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A reduction approach for solving the rectangle packing area minimization problem

  • Bortfeldt, Andreas
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    In the rectangle packing area minimization problem (RPAMP) we are given a set of rectangles with known dimensions. We have to determine an arrangement of all rectangles, without overlapping, inside an enveloping rectangle of minimum area. The paper presents a generic approach for solving the RPAMP that is based on two algorithms, one for the 2D Knapsack Problem (KP), and the other for the 2D Strip Packing Problem (SPP). In this way, solving an instance of the RPAMP is reduced to solving multiple SPP and KP instances. A fast constructive heuristic is used as SPP algorithm while the KP algorithm is instantiated by a tree search method and a genetic algorithm alternatively. All these SPP and KP methods have been published previously. Finally, the best variants of the resulting RPAMP heuristics are combined within one procedure. The guillotine cutting condition is always observed as an additional constraint. The approach was tested on 15 well-known RPAMP instances (above all MCNC and GSRC instances) and new best solutions were obtained for 10 instances. The computational effort remains acceptable. Moreover, 24 new benchmark instances are introduced and promising results are reported.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712006066
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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 224 (2013)
    Issue (Month): 3 ()
    Pages: 486-496

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    Handle: RePEc:eee:ejores:v:224:y:2013:i:3:p:486-496
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Wu, Yu-Liang & Huang, Wenqi & Lau, Siu-chung & Wong, C. K. & Young, Gilbert H., 2002. "An effective quasi-human based heuristic for solving the rectangle packing problem," European Journal of Operational Research, Elsevier, vol. 141(2), pages 341-358, September.
    2. Beasley, J. E., 2004. "A population heuristic for constrained two-dimensional non-guillotine cutting," European Journal of Operational Research, Elsevier, vol. 156(3), pages 601-627, August.
    3. Hadjiconstantinou, Eleni & Iori, Manuel, 2007. "A hybrid genetic algorithm for the two-dimensional single large object placement problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1150-1166, December.
    4. Leung, Stephen C.H. & Zhang, Defu & Sim, Kwang Mong, 2011. "A two-stage intelligent search algorithm for the two-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 215(1), pages 57-69, November.
    5. Imahori, S. & Yagiura, M. & Ibaraki, T., 2005. "Improved local search algorithms for the rectangle packing problem with general spatial costs," European Journal of Operational Research, Elsevier, vol. 167(1), pages 48-67, November.
    6. Bortfeldt, Andreas & Mack, Daniel, 2007. "A heuristic for the three-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1267-1279, December.
    7. Bortfeldt, Andreas & Gehring, Hermann, 2001. "A hybrid genetic algorithm for the container loading problem," European Journal of Operational Research, Elsevier, vol. 131(1), pages 143-161, May.
    8. Baldacci, Roberto & Boschetti, Marco A., 2007. "A cutting-plane approach for the two-dimensional orthogonal non-guillotine cutting problem," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1136-1149, December.
    9. Wascher, Gerhard & Hau[ss]ner, Heike & Schumann, Holger, 2007. "An improved typology of cutting and packing problems," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1109-1130, December.
    10. Allen, S.D. & Burke, E.K. & Kendall, G., 2011. "A hybrid placement strategy for the three-dimensional strip packing problem," European Journal of Operational Research, Elsevier, vol. 209(3), pages 219-227, March.
    11. Wang, Pearl Y. & Valenzela, Christine L., 2001. "Data set generation for rectangular placement problems," European Journal of Operational Research, Elsevier, vol. 134(2), pages 378-391, October.
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