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A modified firefly algorithm for general inverse p-median location problems under different distance norms

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  • Behrooz Alizadeh

    (Faculty of Basic Sciences, Sahand University of Technology)

  • Somayeh Bakhteh

    (Faculty of Basic Sciences, Sahand University of Technology)

Abstract

This paper concerns a general inverse p-median location problem on the k-dimensional real space where the aim is to change (increase or reduce) the weights and coordinates of the existing customer points at the minimum total cost subject to given modification bounds so that a set of p predetermined facility points becomes an optimal p-median location under the new weights and coordinates. A modified firefly algorithm is proposed to solve the problem under the rectilinear, Chebyshev and Euclidean distance norms. By computational experiments, the high efficiency of the algorithm is illustrated.

Suggested Citation

  • Behrooz Alizadeh & Somayeh Bakhteh, 2017. "A modified firefly algorithm for general inverse p-median location problems under different distance norms," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 618-636, September.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:3:d:10.1007_s12597-016-0296-z
    DOI: 10.1007/s12597-016-0296-z
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    References listed on IDEAS

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    1. Kien Trung Nguyen, 2016. "Inverse 1-Median Problem on Block Graphs with Variable Vertex Weights," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 944-957, March.
    2. Fahimeh Baroughi Bonab & Rainer Burkard & Behrooz Alizadeh, 2010. "Inverse median location problems with variable coordinates," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 365-381, September.
    3. Behrooz Alizadeh & Rainer Burkard, 2013. "A linear time algorithm for inverse obnoxious center location problems on networks," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 585-594, September.
    4. Stanimirovic, Zorica & Kratica, Jozef & Dugosija, Djordje, 2007. "Genetic algorithms for solving the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 182(3), pages 983-1001, November.
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    6. Fahimeh Baroughi Bonab & Rainer Burkard & Elisabeth Gassner, 2011. "Inverse p-median problems with variable edge lengths," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(2), pages 263-280, April.
    7. Nguyen, Kien Trung & Chassein, André, 2015. "The inverse convex ordered 1-median problem on trees under Chebyshev norm and Hamming distance," European Journal of Operational Research, Elsevier, vol. 247(3), pages 774-781.
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    9. Kratica, Jozef & Stanimirovic, Zorica & Tosic, Dusan & Filipovic, Vladimir, 2007. "Two genetic algorithms for solving the uncapacitated single allocation p-hub median problem," European Journal of Operational Research, Elsevier, vol. 182(1), pages 15-28, October.
    10. Mladenovic, Nenad & Brimberg, Jack & Hansen, Pierre & Moreno-Perez, Jose A., 2007. "The p-median problem: A survey of metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 179(3), pages 927-939, June.
    11. Puerto, Justo & Pérez-Brito, Dionisio & García-González, Carlos G., 2014. "A modified variable neighborhood search for the discrete ordered median problem," European Journal of Operational Research, Elsevier, vol. 234(1), pages 61-76.
    12. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F., 2012. "Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 54-64.
    13. Elisabeth Gassner, 2008. "The inverse 1-maxian problem with edge length modification," Journal of Combinatorial Optimization, Springer, vol. 16(1), pages 50-67, July.
    14. Kien Trung Nguyen & Ali Reza Sepasian, 2016. "The inverse 1-center problem on trees with variable edge lengths under Chebyshev norm and Hamming distance," Journal of Combinatorial Optimization, Springer, vol. 32(3), pages 872-884, October.
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    Cited by:

    1. Alizadeh, Behrooz & Afrashteh, Esmaeil, 2020. "Budget-constrained inverse median facility location problem on tree networks," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    2. Behrooz Alizadeh & Esmaeil Afrashteh & Fahimeh Baroughi, 2018. "Combinatorial Algorithms for Some Variants of Inverse Obnoxious Median Location Problem on Tree Networks," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 914-934, September.
    3. Esmaeil Afrashteh & Behrooz Alizadeh & Fahimeh Baroughi & Kien Trung Nguyen, 2018. "Linear Time Optimal Approaches for Max-Profit Inverse 1-Median Location Problems," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 35(05), pages 1-22, October.
    4. Kien Trung Nguyen & Huong Nguyen-Thu & Nguyen Thanh Hung, 2018. "On the complexity of inverse convex ordered 1-median problem on the plane and on tree networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 147-159, October.
    5. Sarker, Bhaba R. & Wu, Bingqing & Paudel, Krishna P., 2019. "Modeling and optimization of a supply chain of renewable biomass and biogas: Processing plant location," Applied Energy, Elsevier, vol. 239(C), pages 343-355.

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