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Method of sentinels for packing items within arbitrary convex regions

Author

Listed:
  • E G Birgin

    (University of São Paulo)

  • J M Martínez

    (University of Campinas, Campinas)

  • W F Mascarenhas

    (University of São Paulo)

  • D P Ronconi

    (University of São Paulo)

Abstract

A new method is introduced for packing items in convex regions of the Euclidian n-dimensional space. By means of this approach the packing problem becomes a global finite-dimensional continuous optimization problem. The strategy is based on the new concept of sentinels. Sentinels sets are finite subsets of the items to be packed such that, when two items are superposed, at least one sentinel of one item is in the interior of the other. Minimal sets of sentinels are found in simple two-dimensional cases. Numerical experiments and pictures showing the potentiality of the new technique are presented.

Suggested Citation

  • E G Birgin & J M Martínez & W F Mascarenhas & D P Ronconi, 2006. "Method of sentinels for packing items within arbitrary convex regions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 735-746, June.
    • Handle: RePEc:pal:jorsoc:v:57:y:2006:i:6:d:10.1057_palgrave.jors.2602067
    DOI: 10.1057/palgrave.jors.2602067
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    References listed on IDEAS

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    Cited by:

    1. Carlos A. Vega-Mejía & Jairo R. Montoya-Torres & Sardar M. N. Islam, 2019. "Consideration of triple bottom line objectives for sustainability in the optimization of vehicle routing and loading operations: a systematic literature review," Annals of Operations Research, Springer, vol. 273(1), pages 311-375, February.
    2. Bouzid, Mouaouia Cherif & Salhi, Said, 2020. "Packing rectangles into a fixed size circular container: Constructive and metaheuristic search approaches," European Journal of Operational Research, Elsevier, vol. 285(3), pages 865-883.
    3. Tiago Montanher & Arnold Neumaier & Mihály Csaba Markót & Ferenc Domes & Hermann Schichl, 2019. "Rigorous packing of unit squares into a circle," Journal of Global Optimization, Springer, vol. 73(3), pages 547-565, March.

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