Abstract
Given a connected, undirected and weighted graph \(G = (V, E)\), a set of infrastructure nodes \(J\) and a set of customers \(C\) include two customer types whereby customers \(C_{1}\) require a single connection (type-1) and customers \(C_{2}\) need to be redundantly connected (type-2). Survivable network design problem (SNDP) seeks a sub-graph of \(G\) with the smallest weight in which all customers are connected to infrastructure nodes. SNDP has applications in the design of the last mile of the real-world communication networks. SNDP is NP-hard so heuristic approaches are normally adopted to solve this problem, especially for large-scale networks. This paper proposes a new heuristic algorithm and a new genetic algorithm for solving SNDP. The proposed algorithms are experimented on real-world instances and random instances. Results of computational experiments show that the proposed heuristic algorithm is much more efficient than the other heuristics in running time, and the proposed genetic algorithm is much more efficient than the other heuristics in terms of minimizing the network cost.
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References
Bachhiesl P (2005) The OPT- and the SST-problems for real world access network design basic definitions and test instances. Working report 01/2005, Carinthia Tech Institue, Department of Telematics and Network Engineering, Klagenfurt, Austria
Bhandari R (1999) Survivable networks: algorithms for diverse routing. Springer Int Ser Eng Comput Sci 477:46
Bucsics T (2007) Metaheuristic approaches for designing survivable fiber-optic networks. Master’s thesis, Vienna University of Technology, Institute of Computer Graphics and Algorithms, Vienna, Austria
Canuto SA, Resende MGC, Ribeiro CC (2001) Local search with perturbations for the prize-collecting Steiner tree problem in graphs. Networks 38:50–58
Chapovska O, Punnen AP (2006) Variations of the prize-collecting Steiner tree problem. Networks 47(4):199–205
Cormen TH, Leiserson CE, Rivest RL, Stein C (2009) Introduction to algorithms, 3rd edn. The MIT Press, Cambridge
Da Cunha AS, Lucena A, Maculan N, Resende MGC (2009) A relax-and-cut algorithm for the prize-collecting Steiner problem in graph. Discrete Appl Math 157(6):1198–1217
IBM (2006) ILOG CPLEX optimizer performance benchmarks 10.0. http://www.cs.cornell.edu/w8/iisi/ilog/cplex100/index.html. Accessed 15 Aug 2014
Kerivin H, Mahjoub AR (2005) Design of survivable networks: a survey. Networks 46:1–21
Leitner M (2010) Solving two network design problems by mixed integer programming and hybrid optimization methods. Ph.D. thesis, Vienna University of Technology, Institute of Computer Graphics and Algorithms, Vienna, Austria
Leitner M, Raidl GR (2008) Lagrangian decomposition, meta-heuristics, and hybrid approaches for the design of the last mile in fiber optic networks. In: Blesa MJ et al (ed) Hybrid Metaheuristics, LNCS, vol 5296. Springer, Berlin, Heidelberg, pp 158–174
Leitner M, Raidl GR (2010) Strong lower bounds for a survivable network design problem. International symposium on combinatorial optimization. Hammamet, Tunisia, pp 295–302
Ljubić I, Weiskircher R, Pferschy U, Klau G, Mutzel P, Fischetti M (2006) An algorithmic framework for the exact solution of the prize-collecting Steiner tree problem. Math Program Ser B 105(2–3):427–449
Lucena A, Resende MGC (2004) Strong lower bounds for the prize collecting Steiner problem in graphs. Discrete Appl Math 141(1–3):277–294
Nakayama MK (2002) Simulation output analysis. In: Proceedings of the winter simulation conference, pp 23–34
Nguyen MT, Vo TK, Huynh BTT (2012) Heuristic algorithms for solving the survivable problem in the design of last mile communication networks. In: Proceedings of the 9th IEEE-RIVF international conference on computing and communication technologies, Ho Chi Minh, Vietnam, pp 1–6
Uchoa E (2006) Reduction tests for the prize-collecting Steiner problem. Oper Res Lett 34(4):437–444
Vo TK, Nguyen MT, Huynh BTT (2012) Heuristic algorithms for solving survivability problem in the design of last mile communication network. In: Proceedings of the 4th Asian conference on intelligent information and database systems, Kaohsiung, Taiwan, pp 519–528
Wagner D, Pferschy U, Mutzel P, Raidl GR, Bachhiesl P (2007) A directed cut model for the design of the last mile in real-world fiber optic networks. In: Proceedings of the international network optimization conference 2007, Spa, Belgium, pp 1–6
Wagner D, Raidl GR, Pferschy U, Mutzel P, Bachhiesl P (2007) A multi-commodity flow approach for the design of the last mile in real-world fiber optic networks. In: Waldmann KH, Stocker UM (ed) Operations research proceedings, vol 2006, pp 197–202
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This work was supported by the project “Models for the next generation of a robust Internet,” Grant Number 12/2012/HD-NDT, funded by the Ministry of Science and Technology, Vietnam.
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Communicated by V. Loia.
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Binh, H.T.T., Duong, N.T. Heuristic and genetic algorithms for solving survivability problem in the design of last mile communication networks. Soft Comput 19, 2619–2632 (2015). https://doi.org/10.1007/s00500-014-1429-z
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DOI: https://doi.org/10.1007/s00500-014-1429-z