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Annals of Operations Research

, Volume 167, Issue 1, pp 87–105 | Cite as

A robust and efficient algorithm for planar competitive location problems

  • J. L. Redondo
  • J. Fernández
  • I. García
  • P. M. Ortigosa
Article

Abstract

In this paper we empirically analyze several algorithms for solving a Huff-like competitive location and design model for profit maximization in the plane. In particular, an exact interval branch-and-bound method and a multistart heuristic already proposed in the literature are compared with uego (Universal Evolutionary Global Optimizer), a recent evolutionary algorithm. Both the multistart heuristic and uego use a Weiszfeld-like algorithm as local search procedure. The computational study shows that uego is superior to the multistart heuristic, and that by properly fine-tuning its parameters it usually (in the computational study, always) find the global optimal solution, and this in much less time than the interval branch-and-bound method. Furthermore, uego can solve much larger problems than the interval method.

Keywords

Continuous location Competition Weiszfeld-like algorithm Heuristic Evolutionary algorithm Computational study 

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References

  1. Benati, S., & Laporte, G. (1994). Tabu search algorithms for the (r|X p)-medianoid and (r|p)-centroid problems. Location Science, 2, 193–204. Google Scholar
  2. Drezner, Z. (1984). The p-center problem: heuristic and optimal algorithms. Journal of the Operational Research Society, 35, 741–748. CrossRefGoogle Scholar
  3. Drezner, T. (1994). Optimal continuous location of a retail facility, facility attractiveness, and market share: an interactive model. Journal of Retailing, 70, 49–64. CrossRefGoogle Scholar
  4. Drezner, T. (1995). Competitive location in the plane. In Facility location: a survey of applications and methods (pp. 285–300). Berlin: Springer. Google Scholar
  5. Drezner, T. (1998). Location of multiple retail facilities with a limited budget – in continuous space. Journal of Retailing and Consumer Services, 5, 173–184. CrossRefGoogle Scholar
  6. Drezner, T., & Drezner, Z. (2004). Finding the optimal solution to the Huff based competitive location model. Computational Management Science, 1, 193–208. CrossRefGoogle Scholar
  7. Drezner, Z., & Suzuki, A. (2004). The big triangle small triangle method for the solution of non-convex facility location problems. Operations Research, 52, 128–135. CrossRefGoogle Scholar
  8. Drezner, T., Drezner, Z., & Salhi, S. (2002). Solving the multiple competitive facilities location problem. European Journal of Operational Research, 142, 138–151. CrossRefGoogle Scholar
  9. Erkut, E., & Neuman, S. (1989). Analytical models for locating undesirable facilities. European Journal of Operational Research, 40, 275–291. CrossRefGoogle Scholar
  10. Fernández, J., & Pelegrín, B. (2001). Using interval analysis for solving planar single-facility location problems: new discarding tests. Journal of Global Optimization, 19, 61–81. CrossRefGoogle Scholar
  11. Fernández, J., Fernández, P., & Pelegrín, B. (2000). A continuous location model for siting a non-noxious undesirable facility within a geographical region. European Journal of Operational Research, 121, 259–274. CrossRefGoogle Scholar
  12. Fernández, J., Fernández, P., & Pelegrín, B. (2002). Estimating actual distances by norm functions: a comparison between the l k,p,θ-norm and the \(l_{b_{1},b_{2},\theta}\) -norm and a study about the selection of the data set. Computers and Operations Research, 29, 609–623. CrossRefGoogle Scholar
  13. Fernández, J., Pelegrín, B., Plastria, F., & Tóth, B. (2007). Solving a Huff-like competitive location and design model for profit maximization in the plane. European Journal of Operational Research, 179, 1274–1287. CrossRefGoogle Scholar
  14. Glover, F., & Laguna, M. (1997). Tabu search. Dordrecht: Kluwer Academic. Google Scholar
  15. Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning. Reading: Addison–Wesley. Google Scholar
  16. González-Linares, J. M., Guil, N., Zapata, E. L., Ortigosa, P. M., & García, I. (2000). Deformable shapes detection by stochastic optimization. In 2000 IEEE international conference on image processing (ICIP’2000), Vancouver, Canada, 10–13 September 2000. Google Scholar
  17. Hakimi, S. L. (1990). Locations with spatial interactions: competitive locations and games. In R. L. Francis & P. B. Mirchandani (Eds.), Discrete location theory (pp. 439–478). New York: Wiley/Interscience. Google Scholar
  18. Hammer, R., Hocks, M., Kulisch, U., & Ratz, D. (1995). C++ Toolbox for verified computing, I: basic numerical problems: theory, algorithms, and programs. Berlin: Springer. Google Scholar
  19. Hansen, P., & Mladenović, N. (2001). Variable neighborhood search: principles and applications. European Journal of Operational Research, 130, 449–467. CrossRefGoogle Scholar
  20. Hansen, P., Peeters, D., Richard, D., & Thisse, J. F. (1985). The minisum and minimax location problems revisited. Operations Research, 33, 1251–1265. CrossRefGoogle Scholar
  21. Hansen, P., Jaumard, B., & Tuy, H. (1995). Global optimization in location. In Facility location: a survey of applications and methods (pp. 43–68). Berlin: Springer. Google Scholar
  22. Huff, D. L. (1964). Defining and estimating a trading area. Journal of Marketing, 28, 34–38. CrossRefGoogle Scholar
  23. Jamarillo, J. H., Bhadury, J., & Batta, R. (2002). On the use of genetic algorithms to solve location problems. Computers and Operations Research, 29, 761–779. CrossRefGoogle Scholar
  24. Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680. CrossRefGoogle Scholar
  25. Knüppel, O. (1993). PROFIL/BIAS—a fast interval library. Computing, 53, 277–287. CrossRefGoogle Scholar
  26. Ortigosa, P. M., García, I., & Jelasity, M. (2001). Reliability and performance of uego, a clustering-based global optimizer. Journal of Global Optimization, 9, 265–289. CrossRefGoogle Scholar
  27. Pelegrín, B., & Cánovas, L. (1998). A new assignment rule to improve seed points algorithms for the continuous k-center problem. European Journal of Operational Research, 104, 266–374. CrossRefGoogle Scholar
  28. Pérez-Brito, D., Moreno-Pérez, J. A., & García-González, C. G. (2004). Búsqueda por entornos variables: desarrollo y aplicaciones en localización. In B. Pelegrín (Ed.), Avances en localización de servicios y aplicaciones (pp. 349–381). Murcia: Servicio de Publicaciones Universidad de Murcia. Google Scholar
  29. Plastria, F. (1992). GBSSS: The generalized big square small square method for planar single-facility location. European Journal or Operational Research, 62, 163–174. CrossRefGoogle Scholar
  30. Redondo, J. L., Ortigosa, P. M., García, I., & Fernández, J. J. (2004). Image registration in electron microscopy. A stochastic optimization approach. In Lecture notes in computer science : Vol. 3212. Proceedings of the international conference on image analysis and recognition, ICIAR 2004 II (pp. 141–149). Berlin: Springer. Google Scholar
  31. Solis, F. J., & Wets, R. J. B. (1981). Minimization by random search techniques. Mathematics of Operations Research, 6, 19–30. CrossRefGoogle Scholar
  32. Tuy, H., Al-Khayyal, F., & Zhou, F. (1995). A D.C. optimization method for single facility location problems. Journal of Global Optimization, 7, 209–227. CrossRefGoogle Scholar
  33. Weber, A. (1909). Über den Standort der Industrien. 1. Teil: Reine Theorie des Standordes. Germany: Tübingen. Google Scholar
  34. Weiszfeld, E. (1937). Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Mathematical Journal, 43, 355–386. Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • J. L. Redondo
    • 1
  • J. Fernández
    • 2
    • 3
  • I. García
    • 1
  • P. M. Ortigosa
    • 1
  1. 1.Department of Computer Arquitecture and ElectronicsUniversity of AlmeríaAlmeríaSpain
  2. 2.Facultad de MatemáticasUniversidad de MurciaEspinardoSpain
  3. 3.Department of Statistics and Operations ResearchUniversity of MurciaMurciaSpain

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