Solving the Two-Dimensional Bin-Packing Problem with Variable Bin Sizes by Greedy Randomized Adaptive Search Procedures and Variable Neighborhood Search

  • Andreas M. Chwatal
  • Sandro Pirkwieser
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6927)


In this work we present new metaheuristic algorithms to a special variant of the two-dimensional bin-packing, or cutting-stock problem, where a given set of rectangular items (demand) must be produced out of heterogeneous stock items (bins). The items can optionally be rotated, guillotine-cuttable and free layouts are considered. The proposed algorithms use various packing-heuristics which are embedded in a greedy randomized adaptive search procedure (GRASP) and variable neighborhood search (VNS) framework. Our results for existing benchmark-instances show the superior performance of our algorithms, in particular the VNS, with respect to previous approaches.


Packing Problem Variable Neighborhood Search Metaheuristic Algorithm Construction Heuristic Variable Neighborhood Descent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dyckhoff, H.: A typology of cutting and packing problems. European Journal of Operational Research 44(2), 145–159 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Wascher, G., Hausner, H., Schumann, H.: An improved typology of cutting and packing problems. European Journal of Operational Research 183, 1109–1130 (2007)CrossRefzbMATHGoogle Scholar
  3. 3.
    Ntene, N.: An Algorithmic Approach to the 2D Oriented Strip Packing Problem. PhD thesis, University of Stellenbosch, South Africa (2007)Google Scholar
  4. 4.
    Garey, M.R., Johnson, D.S.: “Strong” NP-completeness results: Motivation, examples, and implications. Journal of the ACM 25, 499–508 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: A survey. European Journal of Operational Research 141, 241–252 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Lodi, A., Martello, S., Vigo, D.: Recent advances on two-dimensional bin packing problems. Discrete Applied Mathematics 123, 379–396 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Hopper, E., Turton, B.C.H.: An empirical study of meta-heuristics applied to 2d rectangular bin packing - part i. Studia Informatica Universalis 2, 77–92 (2002)Google Scholar
  8. 8.
    Hopper, E., Turton, B.C.H.: An empirical study of meta-heuristics applied to 2d rectangular bin packing - part ii. Studia Informatica Universalis 2, 93–106 (2002)Google Scholar
  9. 9.
    Pisinger, D., Sigurd, M.: The two-dimensional bin packing problem with variable bin sizes and costs. Discrete Optimization 2, 154–167 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Alvarez-valdes, R., Parajon, A., Tamarit, J.M.: A computational study of heuristic algorithms for two-dimensional cutting stock problems. In: MIC 2001 Metaheuristics International Conference (2001)Google Scholar
  11. 11.
    Cintra, G., Miyazawa, F., Wakabayashi, Y., Xavier, E.: Algorithms for two-dimensional cutting stock and strip packing problems using dynamic programming and column generation. European Journal of Operational Research 191, 61–85 (2008)CrossRefzbMATHGoogle Scholar
  12. 12.
    Chazelle, B.: The bottom-left bin-packing heuristic: An efficient implementation. IEEE Transactions on Computers 32, 697–707 (1983)CrossRefzbMATHGoogle Scholar
  13. 13.
    Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6, 109–133 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Mladenović, N., Hansen, P.: Variable neighborhood search. Computers & Operations Research 24, 1097–1100 (1997)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andreas M. Chwatal
    • 1
  • Sandro Pirkwieser
    • 1
    • 2
  1. 1.Destion – IT Consulting OGViennaAustria
  2. 2.Institute of Computer Graphics and AlgorithmsVienna University of TechnologyViennaAustria

Personalised recommendations