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A variable neighborhood search for the network design problem with relays

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Abstract

Given a set of commodities to be routed over a network, the network design problem with relays involves selecting a route for each commodity and determining the location of relays where the commodities must be reprocessed at certain distance intervals. We propose a hybrid approach based on variable neighborhood search. The variable neighborhood algorithm searches for the route for each commodity and the optimal relay locations for a given set of routes are determined by an implicit enumeration algorithm. We show that dynamic programming can be used to determine the optimal relay locations for a single commodity. Dynamic programming is embedded into the implicit enumeration algorithm to solve the relay location problem optimally for multiple commodities. The special structure of the problem is leveraged for computational efficiency. In the variable neighborhood search algorithm, the routes of the current solution are perturbed and reconstructed to generate neighbor solutions using random and greedy construction heuristics. Computational experiments on three sets of problems (80 instances) show that the variable neighborhood search algorithm with optimal relay allocations outperforms all existing algorithms in the literature.

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Acknowledgements

This work is partly supported by the National Natural Science Foundation of China under Grant No. 71271009.

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Authors and Affiliations

  1. School of Reliability and System Engineering, Beihang University, Beijing, 100191, China

    Yiyong Xiao

  2. Information Sciences and Technology, Penn State Berks, Tulpehocken Road, P.O. Box 7009, Reading, PA, 19610-6009, USA

    Abdullah Konak

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  1. Yiyong Xiao
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  2. Abdullah Konak
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Corresponding author

Correspondence to Abdullah Konak.

Appendix

Appendix

Fig. 12
figure 12

New best-known solution for No. 15 instance of Type-I (\(\hbox {cost}=463.16\))

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Fig. 13
figure 13

New best-known solution for No. 19 instance of Type-I (\(\hbox {cost}=404.96\))

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Fig. 14
figure 14

New best-known solution for No. 20 instance of Type-I (\(\hbox {cost}=392.24\))

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Xiao, Y., Konak, A. A variable neighborhood search for the network design problem with relays. J Heuristics 23, 137–164 (2017). https://doi.org/10.1007/s10732-017-9332-2

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  • DOI: https://doi.org/10.1007/s10732-017-9332-2

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