Abstract
A GA-based approach is introduced to address the continuous location–allocation problem. Selection and removal procedures based on groups of chromosomes instead of individual chromosomes are put forward and specific crossover and mutation operators that rely on the impact of the genes are proposed. A new operator that injects once in a while new chromosomes into the population is also introduced. This provides diversity within the search and attempts to avoid early convergence. This approach is tested on existing data sets using several runs to evaluate the robustness of the proposed GA approach.
Similar content being viewed by others
References
Bongartz, I., P.H. Calamai and A.R. Conn. (1994). “A Projection Method for lp-Norm Location–Allocation Problems.” Mathematical Programming 66, 283–312.
Brimberg, J., P. Hansen, N. Mladenović, and E.D. Taillard. (2000). “Improvements and Comparison of Heuristics for Solving the Uncapacitated Multisource Weber Problem.” Operations Research 48, 444–460.
Brimberg, J. and N. Mladenović. (1996a). “Variable Neighbourhood Algorithm for Solving the Continuous Location–Allocation Problem.” Studies in Locational Analysis 10, 1–10.
Brimberg, J. and N. Mladenović. (1996b). “Solving the Continuous Location–Allocation Problem with Tabu Search.” Studies in Locational Analysis 8, 23–32.
Cooper, L. (1963). “Location–Allocation Problem.” Operations Research 11, 331–343.
Cooper, L. (1964). “Heuristic Methods for Location–Allocation Problems.” SIAM Review 6, 37–53.
Drezner, Z. (1984). “The Planar Two-Center and Two-Median Problems.” Transportation Science 18, 351–361.
Eilon, S., C.D.T. Watson-Gandy, and N. Christofides. (1971). DistributionManagement. NewYork: Hafner.
Gamal, M. (2001). “Constructive and Population Based Heuristics for the Continuous Location–Allocation Problem.” Ph.D. Diss., School of Mathematics and Statistics, University of Birmingham.
Gamal, M.D.H. and S. Salhi. (2001). “Constructive Heuristics for the Uncapacitated Location–Allocation Problem.” Journal of the Operational Research Society 51, 1233–1240.
Gamal, M.D.H. and S. Salhi. (2002). “A Cellular Type Heuristic for the Multi-Weber Problem.” Computers and Operations Research 30.
Hansen, P., N. Mladenović, and E. Taillard. (1998). “Heuristic Solution of the Multisource Weber Problem as a p-Median Problem.” Operations Research Letters 22, 55–62.
Hodgson, H. and S. Salhi. (2003). “A Quadtree Method to Eliminate Aggregation Error in Point to Point Allocation.” Environment and Planning B (revised).
Houck, C.R., J.A. Joines, and M.G. Kay. (1996). “Comparison of Genetic Algorithms, Random Restart and Two-Opt Switching for Solving Large Location–Allocation Problems Problem.” European Journal of Operational Research 20, 387–396.
Kuenne, R.E. and R.M. Solland. (1972). “Exact and Approximate Solutions to the Multisource Weber Problem.” Mathematical Programming 3, 193–209.
Lindley and Scott. (1989). Cambridge Statistical Tables. London: Cambridge Press.
Love, R.F. and H. Juel. (1982). “Properties and SolutionMethods for Large Location–Allocation Problems.” Journal of the Operational Research Society 33, 443–452.
Love, R.F. and J.G. Morris. (1975). “A Computational Procedure for the Exact Solution of Location–Allocation Problems with Rectangular Distances.” Naval Research Logistics Quarterly 22, 441–453.
Michalewicz, Z. (1992). Genetic Algorithms + Data Structures = Evaluation Programs. New York: Springer.
Petch, R.J. (2001). “Constructive and GA Based Heuristics for the Vehicle Routing Problem with Multiple Trips.” Ph.D. Diss., School of Mathematics and Statistics, University of Birmingham.
Rosing, K.E. (1992). “An Optimal Method for Solving the (Generalized) Multi-Weber Problem.” European Journal of Operational Research 58, 414–426.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Salhi, S., Gamal, M. A Genetic Algorithm Based Approach for the Uncapacitated Continuous Location–Allocation Problem. Annals of Operations Research 123, 203–222 (2003). https://doi.org/10.1023/A:1026131531250
Issue Date:
DOI: https://doi.org/10.1023/A:1026131531250