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A novel non-linear approach to minimal area rectangular packing

Author

Listed:
  • Volker Maag
  • Martin Berger
  • Anton Winterfeld
  • Karl-Heinz Küfer

Abstract

This paper discusses the minimal area rectangular packing problem which is to pack a given set of rectangles into a rectangular container of minimal area such that no two rectangles overlap. Current approaches for this problem rely on metaheuristics like simulated annealing, on constraint programming or on non-linear models. Difficulties arise from the non-convexity and the combinatorial complexity. We investigate different mathematical programming approaches for this and introduce a novel approach based on non-linear optimization and the “tunneling effect” achieved by a relaxation of the non-overlapping constraints. We compare our optimization algorithm to a simulated annealing and a constraint programming approach and show that our approach is competitive. Additionally, since it is easy to extend, it is also applicable to a variety of related problems. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Volker Maag & Martin Berger & Anton Winterfeld & Karl-Heinz Küfer, 2010. "A novel non-linear approach to minimal area rectangular packing," Annals of Operations Research, Springer, vol. 179(1), pages 243-260, September.
    • Handle: RePEc:spr:annopr:v:179:y:2010:i:1:p:243-260:10.1007/s10479-008-0462-7
    DOI: 10.1007/s10479-008-0462-7
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    References listed on IDEAS

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    1. David Pisinger, 2007. "Denser Packings Obtained in O ( n log log n ) Time," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 395-405, August.
    2. Kolonko, M., 1999. "Some new results on simulated annealing applied to the job shop scheduling problem," European Journal of Operational Research, Elsevier, vol. 113(1), pages 123-136, February.
    3. Jianzhong Zhang & Nae-Heon Kim & L. Lasdon, 1985. "An Improved Successive Linear Programming Algorithm," Management Science, INFORMS, vol. 31(10), pages 1312-1331, October.
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    Cited by:

    1. Bortfeldt, Andreas, 2013. "A reduction approach for solving the rectangle packing area minimization problem," European Journal of Operational Research, Elsevier, vol. 224(3), pages 486-496.

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