Abstract
For the p-center problem, we propose a new smart local search based on the critical vertex concept and embed it in a GRASP framework. Experimental results attest the robustness of the proposed search procedure and confirm that for benchmark instances it converges to optimal or near/optimal solutions faster than the best known state-of-the-art local search.
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Beasley, J.: A note on solving large \(p\)-median problems. Eur. J. Oper. Res. 21, 270–273 (1985)
Coffin, M., Saltzman, M.: Statistical analysis of computational tests of algorithms and heuristics. INFORMS J. Comput. 12(1), 24–44 (2000)
Daskin, M.: Network and Discrete Location: Models, Algorithms, and Applications. Wiley, New York (1995)
Davidović, T., Ramljak, D., Šelmić, M., Teodorović, D.: Bee colony optimization for the \(p\)-center problem. Comput. Oper. Res. 38(10), 1367–1376 (2011)
Dyer, M., Frieze, A.: A simple heuristic for the \(p\)-centre problem. Oper. Res. Lett. 3(6), 285–288 (1985)
Feo, T., Resende, M.: A probabilistic heuristic for a computationally difficult set covering problem. Oper. Res. Lett. 8, 67–71 (1989)
Feo, T., Resende, M.: Greedy randomized adaptive search procedures. J. Global Optim. 6, 109–133 (1995)
Festa, P., Resende, M.: GRASP: an annotated bibliography. In: Ribeiro, C., Hansen, P. (eds.) Essays and Surveys on Metaheuristics, pp. 325–367. Kluwer Academic Publishers, London (2002)
Festa, P., Resende, M.: An annotated bibliography of GRASP - part I: algorithms. Int. Trans. Oper. Res. 16(1), 1–24 (2009)
Festa, P., Resende, M.: An annotated bibliography of GRASP - part II: applications. Int. Trans. Oper. Res. 16(2), 131–172 (2009)
Goldengorin, B., Kocheturov, A., Pardalos, P.M.: A pseudo-boolean approach to the market graph analysis by means of the p-median model. In: Aleskerov, F., Goldengorin, B., Pardalos, P.M. (eds.) Clusters, Orders, and Trees: Methods and Applications. SOIA, vol. 92, pp. 77–89. Springer, New York (2014). doi:10.1007/978-1-4939-0742-7_5
Goldengorin, B., Krushinsky, D., Pardalos, P.M.: Application of the PMP to cell formation in group technology. In: Goldengorin, B., Krushinsky, D., Pardalos, P.M. (eds.) Cell Formation in Industrial Engineering. SOIA, vol. 79, pp. 75–99. Springer, New York (2013). doi:10.1007/978-1-4614-8002-0_3
Hakimi, S.: Optimum locations of switching centers and the absolute centers and medians of a graph. Oper. Res. 12(3), 450–459 (1964)
Hansen, P., Mladenović, N.: Variable neighborhood search for the \(p\)-median. Locat. Sci. 5(4), 207–226 (1997)
Hochbaum, D., Shmoys, D.: A best possible heuristic for the \(k\)-Center problem. Math. Oper. Res. 10(2), 180–184 (1985)
Kariv, O., Hakimi, S.: An algorithmic approach to network location problems. Part I: the \(p\)-centers. SIAM J. Appl. Math. 37(3), 513–538 (1979)
Kariv, O., Hakimi, S.: An algorithmic approach to network location problems. Part II: the \(p\)-medians. SIAM J. Appl. Math. 37(3), 539–560 (1979)
Martinich, J.S.: A vertex-closing approach to the \(p\)-center problem. Nav. Res. Logist. 35(2), 185–201 (1988)
Matsumoto, M., Nishimura, T.: Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Trans. Model. Comput. Simul. 8(1), 3–30 (1998)
Minieka, E.: The \(m\)-center problem. SIAM Rev. 12(1), 138–139 (1970)
Mladenović, N., Labbé, M., Hansen, P.: Solving the \(p\)-center problem with Tabu Search and variable neighborhood search. Networks 42(April), 48–64 (2003)
Mladenovic, N., Urosevic, D., Prez-Brito, D., Garca-Gonzlez, C.G.: Variable neighbourhood search for bandwidth reduction. Eur. J. Oper. Res. 200(1), 14–27 (2010)
Pardo, E.G., Mladenovi, N., Pantrigo, J.J., Duarte, A.: Variable formulation search for the cutwidth minimization problem. Appl. Soft Comput. 13(5), 2242–2252 (2013)
Reinelt, G.: TSPLIB—A traveling salesman problem library. ORSA J. Comput. 3(4), 376–384 (1991)
Resende, M., Werneck, R.: A hybrid heuristic for the \(p\)-median problem. J. Heuristics 10(1), 59–88 (2004)
Salhi, S., Al-Khedhairi, A.: Integrating heuristic information into exact methods: the case of the vertex p-centre problem. J. Oper. Res. Soc. 61(11), 1619–1631 (2010)
Wilcoxon, F.: Individual comparisons by ranking methods. Biom. Bull. 1(6), 80–83 (1945)
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This work has been realized thanks to the use of the S.Co.P.E. computing infrastructure at the University of Napoli FEDERICO II.
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Ferone, D., Festa, P., Napoletano, A., Resende, M.G.C. (2017). A New Local Search for the p-Center Problem Based on the Critical Vertex Concept. In: Battiti, R., Kvasov, D., Sergeyev, Y. (eds) Learning and Intelligent Optimization. LION 2017. Lecture Notes in Computer Science(), vol 10556. Springer, Cham. https://doi.org/10.1007/978-3-319-69404-7_6
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DOI: https://doi.org/10.1007/978-3-319-69404-7_6
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