IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v218y2012i3p829-837.html
   My bibliography  Save this article

Network design problem with relays: A genetic algorithm with a path-based crossover and a set covering formulation

Author

Listed:
  • Konak, Abdullah

Abstract

The network design problem with relays arises in telecommunications and distribution systems where the payload must be reprocessed at intermediate stations called relays on the route from its origin to its destination. In fiber-optic networks, for example, optical signals may be regenerated several times to overcome signal degradation because of attenuation and other factors. Given a network and a set of commodities, the network design problem with relays involves selecting network edges, determining a route for each commodity, and locating relays to minimize the network design cost. This paper presents a new formulation to the problem based on set covering constraints. The new formulation is used to design a genetic algorithm with a specialized crossover/mutation operator which generates a feasible path for each commodity, and the locations of relays on these paths are determined by solving the corresponding set covering problem. Computational experiments show that the proposed approach can outperform other approaches, particularly on large size problems.

Suggested Citation

  • Konak, Abdullah, 2012. "Network design problem with relays: A genetic algorithm with a path-based crossover and a set covering formulation," European Journal of Operational Research, Elsevier, vol. 218(3), pages 829-837.
    • Handle: RePEc:eee:ejores:v:218:y:2012:i:3:p:829-837
    DOI: 10.1016/j.ejor.2011.11.046
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221711010551
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2011.11.046?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. Gouveia, Luis, 1996. "Multicommodity flow models for spanning trees with hop constraints," European Journal of Operational Research, Elsevier, vol. 95(1), pages 178-190, November.
    2. Marcus Randall & Graham McMahon & Stephen Sugden, 2002. "A Simulated Annealing Approach to Communication Network Design," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 55-65, March.
    3. S. Voß, 1999. "The Steiner tree problem with hop constraints," Annals of Operations Research, Springer, vol. 86(0), pages 321-345, January.
    4. Cabral, Edgar Alberto & Erkut, Erhan & Laporte, Gilbert & Patterson, Raymond A., 2007. "The network design problem with relays," European Journal of Operational Research, Elsevier, vol. 180(2), pages 834-844, July.
    5. Taylor, G. Don & Whicker, Gary L. & Usher, John S., 2001. "Multi-zone dispatching in truckload trucking," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 37(5), pages 375-390, November.
    6. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    7. Halit Üster & Panitan Kewcharoenwong, 2011. "Strategic Design and Analysis of a Relay Network in Truckload Transportation," Transportation Science, INFORMS, vol. 45(4), pages 505-523, November.
    8. Anantaram Balakrishnan & Kemal Altinkemer, 1992. "Using a Hop-Constrained Model to Generate Alternative Communication Network Design," INFORMS Journal on Computing, INFORMS, vol. 4(2), pages 192-205, May.
    9. Gouveia, Luis & Requejo, Cristina, 2001. "A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 132(3), pages 539-552, August.
    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. Hong Zheng & Xiaozheng He & Yongfu Li & Srinivas Peeta, 2017. "Traffic Equilibrium and Charging Facility Locations for Electric Vehicles," Networks and Spatial Economics, Springer, vol. 17(2), pages 435-457, June.
    2. Ozgur Kabadurmus & Alice E. Smith, 2016. "Multi-commodity k-splittable survivable network design problems with relays," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(1), pages 123-133, May.
    3. Leitner, Markus & Ljubić, Ivana & Riedler, Martin & Ruthmair, Mario, 2020. "Exact approaches for the directed network design problem with relays," Omega, Elsevier, vol. 91(C).
    4. Markus Leitner & Ivana Ljubić & Martin Riedler & Mario Ruthmair, 2019. "Exact Approaches for Network Design Problems with Relays," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 171-192, February.
    5. Eusebio Angulo & Ricardo García-Ródenas & José Luis Espinosa-Aranda, 2016. "A Lagrangian relaxation approach for expansion of a highway network," Annals of Operations Research, Springer, vol. 246(1), pages 101-126, November.
    6. Nigam, Ashutosh & Agarwal, Yogesh K., 2014. "Optimal relay node placement in delay constrained wireless sensor network design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 220-233.
    7. Long, Jiancheng & Szeto, W.Y. & Huang, Hai-Jun, 2014. "A bi-objective turning restriction design problem in urban road networks," European Journal of Operational Research, Elsevier, vol. 237(2), pages 426-439.
    8. Yıldız, Barış & Karaşan, Oya Ekin, 2015. "Regenerator Location Problem and survivable extensions: A hub covering location perspective," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 32-55.
    9. Yiyong Xiao & Abdullah Konak, 2017. "A variable neighborhood search for the network design problem with relays," Journal of Heuristics, Springer, vol. 23(2), pages 137-164, June.
    10. Liao, Chung-Shou & Hsieh, Tsung-Jung & Guo, Xian-Chang & Liu, Jian-Hong & Chu, Chia-Chi, 2015. "Hybrid search for the optimal PMU placement problem on a power grid," European Journal of Operational Research, Elsevier, vol. 243(3), pages 985-994.
    11. Kewcharoenwong, Panitan & Li, Qiaofeng & Üster, Halit, 2023. "Lagrangean relaxation algorithms for fixed-charge capacitated relay network design," Omega, Elsevier, vol. 121(C).
    12. Wang, Ning & Xiao, Yiyong & Tian, Tianzi & Yang, Jun, 2023. "The optimal 5G base station location of the wireless sensor network considering timely reliability," Reliability Engineering and System Safety, Elsevier, vol. 236(C).

    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. Yiyong Xiao & Abdullah Konak, 2017. "A variable neighborhood search for the network design problem with relays," Journal of Heuristics, Springer, vol. 23(2), pages 137-164, June.
    2. Li, Xiangyong & Aneja, Y.P. & Huo, Jiazhen, 2012. "Using branch-and-price approach to solve the directed network design problem with relays," Omega, Elsevier, vol. 40(5), pages 672-679.
    3. Akgün, Ibrahim & Tansel, Barbaros Ç., 2011. "New formulations of the Hop-Constrained Minimum Spanning Tree problem via Miller-Tucker-Zemlin constraints," European Journal of Operational Research, Elsevier, vol. 212(2), pages 263-276, July.
    4. Costa, Alysson M. & Cordeau, Jean-François & Laporte, Gilbert, 2008. "Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints," European Journal of Operational Research, Elsevier, vol. 190(1), pages 68-78, October.
    5. Gouveia, Luis & Janssen, Eric, 1998. "Designing reliable tree networks with two cable technologies," European Journal of Operational Research, Elsevier, vol. 105(3), pages 552-568, March.
    6. Iago A. Carvalho & Amadeu A. Coco, 2023. "On solving bi-objective constrained minimum spanning tree problems," Journal of Global Optimization, Springer, vol. 87(1), pages 301-323, September.
    7. Yıldız, Barış & Karaşan, Oya Ekin, 2015. "Regenerator Location Problem and survivable extensions: A hub covering location perspective," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 32-55.
    8. Kewcharoenwong, Panitan & Li, Qiaofeng & Üster, Halit, 2023. "Lagrangean relaxation algorithms for fixed-charge capacitated relay network design," Omega, Elsevier, vol. 121(C).
    9. Markus Leitner & Ivana Ljubić & Martin Riedler & Mario Ruthmair, 2019. "Exact Approaches for Network Design Problems with Relays," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 171-192, February.
    10. James F. Campbell & Morton E. O'Kelly, 2012. "Twenty-Five Years of Hub Location Research," Transportation Science, INFORMS, vol. 46(2), pages 153-169, May.
    11. Nigam, Ashutosh & Agarwal, Yogesh K., 2014. "Optimal relay node placement in delay constrained wireless sensor network design," European Journal of Operational Research, Elsevier, vol. 233(1), pages 220-233.
    12. De Boeck, Jérôme & Fortz, Bernard, 2018. "Extended formulation for hop constrained distribution network configuration problems," European Journal of Operational Research, Elsevier, vol. 265(2), pages 488-502.
    13. Li, Xiangyong & Lin, Shaochong & Tian, Peng & Aneja, Y.P., 2017. "Models and column generation approach for the resource-constrained minimum cost path problem with relays," Omega, Elsevier, vol. 66(PA), pages 79-90.
    14. Barış Yıldız & Oya Ekin Karaşan, 2017. "Regenerator Location Problem in Flexible Optical Networks," Operations Research, INFORMS, vol. 65(3), pages 595-620, June.
    15. Cabral, Edgar Alberto & Erkut, Erhan & Laporte, Gilbert & Patterson, Raymond A., 2007. "The network design problem with relays," European Journal of Operational Research, Elsevier, vol. 180(2), pages 834-844, July.
    16. Gouveia, Luis & Requejo, Cristina, 2001. "A new Lagrangean relaxation approach for the hop-constrained minimum spanning tree problem," European Journal of Operational Research, Elsevier, vol. 132(3), pages 539-552, August.
    17. Gouveia, Luis & Leitner, Markus & Ljubić, Ivana, 2014. "Hop constrained Steiner trees with multiple root nodes," European Journal of Operational Research, Elsevier, vol. 236(1), pages 100-112.
    18. Alfandari, Laurent, 2004. "Choice Rules with Size Constraints for Multiple Criteria Decision Making," ESSEC Working Papers DR 04002, ESSEC Research Center, ESSEC Business School.
    19. 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.
    20. M Horn, 1996. "Analysis and Computational Schemes for p-Median Heuristics," Environment and Planning A, , vol. 28(9), pages 1699-1708, September.

    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:218:y:2012:i:3:p:829-837. 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.