Approximating the Pareto-front of Continuous Bi-objective Problems: Application to a Competitive Facility Location Problem

  • J. L. Redondo
  • J. Fernández
  • J. D. Álvarez
  • A. G. Arrondoa
  • P. M. Ortigosa
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 171)


A new general multi-objective optimization heuristic algorithm, suitable for being applied to continuous multi-objective optimization problems is proposed. It deals with the problem at hand in a fast and efficient way. It combines ideas from different multi-objective and single-objective optimization evolutionary algorithms, although it also incorporates new devices which help to reduce the computational requirements, and also to improve the quality of the provided solutions. To show its applicability, a bi-objective competitive facility location and design problem is considered. This problem has been previously tackled through exact general methods, but they require high computational effort. A comprehensive computational study shows that the heuristic method is competitive, being able to reduce, in average, the computing time of the exact method by approximately 98%, and offering good quality in the final solutions.


Multiobjective Optimization Demand Point Multiobjective Optimization Problem Competitive Location Competitive Facility Location 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)CrossRefGoogle Scholar
  2. 2.
    Fernández, J., Tóth, B.: Obtaining an outer approximation of the efficient set of nonlinear biobjective problems. Journal of Global Optimization 38(2), 315–331 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Fernández, J., Tóth, B.: Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound method. Computational Optimization and Applications 42(3), 393–419 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Hammer, R., Hocks, M., Kulisch, U., Ratz, D.: C++ Toolbox for Verified Computing I: Basic Numerical Problems: Theory, Algorithms, and Programs. Springer, Berlin (1995)zbMATHGoogle Scholar
  5. 5.
    Hendrix, E.M.T., Toth, B.G.: Introduction to Nonlinear and Global Optimization. Springer, New York (2010)zbMATHCrossRefGoogle Scholar
  6. 6.
    Knowles, J.D., Corne, D.W.: The pareto archived evolution strategy: A new baseline algorithm for pareto multiobjective optimisation, vol. 1, pp. 98–105. IEEE Service Center (1999)Google Scholar
  7. 7.
    Knüppel, O.: PROFIL/BIAS - a fast interval library. Computing 1(53), 277–287 (1993)Google Scholar
  8. 8.
    Nebro, A.J., Luna, F., Alba, E., Dorronsoro, B., Durillo, J.J., Beham, A.: AbYSS: Adapting scatter search to multiobjective optimization. IEEE Transactions on Evolutionary Computation 12(4), 439–457 (2008)CrossRefGoogle Scholar
  9. 9.
    Ortigosa, P.M., García, I., Jelasity, M.: Reliability and performance of UEGO, a clustering-based global optimizer. Journal of Global Optimization 19(3), 265–289 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Redondo, J.L., Fernández, J., Arrondo, A.G., García, I., Ortigosa, P.M.: Fixed or variable demand? does it matter when locating a facility? OMEGA-International journal of management science 40(1), 9–20 (2012)CrossRefGoogle Scholar
  11. 11.
    Redondo, J.L., Fernández, J., García, I., Ortigosa, P.M.: A robust and efficient global optimization algorithm for planar competitive location problems. Annals of Operations Research 167(1), 87–106 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K.C., Tsahalis, D.T., Périaux, J., Papailiou, K.D., Fogarty, T. (eds.) Evolutionary Methods for Design Optimization and Control with Applications to Industrial Problems, Athens, Greece, pp. 95–100 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • J. L. Redondo
    • 1
  • J. Fernández
    • 3
  • J. D. Álvarez
    • 2
  • A. G. Arrondoa
    • 3
  • P. M. Ortigosa
    • 4
  1. 1.Dpt. of Computer Architecture and TechnologyUniversity of GranadaGranadaSpain
  2. 2.Dpt. of Computer Sciences and LanguagesUniversity of Almería, ceiA3AlmeríaSpain
  3. 3.Dpt. of Statistics and Operations ResearchUniversity of MurciaMurciaSpain
  4. 4.Dpt. of Computer Architecture and ElectronicsUniversity of Almería, ceiA3AlmeríaSpain

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