Automation and Remote Control

, Volume 65, Issue 3, pp 431–438

Algorithms of Ant System and Simulated Annealing for the p-median Problem

  • T. V. Levanova
  • M. A. Loresh


Consideration was given to the p-median problem for minimum in the integer formulation which is known to be NP-hard. Variants of the algorithms of ant system and simulated annealing were proposed for it, and the results of computer experiments were analyzed.


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  1. 1.
    Grishukhin, V.P., Polynomiality in the Simplest Location Problem, Preprint of Central Economics Math. Inst., Russ. Acad. Sci., Moscow, 1987.Google Scholar
  2. 2.
    Kariv, O. and Hakimi, S.L., An Algorithmic Approach to Network Location Problems, SIAM J. Appl. Math., 1979, vol. 37, no. 3, pp. 513–560.Google Scholar
  3. 3.
    Dorigo, M., Maniezzo, V., and Colorny, A., Ant System: An Autocatalytic Optimizing Process, Report no. TR-91-016, Milan: Politecnici di Milano, 1991.Google Scholar
  4. 4.
    Dorigo, M., Colorny, A., Maniezzo, V., and Trubian, M., Ant System for Job-shop Scheduling, JORBEL/Belgian J. Oper. Res. Statistics Comput. Sci., 1994, no. 34(1), pp. 39–53.Google Scholar
  5. 5.
    Levanova, T.V., Loresh,M.A., and Nikitin, A.G., Algorithms of Ant System and Simulated Annealing for the Simplest Location Problem, Proc. Conf. Discrete Analysis and Operation Research," Novosibirsk, 2002.Google Scholar
  6. 6.
    Levanova, T.V. and Loresh, M.A., Algorithm of Ant System for the Problem of p-median, Inf. Bull. of Math. Progr. Assoc., Scientific Edition, 2003, no. 10, pp. 172–173.Google Scholar
  7. 7.
    Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., Optimization by Simulated Annealing, Science, 1983, vol. 220, pp. 671–680.Google Scholar
  8. 8.
    Lundy, M. and Mees, A., Convergence of an Annealing Algorithm, Math. Program., 1986, vol. 34, pp. 111–124.Google Scholar
  9. 9.
    Cerny, V., A Thermodinamical Approach to the Traveling Salesman Problem: An Efficient Simulated Algorithm, J. Optimiz. Theory Appl., 1985, vol. 45, pp. 41–55.Google Scholar
  10. 10.
    Pirlot, M., General Local Search Methods, Eur. J. Oper. Res., 1996, vol. 92, pp. 493–511.Google Scholar
  11. 11.
    Kochetov, Yu.A., Probabilistic Methods of Local Search for Problems of Discrete Optimization, in Diskretnaya matematika i ee prilozheniya: sb. lektsii molodezhnykh nauchnykh shkol po diskret. mat. i ee prilozheniyam (Discrete Mathematics and its Applications. Collected Panel Papers of Workshops on Discrete Mathematics and its Applications), Moscow: Mosk. Gos. Univ., 2001, pp. 84–117.Google Scholar
  12. 12.
    Goncharov, E.N., Gorbachevskaya, L.E., Kochetov, Yu.A., et al., Library of Benchmarks for Discrete Location Problems, Proc. Int. Conf. Discrete Analysis and Operation Research", Novosibirsk, 2000, pp. 163 ( Scholar
  13. 13.
    Levanova, T.V., Dual Greedy Algorithm for the Problem of p-median and Its Generalizations, Preprint of Omsk State Univ., 1998, no. 98-4, pp. 13.Google Scholar
  14. 14.
    Beasley, J., Or-Library: Distributing Test Problems by Electronic Mail, J. Opl. Res. Soc., 1990, no. 41(11), pp. 1069–1072.Google Scholar
  15. 15.
    Whitaker, R., A Fast Algorithm for the Greedy Interchange of Large-scale Clustering and Median Location Problems, INFOR, 1983, no. 21, pp. 95–108.Google Scholar
  16. 16.
    Resende, M.G.C. and Werneck, R.F., On the Implementation of a Swap-based Local Search Procedure for the p-median Problem, Technical Report TD-5E4QKA, AT&T Labs Research, 2002.Google Scholar
  17. 17.
    Chiyoshi, F. and Galvao, R., A Statistical Analisys of Simulated Annealing Applied to the p-median Problem, Ann. Oper. Res., 2000, no. 96, pp. 61–74.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2004

Authors and Affiliations

  • T. V. Levanova
    • 1
  • M. A. Loresh
    • 2
  1. 1.Omsk Affiliated Institute of Mathematics, Siberian Branch, Russian Academy of SciencesOmskRussia
  2. 2.Omsk State UniversityOmskRussia

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