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Deterministic and stochastic global optimization techniques for planar covering with ellipses problems

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  • Andretta, M.
  • Birgin, E.G.

Abstract

Problems of planar covering with ellipses are tackled in this work. Ellipses can have a fixed angle or each of them can be freely rotated. Deterministic global optimization methods are developed for both cases, while a stochastic version of the method is also proposed for large instances of the latter case. Numerical results show the effectiveness and efficiency of the proposed methods.

Suggested Citation

  • Andretta, M. & Birgin, E.G., 2013. "Deterministic and stochastic global optimization techniques for planar covering with ellipses problems," European Journal of Operational Research, Elsevier, vol. 224(1), pages 23-40.
    • Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:23-40
    DOI: 10.1016/j.ejor.2012.07.020
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    References listed on IDEAS

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    1. H Younies & G O Wesolowsky, 2007. "Planar maximal covering location problem under block norm distance measure," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 740-750, June.
    2. Birgin, E. G. & Martinez, J. M. & Ronconi, D. P., 2005. "Optimizing the packing of cylinders into a rectangular container: A nonlinear approach," European Journal of Operational Research, Elsevier, vol. 160(1), pages 19-33, January.
    3. Berman, Oded & Krass, Dmitry & Drezner, Zvi, 2003. "The gradual covering decay location problem on a network," European Journal of Operational Research, Elsevier, vol. 151(3), pages 474-480, December.
    4. Li, Lushu & Kabadi, S. N. & Nair, K. P. K., 2002. "Fuzzy versions of the covering circle problem," European Journal of Operational Research, Elsevier, vol. 137(1), pages 93-109, February.
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    Cited by:

    1. Tedeschi, Danilo & Andretta, Marina, 2021. "New exact algorithms for planar maximum covering location by ellipses problems," European Journal of Operational Research, Elsevier, vol. 291(1), pages 114-127.
    2. Liu, Yanchao, 2023. "An elliptical cover problem in drone delivery network design and its solution algorithms," European Journal of Operational Research, Elsevier, vol. 304(3), pages 912-925.
    3. Blanco, Víctor & Puerto, Justo, 2021. "Covering problems with polyellipsoids: A location analysis perspective," European Journal of Operational Research, Elsevier, vol. 289(1), pages 44-58.

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