Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Dyckhoff, H.: A typology of cutting and packing problems. European Journal of Operational Research 44(2), 145–159 (1990)
Wascher, G., Hausner, H., Schumann, H.: An improved typology of cutting and packing problems. European Journal of Operational Research 183, 1109–1130 (2007)
Ntene, N.: An Algorithmic Approach to the 2D Oriented Strip Packing Problem. PhD thesis, University of Stellenbosch, South Africa (2007)
Garey, M.R., Johnson, D.S.: “Strong” NP-completeness results: Motivation, examples, and implications. Journal of the ACM 25, 499–508 (1978)
Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: A survey. European Journal of Operational Research 141, 241–252 (2002)
Lodi, A., Martello, S., Vigo, D.: Recent advances on two-dimensional bin packing problems. Discrete Applied Mathematics 123, 379–396 (2002)
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)
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)
Pisinger, D., Sigurd, M.: The two-dimensional bin packing problem with variable bin sizes and costs. Discrete Optimization 2, 154–167 (2005)
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)
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)
Chazelle, B.: The bottom-left bin-packing heuristic: An efficient implementation. IEEE Transactions on Computers 32, 697–707 (1983)
Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6, 109–133 (1999)
Mladenović, N., Hansen, P.: Variable neighborhood search. Computers & Operations Research 24, 1097–1100 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chwatal, A.M., Pirkwieser, S. (2012). Solving the Two-Dimensional Bin-Packing Problem with Variable Bin Sizes by Greedy Randomized Adaptive Search Procedures and Variable Neighborhood Search. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2011. EUROCAST 2011. Lecture Notes in Computer Science, vol 6927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27549-4_58
Download citation
DOI: https://doi.org/10.1007/978-3-642-27549-4_58
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-27548-7
Online ISBN: 978-3-642-27549-4
eBook Packages: Computer ScienceComputer Science (R0)