Advertisement

Matheuristics and Exact Methods for the Discrete (r|p)-Centroid Problem

  • Ekaterina AlekseevaEmail author
  • Yury Kochetov
Part of the Studies in Computational Intelligence book series (SCI, volume 482)

Abstract

In the (r|p)-centroid problem, there are two decision makers which we refer to as a leader and a follower. They compete to serve customers from a given market by opening a certain number of facilities. The decision makers open facilities in turn. At first, the leader decides where to locate p facilities taking into account the follower’s reaction. Later on, the follower opens other r facilities. We assume that the customers’ preferences among the opened facilities are based only on the distances to these facilities rather than the quality of service provided by the decision makers.

Keywords

Feasible Solution Tabu Search Exact Method Tabu List Competitive 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Alekseeva, E., Beresnev V., Kochetov, Y. et al.: Benchmark library: Discrete Location Problems, http://math.nsc.ru/AP/benchmarks/Competitive/p_me_comp_eng.html
  2. 2.
    Alekseeva, E., Kochetova, N., Kochetov, Y., Plyasunov, A.: Heuristic and exact methods for the discrete (r |p)-centroid problem. In: Cowling, P., Merz, P. (eds.) EvoCOP 2010. LNCS, vol. 6022, pp. 11–22. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Ben–Ayed, O.: Bilevel linear programming. Comput. Oper. Res. 20(5), 485–501 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Benati, S., Laporte, G.: Tabu search algorithms for the (r|X p)–medianoid and (r|p)–centroid problems. Location Science 2, 193–204 (1994)zbMATHGoogle Scholar
  5. 5.
    Beresnev, V., Melnikov, A.: Approximate algorithms for the competitive facility location problem. J. Appl. Indust. Math. 5(2), 180–190 (2011)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bhadury, J., Eiselt, H., Jaramillo, J.: An alternating heuristic for medianoid and centroid problems in the plane. Comp. & Oper. Res. 30, 553–565 (2003)zbMATHCrossRefGoogle Scholar
  7. 7.
    Burke, E.K., Kendall, G.: Introductory Tutorials in Optimization and Decision Support Techniques. Springer, US (2005)zbMATHGoogle Scholar
  8. 8.
    Campos-Rodríguez, C.M., Moreno Pérez, J.A.: Multiple voting location problems. European J. Oper. Res. 191, 437–453 (2008)CrossRefGoogle Scholar
  9. 9.
    Campos-Rodríguez, C., Moreno-Pérez, J.A.: Relaxation of the condorcet and simpson conditions in voting location. European J. Oper. Res. 145(3), 673–683 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Campos-Rodríguez, C., Moreno-Pérez, J.A., Notelmeier, H., Santos-Peñate, D.R.: Two-swarm PSO for competitive location. In: Krasnogor, N., Melián-Batista, M.B., Pérez, J.A.M., et al. (eds.) NICSO 2008. SCI, vol. 236, pp. 115–126. Springer, Heidelberg (2009)Google Scholar
  11. 11.
    Campos-Rodríguez, C., Moreno-Pérez, J.A., Santos-Peñate, D.R.: Particle swarm optimization with two swarms for the discrete (r|p)-centroid problem. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds.) EUROCAST 2011, Part I. LNCS, vol. 6927, pp. 432–439. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  12. 12.
    Campos-Rodríguez, C.M., Moreno-Pérez, J.A., Santos-Peñate, D.: An exact procedure and LP formulations for the leader–follower location problem. Business and Economics TOP 18(1), 97–121 (2010)zbMATHGoogle Scholar
  13. 13.
    Carrizosa, E., Davydov, I., Kochetov, Y.: A new alternating heuristic for the (r|p)–centroid problem on the plane. In: Operations Research Proceedings 2011, pp. 275–280. Springer (2012)Google Scholar
  14. 14.
    Davydov, I.: Tabu search for the discrete (r|p)–centroid problem. J. Appl. Ind. Math. (in press)Google Scholar
  15. 15.
    Davydov, I., Kochetov, Y., Plyasunov, A.: On the complexity of the (r|p)–centroid problem on the plane. TOP (in press)Google Scholar
  16. 16.
    Dréo, J., Pétrowski, A., Siarry, P., Taillard, E.: Metaheuristics for Hard Optimization. In: Chatterjee, A., Siarry, P. (eds.) Methods and Case Studies. Springer, Heidelberg (2006)Google Scholar
  17. 17.
    Friesz, T.L., Miller, T., Tobin, R.L.: Competitive network facility location models: a survey. Regional Science 65, 47–57 (1988)Google Scholar
  18. 18.
    Goldman, A.: Optimal center location in simple networks. Transportation Science 5, 212–221 (1971)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Ghosh, A., Craig, C.: A Location allocation model for facility planning in a competitive environment. Geographical Analysis 16, 39–51 (1984)CrossRefGoogle Scholar
  20. 20.
    Garey, M.R., Johnson, D.S.: Computers and intractability (a guide to the theory of NP-completeness). W.H. Freeman and Company, New York (1979)zbMATHGoogle Scholar
  21. 21.
    Glover, F., Laguna, M.: Tabu Search. Kluwer Acad. Publ., Boston (1997)zbMATHCrossRefGoogle Scholar
  22. 22.
    Hakimi, S.L.: Locations with spatial interactions: competitive locations and games. In: Mirchandani, P.B., Francis, R.L. (eds.) Discrete Location Theory, pp. 439–478. Wiley & Sons (1990)Google Scholar
  23. 23.
    Hakimi, S.L.: On locating new facilities in a competitive environment. European J. Oper. Res. 12, 29–35 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Hakimi, S.L.: On locating new facilities in a competitive environment. In: Annual ORSA-TIMS Meeting, Houston (1981)Google Scholar
  25. 25.
    Hotelling, H.: Stability in competition. Economic J. 39, 41–57 (1929)CrossRefGoogle Scholar
  26. 26.
    Hansen, P., Labbé, M.: Algorithms for voting and competitive location on a network. Transportation Science 22(4), 278–288 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  27. 27.
    Hansen, P., Mladenović, N.: Variable neighborhood search: principles and applications. European J. Oper. Res. 130, 449–467 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  28. 28.
    Küçükaudin, H., Aras, N., Altinel, I.K.: Competitive facility location problem with attractiveness adjustment of the follower. A bilevel programming model and its solution. European J. Oper. Res. 208, 206–220 (2011)CrossRefGoogle Scholar
  29. 29.
    Kariv, O., Hakimi, S.: An algoritmic approach to network location problems. The p-medians. SIAM J. Appl. Math. 37, 539–560 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    Kochetov, Y.A.: Facility location: discrete models and local search methods. In: Chvatal, V. (ed.) Combinatorial Optimization. Methods and Applications, pp. 97–134. IOS Press, Amsterdam (2011)Google Scholar
  31. 31.
    Kress, D., Pesch, E.: Sequential competitive location on networks. European J. Oper. Res. 217(3), 483–499 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  32. 32.
    Maniezzo, V., Stützle, T., Voß, S. (eds.): Matheuristics. Hybridizing Metaheuristics and Mathematical Programming. Annals of Information Systems, vol. 10 (2010)Google Scholar
  33. 33.
    Megiddo, N., Zemel, E., Hakimi, S.: The maximum coverage location problem. SIAM J. Algebraic and Discrete Methods 4, 253–261 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  34. 34.
    Mladenovic, N., Brimberg, J., Hansen, P., Moreno-Pérez, J.A.: The p-median problem: a survey of metaheuristic approaches. European J. Oper. Res. 179, 927–939 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  35. 35.
    Noltemeier, H., Spoerhase, J., Wirth, H.: Multiple voting location and single voting location on trees. European J. Oper. Res. 181, 654–667 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  36. 36.
    Plastia, F., Carrizosa, E.: Optimal location and design of a competitive facility. Math. Program., Ser A. 100, 247–265 (2004)CrossRefGoogle Scholar
  37. 37.
    Plastria, F., Vanhaverbeke, L.: Discrete models for competitive location with foresight. Comp. & Oper. Res. 35(3), 683–700 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    Roboredo, M.C., Pessoa, A.A.: A branch-and-cut algorithm for the discrete (r|p)-centroid problem. European J. Oper. Res. (in press)Google Scholar
  39. 39.
    Resende, M., Werneck, R.: On the implementation of a swap-based local search procedure for the p-median problem. In: Ladner, R.E. (ed.) Proceedings of the Fifth Workshop on Algorithm Engineering and Experiments (ALENEX 2003), pp. 119–127. SIAM, Philadelphia (2003)Google Scholar
  40. 40.
    Spoerhase, J.: Competitive and Voting Location. In: Dissertation. Julius Maximilian University of Würzburg (2010)Google Scholar
  41. 41.
    Serra, D., ReVelle, C.: Competitive location in discrete space. In: Drezner, Z. (ed.) Facility Location - A Survey of Applications and Methods, pp. 367–386. Springer, New York (1995)CrossRefGoogle Scholar
  42. 42.
    Serra, D., ReVelle, C.: Market capture by two competitors: the pre-emptive capture problem. J. Reg. Sci. 34(4), 549–561 (1994)CrossRefGoogle Scholar
  43. 43.
    Spoerhase, J., Wirth, H. (r,p)-centroid problems on paths and trees. J. Theor. Comp. Sci. Archive. 410(47–49), 5128–5137 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  44. 44.
    Saidani, N., Chu, F., Chen, H.: Competitive facility location and design with reactions of competitors already in the market. European J. Oper. Res. 219, 9–17 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  45. 45.
    Smith, J.C., Lim, C., Alptekinoglu, A.: Optimal mixed-integer programming and heuristic methods for a bilevel Stackelberg product introduction game. Nav. Res. Logist. 56(8), 714–729 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  46. 46.
    Santos-Peñate, D.R., Suárez-Vega, R., Dorta-González, P.: The leader-follower location model. Networks and Spatial Economics 7, 45–61 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  47. 47.
    Teramoto, S., Demaine, E., Uehara, R.: Voronoi game on graphs and its complexity. In: IEEE Symposium on Computational Intelligence and Games, pp. 265–271 (2006)Google Scholar
  48. 48.
    Vasilev, I.L., Klimentova, K.B., Kochetov, Y.A.: New lower bounds for the facility location problem with clients preferences. Comp. Math. Math. Phys. 49(6), 1055–1066 (2009)MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia

Personalised recommendations