Abstract
In the discrete (r |p)-centroid problem two decision makers, a leader and a follower, compete to attract clients from a given market. The leader opens p facilities, anticipating that the follower will react to the decision by opening his own r facilities. The decision makers try to maximize their own profits. This Stackelberg game is \(\Sigma_2^P\)-hard. So, we develop a hybrid memetic algorithm for it. A probabilistic tabu search heuristic is applied for improving the offspring. To obtain an upper bound, we reformulate the problem as a mixed integer program with an exponential number of constraints and variables. Selecting some of them, we get the desired upper bound. To find optimal solutions, we iteratively modify the subset of the constraints and variables. This approach is tested on the benchmarks from the library Discrete Location Problems. The optimal solutions are found for r = p = 5, 100 clients, and 100 facilities.
This work was partly supported by the RFBR grant ü 08-07-00037, ADTP grant 2.1.1/3235.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alekseeva, E., Kochetova, N.: Upper and lower bounds for the competitive p-median problem. In: Proceedings of XIV Baikal International School–Seminar Optimization Methods and Their Applications, Irkutsk, vol. 1, pp. 563–569 (2008) (in Russian)
Alekseeva, E., Kochetova, N., Kochetov, Y., Plyasunov, A.: A hybrid memetic algorithm for the competitive p-median problem. In: Preprints of the 13th IFAC Symposium on Information Control Problems in Manufacturing, Moscow, pp. 1516–1520 (2009)
Bertacco, L., Fischetti, M., Lodi, A.: A feasibility pump heuristic for general mixed–integer problems. Discrete Optimization 4(1), 63–76 (2007)
Benati, S., Laporte, G.: Tabu search algorithms for the (r|X p )–medianoid and (r|p)–centroid problems. Location Science 2(4), 193–204 (1994)
Bhadury, J., Eiselt, H., Jaramillo, J.: An alternating heuristic for medianoid and centroid problems in the plane. Computers and Operations Research 30, 553–565 (2003)
Glover, F., Laguna, M.: Tabu Search. Kluwer Acad. Publ., Boston (1997)
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, Chichester (1990)
Kochetov, Y.A., Kononov, A.V., Plyasunov, A.V.: Competitive facility location models. Computational Mathematics and Mathematical Physics 49, 994–1009 (2009)
Noltermeier, H., Spoerhose, J., Wirth, H.C.: Multiple voting location and single voting location on trees. European J. Oper. Res. 181, 654–667 (2007)
Rodriguez, C.M.C., Perez, J.A.M.: Multiple voting location problems. European J. of Oper. Res. 191(2), 437–453 (2008)
Sastry, K., Goldberg, D., Kendall, G.: Genetic algorithms. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies. Introductory Tutorials in Optimization and Decision Support Techniques, pp. 97–126. Springer, Heidelberg (2005)
Vasil’ev, I.L., Klimentova, K.B., Kochetov, Y.A.: New lower bounds for the facility location problem with clients’ preferences. Computational Mathematics and Mathematical Physics 49, 1010–1020 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Alekseeva, E., Kochetova, N., Kochetov, Y., Plyasunov, A. (2010). Heuristic and Exact Methods for the Discrete (r |p)-Centroid Problem. In: Cowling, P., Merz, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2010. Lecture Notes in Computer Science, vol 6022. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12139-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-12139-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12138-8
Online ISBN: 978-3-642-12139-5
eBook Packages: Computer ScienceComputer Science (R0)