Abstract
Enhancements to two exact algorithms from the literature to solve the vertex P-center problem are proposed. In the first approach modifications of some steps are introduced to reduce the number of ILP iterations needed to find the optimal solution. In the second approach a simple enhancement which uses tighter initial lower and upper bounds, and a more appropriate binary search method are proposed to reduce the number of subproblems to be solved. These ideas are tested on two well known sets of problems from the literature (i.e., OR-Lib and TSP-Lib problems) with encouraging results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Beasley, J. E.: A note on solving large P-median problems, European J. Oper. Res. 21 (1985), 270–273.
Beasley, J. E.: OR library: Distributing test problems by electronic mail, J. Oper. Res. Soc. 41(11) (1990), 1069–1072.
Daskin, M. S.: Network and Discrete Locations: Models, Algorithms, and Applications, Wiley, New York, 1995, pp. 154–191.
Daskin, M.: A new approach to solve the vertex P-center problem to optimality: Algorithm and computational results, Comm. Oper. Res. Soc. Japan 45(9) (2000), 428–436.
Elloumi, S., Labbé, M. and Pochet, Y.: New formulation and resolution method for the P-center problem, http://www.optimization-online.org/DB.HTML/2001/10/394.html, 2001.
Floyd, R.W.: Algorithm 97, Shortest Path, Comm. Assoc. Comput. Mach. 5 (1962), 345.
Hakimi, S. L.: Optimum locations of switching centers and the absolute centers and medians of a graph, Oper. Res. 12 (1964), 450–459.
Hakimi, S. L.: Optimum distribution of switching centers in a communications network and some related graph theoretic problems, Oper. Res. 13 (1965), 462–475.
Ilhan, T. and Pinar, M.C.: An efficient exact algorithm for the vertex P-center problem, http://www.optimization-online.org/DB.HTML/2001/09/376.html, 2001.
Kariv, O. and Hakimi, S.: An algorithmic approach to network location problems. Part I: The P-centers, SIAM J. Appl. Math. 37 (1979), 513–538.
Minieka, E.: The m-center problem, SIAM Rev. 12 (1970), 138–139.
Reinelt, G.: TSPLIB – A traveling salesman problem library, ORSA J. Comput. 3 (1991), 376–384.
Author information
Authors and Affiliations
Additional information
Mathematics Subject Classifications (2000)
90B10, 90B80, 90C09, 90C47.
Rights and permissions
About this article
Cite this article
Al-khedhairi, A., Salhi, S. Enhancements to Two Exact Algorithms for Solving the Vertex P-Center Problem. J Math Model Algor 4, 129–147 (2005). https://doi.org/10.1007/s10852-004-4072-3
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10852-004-4072-3