IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v241y2015i3p606-621.html
   My bibliography  Save this article

The continuous p-centre problem: An investigation into variable neighbourhood search with memory

Author

Listed:
  • Elshaikh, Abdalla
  • Salhi, Said
  • Nagy, Gábor

Abstract

A VNS-based heuristic using both a facility as well as a customer type neighbourhood structure is proposed to solve the p-centre problem in the continuous space. Simple but effective enhancements to the original Elzinga–Hearn algorithm as well as a powerful ‘locate–allocate’ local search used within VNS are proposed. In addition, efficient implementations in both neighbourhood structures are presented. A learning scheme is also embedded into the search to produce a new variant of VNS that uses memory. The effect of incorporating strong intensification within the local search via a VND type structure is also explored with interesting results. Empirical results, based on several existing data set (TSP-Lib) with various values of p, show that the proposed VNS implementations outperform both a multi-start heuristic and the discrete-based optimal approach that use the same local search.

Suggested Citation

  • Elshaikh, Abdalla & Salhi, Said & Nagy, Gábor, 2015. "The continuous p-centre problem: An investigation into variable neighbourhood search with memory," European Journal of Operational Research, Elsevier, vol. 241(3), pages 606-621.
    • Handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:606-621
    DOI: 10.1016/j.ejor.2014.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221714008108
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2014.10.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mladenovic, Nenad & Urosevic, Dragan & Pérez-Brito, Dionisio & García-González, Carlos G., 2010. "Variable neighbourhood search for bandwidth reduction," European Journal of Operational Research, Elsevier, vol. 200(1), pages 14-27, January.
    2. Pierre Hansen & Nenad Mladenović & José Moreno Pérez, 2010. "Variable neighbourhood search: methods and applications," Annals of Operations Research, Springer, vol. 175(1), pages 367-407, March.
    3. Jack Elzinga & Donald W. Hearn, 1972. "Geometrical Solutions for Some Minimax Location Problems," Transportation Science, INFORMS, vol. 6(4), pages 379-394, November.
    4. S Salhi & A Al-Khedhairi, 2010. "Integrating heuristic information into exact methods: The case of the vertex p-centre problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(11), pages 1619-1631, November.
    5. Zvi Drezner, 1984. "The Planar Two-Center and Two-Median Problems," Transportation Science, INFORMS, vol. 18(4), pages 351-361, November.
    6. Lu, Chung-Cheng, 2013. "Robust weighted vertex p-center model considering uncertain data: An application to emergency management," European Journal of Operational Research, Elsevier, vol. 230(1), pages 113-121.
    7. Donald W. Hearn & James Vijay, 1982. "Efficient Algorithms for the (Weighted) Minimum Circle Problem," Operations Research, INFORMS, vol. 30(4), pages 777-795, August.
    8. Murray, Alan T. & Wei, Ran, 2013. "A computational approach for eliminating error in the solution of the location set covering problem," European Journal of Operational Research, Elsevier, vol. 224(1), pages 52-64.
    9. H. A. Eiselt & G. Charlesworth, 1986. "A Note on p -Center Problems in the Plane," Transportation Science, INFORMS, vol. 20(2), pages 130-133, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Callaghan, Becky & Salhi, Said & Nagy, Gábor, 2017. "Speeding up the optimal method of Drezner for the p-centre problem in the plane," European Journal of Operational Research, Elsevier, vol. 257(3), pages 722-734.
    2. Sze, Jeeu Fong & Salhi, Said & Wassan, Niaz, 2017. "The cumulative capacitated vehicle routing problem with min-sum and min-max objectives: An effective hybridisation of adaptive variable neighbourhood search and large neighbourhood search," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 162-184.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chandra Ade Irawan & Said Salhi & Zvi Drezner, 2016. "Hybrid meta-heuristics with VNS and exact methods: application to large unconditional and conditional vertex $$p$$ p -centre problems," Journal of Heuristics, Springer, vol. 22(4), pages 507-537, August.
    2. Callaghan, Becky & Salhi, Said & Nagy, Gábor, 2017. "Speeding up the optimal method of Drezner for the p-centre problem in the plane," European Journal of Operational Research, Elsevier, vol. 257(3), pages 722-734.
    3. M. Cera & J. A. Mesa & F. A. Ortega & F. Plastria, 2008. "Locating a Central Hunter on the Plane," Journal of Optimization Theory and Applications, Springer, vol. 136(2), pages 155-166, February.
    4. R. Chen & G. Y. Handler, 1987. "Relaxation method for the solution of the minimax location‐allocation problem in euclidean space," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 775-788, December.
    5. Minnie H. Patel & Deborah L. Nettles & Stuart J. Deutsch, 1993. "A linear‐programming‐based method for determining whether or not n demand points are on a hemisphere," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(4), pages 543-552, June.
    6. Palubeckis, Gintaras & Tomkevičius, Arūnas & Ostreika, Armantas, 2019. "Hybridizing simulated annealing with variable neighborhood search for bipartite graph crossing minimization," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 84-101.
    7. Zvi Drezner, 1987. "On the rectangular p‐center problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(2), pages 229-234, April.
    8. Tammy Drezner & Zvi Drezner, 2016. "Sequential location of two facilities: comparing random to optimal location of the first facility," Annals of Operations Research, Springer, vol. 246(1), pages 5-18, November.
    9. Okabe, Atsuyuki & Suzuki, Atsuo, 1997. "Locational optimization problems solved through Voronoi diagrams," European Journal of Operational Research, Elsevier, vol. 98(3), pages 445-456, May.
    10. 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.
    11. Gilberto F. Sousa Filho & Teobaldo L. Bulhões Júnior & Lucidio A. F. Cabral & Luiz Satoru Ochi & Fábio Protti, 2017. "New heuristics for the Bicluster Editing Problem," Annals of Operations Research, Springer, vol. 258(2), pages 781-814, November.
    12. Schnepper, Teresa & Klamroth, Kathrin & Stiglmayr, Michael & Puerto, Justo, 2019. "Exact algorithms for handling outliers in center location problems on networks using k-max functions," European Journal of Operational Research, Elsevier, vol. 273(2), pages 441-451.
    13. Lu, Chung-Cheng & Ying, Kuo-Ching & Chen, Hui-Ju, 2016. "Real-time relief distribution in the aftermath of disasters – A rolling horizon approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 93(C), pages 1-20.
    14. Kılcı, Fırat & Kara, Bahar Yetiş & Bozkaya, Burçin, 2015. "Locating temporary shelter areas after an earthquake: A case for Turkey," European Journal of Operational Research, Elsevier, vol. 243(1), pages 323-332.
    15. Zvi Drezner & G. O. Wesolowsky, 1991. "Facility location when demand is time dependent," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(5), pages 763-777, October.
    16. H. Asefi & S. Lim & M. Maghrebi & S. Shahparvari, 2019. "Mathematical modelling and heuristic approaches to the location-routing problem of a cost-effective integrated solid waste management," Annals of Operations Research, Springer, vol. 273(1), pages 75-110, February.
    17. O Berman & Z Drezner, 2003. "A probabilistic one-centre location problem on a network," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 871-877, August.
    18. Acar, Müge & Kaya, Onur, 2019. "A healthcare network design model with mobile hospitals for disaster preparedness: A case study for Istanbul earthquake," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 130(C), pages 273-292.
    19. Murray, Alan T., 2021. "Contemporary optimization application through geographic information systems," Omega, Elsevier, vol. 99(C).
    20. Zvi Drezner & Said Salhi, 2017. "Incorporating neighborhood reduction for the solution of the planar p-median problem," Annals of Operations Research, Springer, vol. 258(2), pages 639-654, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:241:y:2015:i:3:p:606-621. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.