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An Efficient Genetic Algorithm for the p-Median Problem

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Abstract

We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.

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References

  • Avella, P. and tA. Sassano. (2001). “On the p-Median Polytope.” Mathematical Programming 89(3), 395–411.

    Google Scholar 

  • Beasley, J.E. (1990). “OR-Library –Distributing Test Problems by Electronic Mail.” Journal of the Operational Research Society 41(11), 1069–1072.

    Google Scholar 

  • Berman, O., tZ. Drezner, and G.O. Wesolowsky. (2002). “Locating Unreliable Service Facilities that Are Distance Sensitive.” Computers and Operations Research, in press.

  • Bozkaya, B., tJ. Zhang, and E. Erkut. (2002). “A Genetic Algorithm for the p-Median Problem.” In Z. Drezner and H. Hamacher (eds.), Facility Location: Applications and Theory. Berlin: Springer.

    Google Scholar 

  • Chiyoshi, F. and tR.D. Galvão. (2000). “A Statistical Analysis of Simulated Annealing Applied to the p-Median Problem.” Annals of Operations Research 96, 61–74.

    Google Scholar 

  • Cornuejols, G., tM.L. Fisher, and G.L. Nemhauser. (1977). “Location of Bank Accounts to Optimise Float: an Analytic Study of Exact and Approximate Algorithms.” Management Science 23, 789–810.

    Google Scholar 

  • Daskin, M.S. (1995). Network and Discrete Location: Models, Algorithms and Applications. New York: Wiley (SITATION can be downloaded from http://users.iems.nwu.edu/~msdaskin/BookSoftware.htm –as of July 2002).

    Google Scholar 

  • Densham, P.J. and tG. Rushton. (1992). “AMore Efficient Heuristic for Solving Large p-Median Problems.” Papers in Regional Science 71, 307–329.

    Google Scholar 

  • Dibble, C. and tP.J. Densham. (1993). “Generating Interesting Alternatives in GIS and SDSS Using Genetic Algorithms.” In GIS/LIS 1993.

  • Dowsland, K.A. (1996). “Genetic Algorithms –A Tool for OR?” Journal of Operational Research Society 47, 550–561.

    Google Scholar 

  • Erkut, E., tT. Myroon, and K. Strangway. (2000). “TransAlta Redesigns Its Service Delivery Network.” Interfaces 30(2), 54–69.

    Google Scholar 

  • Fitzsimmons, J.A. and tA.L. Austin. (1983). “AWarehouse Location Model Helps Texas Comptroller Select Out-of-State Audit Offices.” Interfaces 13(5), 40–46.

    Google Scholar 

  • Galvão, R.D. (1980). “A Dual-Bounded Algorithm for the p-Median Problem.” Operations Research 28(5), 1112–1121.

    Google Scholar 

  • Galvão, R.D. and tL.A. Raggi. (1989). “A Method for Solving to Optimality Uncapacitated Location Problems.” Annals of Operations Research 18, 225–244.

    Google Scholar 

  • Galvão, R.D. and tC. ReVelle. (1996). “A Lagrangean Heuristic for the Maximal Covering Location Problem.” European Journal of Operations Research 88, 114–123.

    Google Scholar 

  • Hosage, C.M. and tM.F. Goodchild. (1986). “Discrete Space Location–Allocation Solutions from Genetic Algorithms.” Annals of Operations Research 6, 35–46.

    Google Scholar 

  • Koerkel, M. (1989). “On the Exact Solution of Large-Scale Simple Plant Location Problems.” European Journal of Operations Research 39, 157–173.

    Google Scholar 

  • Moreno-Perez, J.A., tJ.M. Moreno-Vega, and N. Mladenovic. (1994). “Tabu Search and Simulated Annealing in p-Median Problem.” In Proceedings of the Canadian Operational Research Society Conference, Montreal.

  • Murray, A.T. and R.L. Church. (1996). “Applying Simulated Annealing to Location-Planning Models.” Journal of Heuristics 2, 31–53.

    Google Scholar 

  • Narula, S.C., tU.I. Ogbu, and H.M. Samuelsson. (1997). “An Algorithm for the p-Median Problem.” Operations Research 25, 709–712.

    Google Scholar 

  • Pizzolato, N.D. (1994). “A Heuristic for Large-Size p-Median Location Problems with Application to School Location.” Annals of Operations Research, 50 473–485.

    Google Scholar 

  • Reeves, C.R. (1993). “Genetic Algorithms.” In C.R. Reeves (ed.), Modern Heuristic Techniques for Combinatorial Problems. Chapter 4, pp. 151–196.

  • ReVelle, C. and tR. Swain. (1970). “Central Facilities Location.” Geographical Analysis 2, 30–42.

    Google Scholar 

  • Rolland, E., tD.A. Schilling, and J.R. Current. (1997). “An Efficient Tabu Search Procedure for the p-Median Problem.” European Journal of Operational Research 96, 329–342.

    Google Scholar 

  • Rosing, K.E. and tC.S. ReVelle. (1997). “Heuristic Concentration: Two-Stage Solution Construction.” European Journal of Operational Research 97, 75–86.

    Google Scholar 

  • Rosing, K.E., tC.S. ReVelle, and D.A. Schilling. (1999). “A Gamma Heuristic for the p-Median Problem.” European Journal of Operational Research 117, 522–532.

    Google Scholar 

  • Teitz, M.B. and tP. Bart. (1968). “Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph.” Operations Research 16, 955–961.

    Google Scholar 

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Alp, O., Erkut, E. & Drezner, Z. An Efficient Genetic Algorithm for the p-Median Problem. Annals of Operations Research 122, 21–42 (2003). https://doi.org/10.1023/A:1026130003508

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