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

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  • 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.

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  • 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
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    Cited by:

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    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).

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