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Heuristics for the network design problem with connectivity requirements

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Abstract

We consider the NP-complete problem of finding a spanning \(k\)-tree of minimum weight in a complete weighted graph. This problem has a number of applications in designing reliable backbone telecommunication networks. We propose effective algorithms based on a greedy strategy and several variable neighborhood search metaheuristics. We also develop an integer linear programming model for calculating a lower bound. Preliminary numerical experiments using random and real-word data sets are reported to show the effectiveness of our approach. In addition, we compare our approach with known metaheuristics.

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Acknowledgments

The authors are grateful to professors D. Skoryn-Kapov and A. Koster for their interest in the problem and constructive suggestions, to professors F. Beltran, A. Candia and G. Fernandez for providing the codes of known metaheuristics. Research by P. Pardalos was conducted at National Research University Higher School of Economics and supported by RSF Grant 14-41-00039.

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Authors and Affiliations

  1. Department of Computational Mathematics and Informatics, South Ural State University, Cheliabinsk, Russia

    Roman E. Shangin

  2. Department of Industrial and Systems Engineering, University of Florida, Gainesville, USA

    Panos Pardalos

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  1. Roman E. Shangin
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  2. Panos Pardalos
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Correspondence to Roman E. Shangin.

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Shangin, R.E., Pardalos, P. Heuristics for the network design problem with connectivity requirements. J Comb Optim 31, 1461–1478 (2016). https://doi.org/10.1007/s10878-015-9834-5

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