Computational study of large-scale p-Median problems (original) (raw)

References

  1. OR–Library. Available at the web address http://mscmga.ms.ic.ac.uk/info.html.
  2. Tsplib. Available at the web address http://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/.
  3. Avella, P., Sassano, A.: On the p-median polytope. Mathematical Programming, 89, 395–411 (2001)
    Article MATH MathSciNet Google Scholar
  4. Barahona, F., Anbil, R.: The volume algorithm: producing primal solutions with a subgradient algorithm. Mathematical Programming, 87, 385–399 (2000)
    Article MATH MathSciNet Google Scholar
  5. Barahona, F., Chudak, F.: Solving large scale uncapacitated facility location problems. In: Pardalos, P. (ed.), Approximation and Complexity in Numerical Optimization, pp. 48–62, 2000
  6. Beasley, J.E.: A note on solving large scale _p_-median problems. EJOR, 21, 270–273 (1985)
    Article MATH MathSciNet Google Scholar
  7. Beasley, J.E.: Lagrangean heuristics for location problems. EJOR, 65, 383–399 (1993)
    Article MATH Google Scholar
  8. Bradley, P.S., Mangasarian, O.L.: Feature selection via concave minimization and support vector machines. In: Shavlik, J. (ed.), Machine Learning Proceedings of the Fifteenth International Conference (ICML'98), San Francisco, California, pp. 82–90, 1998
  9. Briant, O., Naddef, D.: The optimal diversity management problem. accepted at Operations Research, 52 (4), (2004)
  10. Chiyoshi, F., Galvao, D.: A statistical analysis of simulated annealing applied to the _p_-median problem. Annals of Operations Research, 96, 61–74 (2000)
    Article MATH Google Scholar
  11. Christofides, N., Beasley, J.E.: A tree search algorithm for the _p_-median problem. EJOR, 10, 196–204 (1982)
    Article MATH MathSciNet Google Scholar
  12. Chudak, F.A.: Improved approximation algorithms for the uncapacitated facility location problem. PhD thesis, Cornell University, 1998
  13. Cornuejols, G., Fisher, M.L., Nemhauser, G.L.: Location of bank accounts to optimize float : An analytic study of exact and approximate algorithms. Management Science, 23, 789–810 (1977)
    MATH MathSciNet Google Scholar
  14. Correa, E.S., Steiner, M.T.A., Freitas, A.A., Carnieri, C.: A genetic algorithm for the _p_-median problem. In: Procedings of 2001 Genetic and Evolutionary Computation Conf. (GECCO-2001), pp. 1268–1275, 2001
  15. Crainic, T.G., Gendreau, M., Hansen, P., Mladenovic, N.: Cooperative parallel variable neighborhood search for the p-median. Journal of Heuristics, 10 (3), 293–314 (2004)
    Article Google Scholar
  16. du Merle, O., Villeneuve, D., Desrosiers, J., Hansen, P.: Stabilized column generation. discrete mathematics. Discrete Mathematics, 194, 229–237 (1999)
    MATH Google Scholar
  17. Erkut, E., Bozkaya, B., Zhang, J.: An effective genetic algorithm for the _p_-median problem. Paper presented at INFORMS conference in Dallas, 1997
  18. Fung, G., Mangasarian, O.L.: Semi-supervised support vector machines for unlabeled data classification. Optimization Methods and Software, 1 (15), 29–44 (2000)
    Google Scholar
  19. Galvao, R.D.: A dual-bounded algorithm for the _p_-median problem, operations research. Operations Research, 28, 1112–1121 (1980)
    MATH MathSciNet Google Scholar
  20. Garcia-Lopez, F., Melian-Batista, B., Moreno-Perez, J.A., Moreno-Vega, J.M.: The parallel variable neighborhood search for the p-median problem. Journal of Heuristics, 8 (3), 375–388 (2002)
    Article Google Scholar
  21. Garcia-Lopez, F., Melian-Batista, B., Moreno-Perez, J.A., Moreno-Vega, J.M.: Parallelization of the scatter search for the p-median problem. Parallel Computing, 29 (3), 575–589 (2003)
    Article Google Scholar
  22. Garfinkel, R.S., Neebe, A.W., Rao, M.R.: An algorithm for the m-median plant location problem. Transportation Science, 25, 183–187 (1974)
    MathSciNet Google Scholar
  23. Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Springer, Berlin Heidelberg New York, 1993
  24. Hansen, P., Jaumard, B.: Cluster analysis and mathematical programming. Mathematical Programming, 79, 191–215 (1997)
    Article MATH MathSciNet Google Scholar
  25. Hansen, P., Mladenovic, N.: Variable neighbourhood search for the p-median. Location Science, 5, 207–226 (1997)
    Article MATH Google Scholar
  26. Hansen, P., Mladenovic, N., Perez-Brito, D.: Variable neighbourhood decomposition search. Journal of Heuristics, 7, 335–350 (2001)
    Article MATH Google Scholar
  27. Hoffman, K., Padberg, M.: Solving airline crew scheduling problems by branch-and-cut. Management Science, 39 (6), 657–682 (1993)
    Google Scholar
  28. Hosage, C.M., Goodchild, M.F.: Discrete space location-allocation solutions from genetic algorithms. Annals of Operational Research, 6, 35–46 (1986)
    Article Google Scholar
  29. Kariv, O., Hakimi, L.: An algorithmic approach to network location problems. ii: the _p_-medians. Operations Research, 37 (3), 539–560 (1979)
    MathSciNet Google Scholar
  30. Mannino, C., Sassano, A.: An exact algorithm for the maximum stable set problem. Computational Optimization and Applications, 3 (4), 243–258 (1994)
    Article MathSciNet Google Scholar
  31. Mirchandani, P.B., Oudjit, A., Wong, R.T.: Multidimensional extensions and a nested dual approach for the m-median problem. EJOR, 21, 121–137 (1995)
    Article MathSciNet Google Scholar
  32. Mulvey, J.M., Crowder, H.P.: Cluster analysis: an application of lagrangian relaxation. Management Science, 25, 329–340 (1979)
    MATH Google Scholar
  33. Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Willey, 1988
  34. Rao, M.R.: Cluster analysis and mathematical programming. Journal of the American Statistical Association, 6, 622–626 (1971)
    Article Google Scholar
  35. Resende, M.G.C., Werneck, R.F.: On the implementation of a swap-based local search procedure for the p-median problem. In: Ladner, R.E. (ed.), Proceedings of the 5th Workshop on Algorithm Engineering and Experiments (ALENEX'03), pp. 119–127, 2003
  36. Resende, M.G.C., Werneck, R.F.: A hybrid heuristic for the p-median problem. Journal of Heuristics, 10 (1), 59–88 (2004)
    Article MathSciNet Google Scholar
  37. Rolland, E., Schilling, D.A., Current, J.R.: An efficient tabu search procedure for the _p_-median problem. EJOR, 96, 329–342 (1996)
    Article Google Scholar
  38. Senne, E.L.F., Lorena, L.A.N.: Lagrangean/surrogate heuristics for p-median problems. In: Laguna, M., Gonzalez-Velarde, J.L., (eds.), Computing Tools for Modeling, Optimization and Simulation: Interfaces in Computer Science and Operations Research, Kluwer Academic Publishers, pp. 115–130, 2001
  39. Senne, E.L.F., Lorena, L.A.N.: Stabilizing column generation using lagrangean/surrogate relaxation: an application to p-median location problems. EURO 2001 - THE EUROPEAN OPERATIONAL RESEARCH CONFERENCE - Erasmus University Rotterdam, July 9–11, 2001
  40. Senne, E.L.F., Lorena, L.A.N., Pereira, M.A.: A branch-and-price approach to p-median location problems. accepted in Computers and Operations Research, 2004
  41. Teitz, M.B., Bart, P.: Heuristic methods for estimating the generalized vertex median of a weighted graph. Operations Research, 16, 955–961 (1968)
    Article MATH Google Scholar
  42. Vinod, H.D.: Integer programming and the theory of groups. Journal of the American Statistical Association, 6, 506–519 (1969)
    Article Google Scholar
  43. Whitaker, R.A.: A fast algorithm for the greedy interchange for large-scale clustering and median location problems. INFORS, 21, 95–108 (1983)
    MATH Google Scholar

Download references