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A Two-Stage Look-Ahead Heuristic for Packing Spheres into a Three-Dimensional Bin of Minimum Length

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Book cover Recent Advances in Computational Optimization

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

Abstract

In this work we propose a two-stage look-ahead heuristic for packing a given set of spheres into a three-dimensional bin of fixed height and depth but variable length. The problem consists to pack all the spheres into the bin of minimum length. This problem is also known under the name of three-dimensional strip packing problem. The computational results conducted on a set of benchmark instances taken from the literature indicates that the proposed method is effective since it improves most of the best known results by finding new upper bounds for the length of the bin.

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References

  1. H. Akeb, M. Hifi, D. Lazure, An improved algorithm for the strip packing problem, in Proceedings of the Federated Conference on Computer Science and Information Systems, FedCSIS (Wroclaw, Poland, 2012), pp. 357–364. ISBN 978-83-60810-51-4

    Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  3. R.S. Farr, Random close packing fractions of lognormal distributions of hard spheres. Powder Technol. 245, 28–34 (2013)

    Article  Google Scholar 

  4. E.O. Gavriliouk, Unequal Sphere Packing Problem in the Context of Stereotactic Radiosurgery (Shaker Verlag, 2007), 96 p

    Google Scholar 

  5. W.Q. Huang, Y. Li, H. Akeb, C.M. Li, Greedy algorithms for packing unequal circles into a rectangular container. J. Oper. Res. Soc. 56, 539–548 (2005)

    Article  MATH  Google Scholar 

  6. 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, 739–753 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. L.K. Lenstra, A.H.G. Rinnooy Kan, Complexity of packing, covering, and partitioning problems, in Packing and Covering in Combinatorics, ed. by A. Schrijver (Mathematisch Centrum, Amsterdam, 1979), pp. 275–291

    Google Scholar 

  8. M. Lin, R. Chen, J.S. Liu, Lookahead strategies for sequential Monte Carlo. Stat. Sci. 28, 69–94 (2013)

    Article  MathSciNet  Google Scholar 

  9. 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)

    Article  MathSciNet  Google Scholar 

  10. K. Lochmann, L. Oger, D. Stoyan, Statistical analysis of random sphere packings with variable radius distribution. Solid State Sci. 8, 1397–1413 (2006)

    Article  MATH  Google Scholar 

  11. R. M’Hallah, A. Alkandari, N. Mladenović, Packing unit spheres into the smallest sphere using VNS and NLP. Comput. Oper. Res. 40, 603–615 (2013)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  13. 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 

  14. 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 

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

    Article  MathSciNet  MATH  Google Scholar 

  16. S. Vance, Improved sphere packing lower bounds from Hurwitz lattices. Adv. Math. 227(5), 2144–2156 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Wang, Packing of unequal spheres and automated radiosurgical treatment planning. J. Comb. Optim. 3, 453–463 (1999)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. ISC Paris Business School, 22 boulevard du Fort de Vaux, 75017, Paris, France

    Hakim Akeb

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  1. Hakim Akeb
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Correspondence to Hakim Akeb .

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

    Stefka Fidanova

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Akeb, H. (2016). A Two-Stage Look-Ahead Heuristic for Packing Spheres into a Three-Dimensional Bin of Minimum Length. 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_8

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  • DOI: https://doi.org/10.1007/978-3-319-21133-6_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21132-9

  • Online ISBN: 978-3-319-21133-6

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