Solving a Bicriteria Problem of Optimal Service Centers Location

  • Alexander A. Kolokolov
  • Lidia A. Zaozerskaya


The problem of service centers location is formulated as a bicriteria optimization problem of finding a dominating set in graph. We investigate the properties of this problem and propose the methods for its solving. The results of computational experiment for instances with random data are presented.


Integer programming Multiple-criterion optimization Graphs Service center Location problem L-class enumeration algorithm Trade offs 


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  1. 1.
    Balas, E., Carrera, M.C.: A dynamic subgradient-based branch and bound procedure for set covering. Oper. Res. 44(6), 875–890 (1996)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Balas, E., Ho, A.: Set covering algorithms using cutting planes, heuristics and subgradient optimization: a computational study. Math. Program. Study 12, 37–60 (1980)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Beasley, J.E., Chu P.C.: A genetic algorithm for the set covering problem. Eur. J. Oper. Res. 94(2), 394–404 (1996)CrossRefGoogle Scholar
  4. 4.
    Beasley, J.E., Jörnsten, K.: Enhancing an algorithm for set covering problems. Eur. J. Oper. Res. 58, 293–300 (1992)MATHCrossRefGoogle Scholar
  5. 5.
    Caprara, A., Fischetti, M., Toth, P.: Algorithms for the set covering problem. In: Technical Report OR-98-3, DEIS-Operations Research Group (1998)Google Scholar
  6. 6.
    Christofides, N.: Graph theory. An algorithmic approach. Management Science, Imperial College, Academic press Inc. London Ltd., 2nd printing (1977)Google Scholar
  7. 7.
    Ehrgott, M., Gandibleux, X.: Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys. International Series in Operations Research & Management Science, vol. 52. Springer, Heidelberg (2002)Google Scholar
  8. 8.
    Emelichev V.A., Kravtsov, M.K.: On the nonsolvability of the discrete optimization vectors problem on the subsets systems in the class of the algorithms of linear convolution of the criteria. Doclady Mathematics 334(1), 9–11, (1994) (in Russian)MathSciNetGoogle Scholar
  9. 9.
    Emelichev, V.A., Kravtsov, M.K., Yanushkevich, O.A.: Lexicographical optima of multicriteria discrete optimization problem. Matematicheskie Zametki. 58(3), 365–371 (1995) (in Russian)MathSciNetGoogle Scholar
  10. 10.
    Emelichev, V.A., Perepelitsa, V.A.: The complexity of discrete multicriteria problems. Discrete Math. Appl. 4(2), 89–117 (1994)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Eremeev, A.V.: A genetic algorithm with a non-binary representation for the set covering problem. In: Proceedings of OR’98, pp. 175–181. Springer-Verlag, New York (1999)Google Scholar
  12. 12.
    Eremeev, A.V., Kolokolov, A.A., Zaozerskaya, L.A.: A hybrid algorithm for set covering. In: Proceedings of International Workshop on Discrete Optimization Metods Design, pp. 123–129. Minsk (2000)Google Scholar
  13. 13.
    Eremeev, A.V., Zaozerskaya, L.A., Kolokolov, A.A.: A set covering problem: complexity, algoritms, experimental research. Discretnyi Analiz i Issledovanie Operatsii. 7(2), 22–46 (2000) (in Russian)MathSciNetMATHGoogle Scholar
  14. 14.
    Grossman, T., Wool, A.: Computational experience with approximation algorithms for the set covering problem. Eur. J. Oper. Res. 101(1), 81–92 (1997)MATHCrossRefGoogle Scholar
  15. 15.
    Jaszkiewicz, A.: A comparative study of multiple-objective metaheuristics on the bi-objective set covering problem and the pareto memetic algorithm. Ann. Oper. Res. 131(1–4), 135–158 (2004)MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Kitrinou, E., Kolokolov, A.A., Zaozerskaya, L.A.: The location choice for telecenters in remote areas. The case of the aegean islands. In: Proceedings of Discrete Optimization Methods in Production and Logistics (DOM-2004), pp. 61–65. Omsk, Nasledie Dialog-Sibir (2004)Google Scholar
  17. 17.
    Kolokolov, A.A.: Regular partitions and cuts in integer programming. Discrete Analysis and Operations Research, pp. 59–79. Kluver Academic Publisher, Netherland (1996)CrossRefGoogle Scholar
  18. 18.
    Kolokolov, A.A., Zaozerskaya, L.A.: A bicriteria problem of optimal service centers location. In: Proceedings of 12th IFAC International Symposium. vol. III, pp. 429–434. St. Etienne, France (2006)Google Scholar
  19. 19.
    Mannino, C., Sassano, A.: An exact algorithm for the maximum stable set problem. Comput. Optim. Appl. 3, 243–258 (1994)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Podinovski V.V., Gavrilov, V.M.: Optimization by Consequently Applied Criteria. Sovetskoe Radio Moscow (1975) (in Russian)Google Scholar
  21. 21.
    Solar, M., Parada, V., Urrutia, R.: A parallel genetic algorithm to solve the set-covering problem. Comput. Oper. Res. 29, 1221–1235 (2002)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Zaozerskaya, L.A. On L-class enumeration algorithm for set covering problem. In: Proc. of 11-th Baikal Intern. School-Seminar “Optimization Methods and Their Applications”. pp. 139–142 (1998) (in Russian)Google Scholar
  23. 23.
    Zaozerskaya, L.A., Kolokolov, A.A.: Study and solution of bicriteria set covering problem. Problemy Informatiki. 2, 11–18 (2009) (in Russian)Google Scholar

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • Alexander A. Kolokolov
    • 1
  • Lidia A. Zaozerskaya
    • 1
  1. 1.Omsk Branch of Sobolev Institute of MathematicsSiberian Branch of Russian Academy of SciencesOmskRussia

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