Abstract
A generalization of the Ring Star Problem, called Two-Node-connected Star Problem (2NCSP), is here addressed. We are given an undirected graph, pendant-costs and core-costs. The goal is to find the minimum-cost spanning graph, where the core is a two-node-connected component, and the remaining nodes are pendant to this component.
First, we show that the 2NCSP belongs to the \(\mathcal {NP}\)-Hard class. Therefore, a GRASP heuristic is developed, enriched with a Variable Neighborhood Descent (VND). The neighborhood structures include exact integer linear programming models to find best paths as well as a shaking operation in order not to get stuck in a local minima.
We contrast our GRASP/VND methodology with prior works from RSP using TSPLIB, in order to highlight the effectiveness of our heuristic. Our solution outperforms several instances considered in a previous reference related to the RSP. A discussion of the results and trends for future work is provided.
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References
Calvete, H.I., Gal, C., Iranzo, J.A.: An efficient evolutionary algorithm for the ring star problem. Eur. J. Oper. Res. 231(1), 22–33 (2013)
Dias, T.C.S., de Sousa Filho, G.F., Macambira, E.M., dos Anjos F. Cabral, L., Fampa, M.H.C.: An efficient heuristic for the ring star problem. In: Àlvarez, C., Serna, M. (eds.) WEA 2006. LNCS, vol. 4007, pp. 24–35. Springer, Heidelberg (2006)
Festa, P., Pardalos, P., Resende, M., Ribeiro, C.: Randomized heuristics for the max-cut problem. Optim. Methods Softw. 17(6), 1033–1058 (2002)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, pp. 85–103. Plenum Press (1972)
Labbé, M., Laporte, G., Martín, I.R., González, J.J.S.: The ring star problem: polyhedral analysis and exact algorithm. Networks 43(3), 177–189 (2004)
Monma, C.L., Munson, B.S., Pulleyblank, W.R.: Minimum-weight two-connected spanning networks. Math. Program. 46(1–3), 153–171 (1990)
Pérez, J.A.M., Moreno-Vega, J.M., Martín, I.R.: Variable neighborhood tabu search and its application to the median cycle problem. Eur. J. Oper. Res. 151(2), 365–378 (2003)
Resende, M., Ribeiro, C.: GRASP: greedy randomized adaptive search procedures. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies, pp. 287–312. Springer, US (2014)
Robledo Amoza, F.: GRASP heuristics for Wide Area Network design. Ph.D. thesis, INRIA/IRISA, Université de Rennes I, Rennes, France (2005)
Romero, P.: Mathematical analysis of scheduling policies in Peer-to-Peer video streaming networks. Ph.D. thesis, Facultad de Ingeniería, Universidad de la República, Montevideo, Uruguay, November 2012
Simonetti, L., Frota, Y., de Souza, C.: The ring-star problem: a new integer programming formulation and a branch-and-cut algorithm. Discrete Appl. Math. 159(16), 1901–1914 (2011). 8th Cologne/Twente Workshop on Graphs and Combinatorial Optimization (CTW 2009)
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Recoba, R., Robledo, F., Romero, P., Viera, O. (2016). A GRASP/VND Heuristic for a Generalized Ring Star Problem. In: Blesa, M., et al. Hybrid Metaheuristics. HM 2016. Lecture Notes in Computer Science(), vol 9668. Springer, Cham. https://doi.org/10.1007/978-3-319-39636-1_8
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DOI: https://doi.org/10.1007/978-3-319-39636-1_8
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