New Fast Heuristics for the 2D Strip Packing Problem with Guillotine Constraint

  • Minh Hoang Ha
  • François Clautiaux
  • Saïd Hanafi
  • Christophe Wilbaut
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6049)

Abstract

In this paper, we propose new and fast level-packing algorithms to solve the two-dimensional strip rectangular packing problem with guillotine constraints. Our methods are based on constructive and destructive strategies. The computational results on many different instances show that our method leads to the best results in many cases among fast heuristics.

Keywords

strip packing fast heuristic level algorithms construction and destruction 

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References

  1. 1.
    Beasley, J.E.: Algorithms for unconstrained two-dimensional guillotine cutting. Journal of the Operational Research Society 36, 297–306 (1985)MATHGoogle Scholar
  2. 2.
    Beasley, J.E.: An exact two-dimensional non-guillotine cutting tree search procedure. Operations Research 33, 49–64 (1985)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bengtsson, B.E.: Packing rectangular pieces - a heuristic approach. The computer journal 25, 353–357 (1982)MathSciNetGoogle Scholar
  4. 4.
    Bortfeldt, A.: A genetic algorithm for the two dimensional strip packing problem. European Journal of Operational Research 172, 814–837 (2006)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Burke, E.K., Kendall, G., Whitwell, G.: A new placement heuristic for the orthogonal stock-cutting problem. Operations Research 52(4), 655–671 (2004)MATHCrossRefGoogle Scholar
  6. 6.
    Christofides, N., Whitlock, C.: An algorithm for two-dimensional cutting problems. Operations Research 25, 30–44 (1977)MATHCrossRefGoogle Scholar
  7. 7.
    Clautiaux, F., Jouglet, A., El Hayek, J.: A new lower bound for the non-oriented two-dimensional bin-packing problem. Operations Research Letters 35(3), 365–373 (2007)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Clautiaux, F., Jouglet, A., Moukrim, A.: A new graph-theoretical model for k-dimensional guillotine-cutting problems. In: McGeoch, C.C. (ed.) WEA 2008. LNCS, vol. 5038, pp. 43–54. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Coffman, E., Garey, M.R., Johnson, D.S., Tarjan, R.E.: Performance bounds for level-oriented two-dimensional packing algorithms. SIAM Journal on Computing 9(4), 808–826 (1980)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Hopper, E., Turton, B.C.H.: An empirical investigation on metaheuristic and heuristic algorithms for a 2D packing problem. European Journal of Operational Research 128, 34–57 (2001)MATHCrossRefGoogle Scholar
  11. 11.
    Hopper, E., Turton, B.C.H.: Problem generators for rectangular packing problems. Studia Informatica Universalis 2(1), 123–136 (2002)Google Scholar
  12. 12.
    Iori, M., Martello, S., Monaci, M.: Metaheuristic algorithms for the strip packing problem. In: Applied Optimization, ch. 7, vol. 78. Springer, Heidelberg (2003)Google Scholar
  13. 13.
    Kenmochi, M., Imamichi, T., Nonobe, K., Yagiura, M., Nagamochi, H.: Exact algorithms for the two-dimensional strip packing problem with and without rotations. European Journal of Operational Research 198(1), 73–83 (2009)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Lodi, A., Martello, S., Vigo, D.: Heuristic and metaheuristic approaches for a class of two dimensional bin packing problem. INFORMS Journal on Computing 11(4), 345–357 (1999)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Lodi, A., Martello, S., Vigo, D.: Neighborhood search algorithm for the guillotine non-oriented two-dimensional bin packing problem. In: MIC 1997: 2nd meta-heuristics international conference, pp. 125–139 (1999)Google Scholar
  16. 16.
    Mumford-Valenzuela, C., Vick, J., Wang, P.Y.: Heuristics for large strip packing problems with guillotine patterns: an empirical study, pp. 501–522 (2004)Google Scholar
  17. 17.
    Ntene, N., van Vuuren, J.H.: A survey and comparison of guillotine heuristics for the 2d oriented offline strip packing problem. Discrete Optimization 6(2), 174–188 (2009)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Ruiz, R., Stutzle, T.: A simple and effective iterated greedy algorithm for the permutation flowshop scheduling problem. European Journal of Operational Research 177(3), 2033–2049 (2007)MATHCrossRefGoogle Scholar
  19. 19.
    Schrimpf, G., Schneider, J., Stamm-Wilbrandt, H., Dueck, G.: Record breaking optimization results using the ruin and recreate principle. Journal of Computational Physics 159, 139–171 (2000)MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Waescher, G., Haussner, H., Schumann, H.: An improved typology for C&P problems. presentation, and final discussion. In: 2nd ESICUP Meeting, Southampton, UK (April 2005)Google Scholar
  21. 21.
    Zhang, D., Kang, Y., Deng, A.: A new heuristic recursive algorithm for the strip rectangular packing problem. Computers and Operations Research 33(8), 2209–2217 (2006)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Minh Hoang Ha
    • 1
    • 2
  • François Clautiaux
    • 3
  • Saïd Hanafi
    • 4
  • Christophe Wilbaut
    • 4
  1. 1.Ecole des Mines de Nantes, IRCCyN UMR CNRS 6597 
  2. 2.Ecole Polytechnique de Montréal, CIRRELT 
  3. 3.Université des Sciences et Technologies de Lille, LIFL UMR CNRS 8022 
  4. 4.Université de Valenciennes et du Hainaut-Cambrésis, LAMIH FRE CNRS 3304 

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