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A new local search for continuous location problems

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  • Brimberg, Jack
  • Drezner, Zvi
  • Mladenović, Nenad
  • Salhi, Said

Abstract

This paper presents a new local search approach for solving continuous location problems. The main idea is to exploit the relation between the continuous model and its discrete counterpart. A local search is first conducted in the continuous space until a local optimum is reached. It then switches to a discrete space that represents a discretisation of the continuous model to find an improved solution from there. The process continues switching between the two problem formulations until no further improvement can be found in either. Thus, we may view the procedure as a new adaption of formulation space search. The local search is applied to the multi-source Weber problem where encouraging results are obtained. This local search is also embedded within Variable Neighbourhood Search producing excellent results.

Suggested Citation

  • Brimberg, Jack & Drezner, Zvi & Mladenović, Nenad & Salhi, Said, 2014. "A new local search for continuous location problems," European Journal of Operational Research, Elsevier, vol. 232(2), pages 256-265.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:2:p:256-265
    DOI: 10.1016/j.ejor.2013.06.022
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    Cited by:

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    2. López, C.O. & Beasley, J.E., 2016. "A formulation space search heuristic for packing unequal circles in a fixed size circular container," European Journal of Operational Research, Elsevier, vol. 251(1), pages 64-73.
    3. Chandra Ade Irawan & Martino Luis & Said Salhi & Arif Imran, 2019. "The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem," Annals of Operations Research, Springer, vol. 275(2), pages 367-392, April.
    4. Areej Alhothali & Budoor Alwated & Kamil Faisal & Sultanah Alshammari & Reem Alotaibi & Nusaybah Alghanmi & Omaimah Bamasag & Manal Bin Yamin, 2022. "Location-Allocation Model to Improve the Distribution of COVID-19 Vaccine Centers in Jeddah City, Saudi Arabia," IJERPH, MDPI, vol. 19(14), pages 1-21, July.
    5. Pawel Kalczynski & Jack Brimberg & Zvi Drezner, 2022. "Less is more: discrete starting solutions in the planar p-median problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 34-59, April.
    6. Murray, Alan T. & Church, Richard L. & Feng, Xin, 2020. "Single facility siting involving allocation decisions," European Journal of Operational Research, Elsevier, vol. 284(3), pages 834-846.
    7. Blanco, Víctor & Puerto, Justo & Ben-Ali, Safae El-Haj, 2016. "Continuous multifacility ordered median location problems," European Journal of Operational Research, Elsevier, vol. 250(1), pages 56-64.
    8. Blanco, Víctor & Gázquez, Ricardo & Ponce, Diego & Puerto, Justo, 2023. "A branch-and-price approach for the continuous multifacility monotone ordered median problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 105-126.
    9. M. Hakan Akyüz & Temel Öncan & İ. Kuban Altınel, 2019. "Branch and bound algorithms for solving the multi-commodity capacitated multi-facility Weber problem," Annals of Operations Research, Springer, vol. 279(1), pages 1-42, August.
    10. 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.
    11. Zvi Drezner & Jack Brimberg & Nenad Mladenović & Said Salhi, 2015. "Solving the planar p-median problem by variable neighborhood and concentric searches," Journal of Global Optimization, Springer, vol. 63(3), pages 501-514, November.
    12. Zvi Drezner & Jack Brimberg & Nenad Mladenović & Said Salhi, 2016. "New local searches for solving the multi-source Weber problem," Annals of Operations Research, Springer, vol. 246(1), pages 181-203, November.
    13. Li Wang & Huan Shi & Lu Gan, 2018. "Healthcare Facility Location-Allocation Optimization for China’s Developing Cities Utilizing a Multi-Objective Decision Support Approach," Sustainability, MDPI, vol. 10(12), pages 1-22, December.

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