Skip to main content
Top

2016 | OriginalPaper | Chapter

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

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference 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 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
2.
go back to reference E.G. Birgin, F.N.C. Sobral, Minimizing the object dimensions in circle and sphere packing problems. Comput. Oper. Res. 35, 2357–2375 (2008)MathSciNetCrossRefMATH E.G. Birgin, F.N.C. Sobral, Minimizing the object dimensions in circle and sphere packing problems. Comput. Oper. Res. 35, 2357–2375 (2008)MathSciNetCrossRefMATH
3.
go back to reference R.S. Farr, Random close packing fractions of lognormal distributions of hard spheres. Powder Technol. 245, 28–34 (2013)CrossRef R.S. Farr, Random close packing fractions of lognormal distributions of hard spheres. Powder Technol. 245, 28–34 (2013)CrossRef
4.
go back to reference E.O. Gavriliouk, Unequal Sphere Packing Problem in the Context of Stereotactic Radiosurgery (Shaker Verlag, 2007), 96 p E.O. Gavriliouk, Unequal Sphere Packing Problem in the Context of Stereotactic Radiosurgery (Shaker Verlag, 2007), 96 p
5.
go back to reference 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)CrossRefMATH 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)CrossRefMATH
6.
go back to reference 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)MathSciNetCrossRefMATH 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)MathSciNetCrossRefMATH
7.
go back to reference 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 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
9.
go back to reference 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)MathSciNetCrossRef 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)MathSciNetCrossRef
10.
go back to reference K. Lochmann, L. Oger, D. Stoyan, Statistical analysis of random sphere packings with variable radius distribution. Solid State Sci. 8, 1397–1413 (2006)CrossRefMATH K. Lochmann, L. Oger, D. Stoyan, Statistical analysis of random sphere packings with variable radius distribution. Solid State Sci. 8, 1397–1413 (2006)CrossRefMATH
11.
go back to reference 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)MathSciNetCrossRef 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)MathSciNetCrossRef
12.
go back to reference R. M’Hallah, A. Alkandari, Packing unit spheres into a cube using VNS. Electron. Notes Discret. Math. 39, 201–208 (2012)MathSciNetCrossRef R. M’Hallah, A. Alkandari, Packing unit spheres into a cube using VNS. Electron. Notes Discret. Math. 39, 201–208 (2012)MathSciNetCrossRef
14.
go back to reference 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 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
15.
go back to reference A. Sutou, Y. Dai, Global optimization approach to unequal sphere packing problems in 3D. J. Optim. Theory Appl. 114, 671–694 (2002)MathSciNetCrossRefMATH A. Sutou, Y. Dai, Global optimization approach to unequal sphere packing problems in 3D. J. Optim. Theory Appl. 114, 671–694 (2002)MathSciNetCrossRefMATH
17.
Metadata
Title
A Two-Stage Look-Ahead Heuristic for Packing Spheres into a Three-Dimensional Bin of Minimum Length
Author
Hakim Akeb
Copyright Year
2016
DOI
https://doi.org/10.1007/978-3-319-21133-6_8

Premium Partner