On heuristic bi-criterion methods for semi-obnoxious facility location

  • P. M. Ortigosa
  • E. M. T. Hendrix
  • J. L. Redondo


Locating a semi-obnoxious facility, like an airport or correctional center is typically a bi-criterion problem combining a convex objective function representing minimum transportation cost with a multi-extremal objective function representing the non-desirable part of the facility. Generic one or bi-objective heuristic methods can be applied to generate efficient locations for the problem. We consider the location of one facility in the plane and show that a simple random or grid search with filtering already provides a very good picture of the trade-off between the two objectives. Moreover, we argue that instead of using bi-criterion meta-heuristics, one could better exploit the convex–nonconvex structure of the problem applying the constraint method. We show how to evaluate the methods systematically using several heuristics from literature.


Location Obnoxious Pareto Bi-criterion Heuristic 



This work has been funded by Grants from the Spanish Ministry (TIN2012-37483), Junta de Andalucía (P10-TIC-6002, P11-TIC-7176 and P12-TIC-301), in part financed by the European Regional Development Fund (ERDF) and Fundación Séneca 15254/PI/10, the Agency of Science and Technology of the Region of Murcia. Juana López Redondo is a fellow of the Spanish “Ramón y Cajal” contract program, co-financed by the European Social Fund.


  1. 1.
    Blanquero, R., Carrizosa, E.: A d.c. biobjective location model. J. Glob. Optim. 23, 139–154 (2002)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Brimberg, J., Juel, H.: A bi-criteria model for locating a semi-desirable facility in the plane. Eur. J. Oper. Res. 1, 144–151 (1998)CrossRefGoogle Scholar
  3. 3.
    Brimberg, J., Juel, H.: A minisum model with forbidden regions for locating a semi-desirable facility in the plane. Locat. Sci. 6, 109–120 (1998)CrossRefGoogle Scholar
  4. 4.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evolut. Comput. 6(2), 182–197 (2002)CrossRefGoogle Scholar
  5. 5.
    Durillo, J., Nebro, A.: jMetal: A Java framework for multi-objective optimization. Adv. Eng. Softw. 42(10), 760–771 (2011)CrossRefGoogle Scholar
  6. 6.
    Ehrgott, M.: Multicriteria Optimization. Lecture Notes in Economics and Mathematical Systems. Springer, New York (2004)Google Scholar
  7. 7.
    Hansen, P., Peeters, D., Richard, D., Thisse, J.F.: The minisum and minimax location problems revisited. Oper. Res. 33, 1251–1265 (1985)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Hendrix, E.M., Toth, B.G.: Introduction to Nonlinear and Global Optimization. Springer, New York (2010)MATHGoogle Scholar
  9. 9.
    Marlin, S.A.: Public Investment Criteria. M.I.T. Press, Cambridge (1967)Google Scholar
  10. 10.
    Melachrinoudis, E.: Bicriteria location of a semi-obnoxious facility. Comput. Ind. Eng. 37, 581–593 (1999)CrossRefGoogle Scholar
  11. 11.
    Melachrinoudis, E., Xanthopulos, Z.: Semi-obnoxious single facility location in euclidean space. Comput. Oper. Res. 30, 2191–2209 (2003)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Nebro, A., Luna, F., Alba, E., Dorronsoro, B., Durillo, J., Beham, A.: AbYSS: adapting scatter search to multiobjective optimization. IEEE Trans. Evolut. Comput. 12(4), 439–457 (2008)CrossRefGoogle Scholar
  13. 13.
    Ortigosa, P., García, I., Jelasity, M.: Reliability and performance of UEGO, a clustering-based global optimizer. J. Glob. Optim. 19(3), 265–289 (2001)CrossRefMATHGoogle Scholar
  14. 14.
    Ortigosa, P., Hendrix, E., Redondo, J.: On Methods for Generating Semi-obnoxious Locations Heuristically. Technical Report, Wageningen School of Social Sciences (2011)Google Scholar
  15. 15.
    Price, W.L.: A controlled random search procedure for global optimization. Comput. J. 20, 367–370 (1979)CrossRefGoogle Scholar
  16. 16.
    Redondo, J., Fernández, J., Álvarez, J., Arrondo, A., Ortigosa, P.: Approximating the pareto-front of a planar bi-objective competitive facility location and design problem. Comput. Oper. Res. doi: 10.1016/j.cor.2014.02.013
  17. 17.
    Romero-Morales, D., Carrizosa, E., Conde, E.: Semi-obnoxious location models: a global optimization approach. Eur. J. Oper. Res. 102(2), 295–301 (1997)CrossRefMATHGoogle Scholar
  18. 18.
    Skriver, A., Andersen, K.: The bicriterion semi-obnoxious location problem (BSLP) solved by an \(\epsilon \)-approximation. Eur. J. Oper. Res. 146, 517–528 (2003)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Yapicioglu, H., Smith, A.E., Dozier, G.: Solving the semi-desirable facility location problem using bi-objective particle swarm. Eur. J. Oper. Res. 177, 733–749 (2007)CrossRefMATHGoogle Scholar
  20. 20.
    Zitzler, E.: Evolutionary algorithms for multiobjective optimization: methods and applications. Swiss Federal Institute of Technology (ETH) Zurich, Shaker Verlag, Germany. ISBN 3-8265-6831-1 (1999)Google Scholar
  21. 21.
    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, pp. 95–100. International center for numerical methods in engineering (CIMNE), Athens, Greece (2002)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • P. M. Ortigosa
    • 1
  • E. M. T. Hendrix
    • 2
  • J. L. Redondo
    • 1
  1. 1.Department of InformaticsUniversity of AlmeríaAlmeríaSpain
  2. 2.Computer Architecture, Universidad de Málaga and Operations Research and LogisticsWageningen UniversityWageningenThe Netherlands

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