. J. Oper. Res. 11, 389–407 (2003)

    MATH  Google Scholar 

  17. A. Sutou, Y. Dai, Global optimization approach to unequal sphere packing problems in 3D. J. Optim. Theory Appl. 114, 671–694 (2002). doi:10.1023/A:1016083231326

    Article  MathSciNet  MATH  Google Scholar 

  18. G. Wascher, H. Haussner, H. Schumann, An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183, 1109–1130 (2007). doi:10.1016/j.ejor.2005.12.047

    Article  Google Scholar 

  19. M. Yavuza, Iterated beam search for the combined car sequencing and level scheduling problem. Int. J. Prod. Res. 51, 3698–3718 (2013). doi:10.1080/00207543.2013.765068

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. EPROAD - EA 4669, Université de Picardie Jules Verne, 7 rue du Moulin Neuf, 80000, Amiens, France

    Mhand Hifi & Labib Yousef

Authors
  1. Mhand Hifi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Labib Yousef
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mhand Hifi .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technology, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Stefka Fidanova

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Hifi, M., Yousef, L. (2016). Handling Lower Bound and Hill-Climbing Strategies for Sphere Packing Problems. In: Fidanova, S. (eds) Recent Advances in Computational Optimization. Studies in Computational Intelligence, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-21133-6_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21133-6_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21132-9

  • Online ISBN: 978-3-319-21133-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation