Abstract
In this paper we focus on the capacitated multi-facility Weber problem with rectilinear, Euclidean, squared Euclidean and l p distances. This problem deals with locating m capacitated facilities in the Euclidean plane so as to satisfy the demand of n customers at the minimum total transportation cost. The location and the demand of each customer is known a priori and the transportation cost is proportional to the distance and the amount of .ow between customers and facilities. We present three new heuristic methods each of which is based on one of the three well-known metaheuristic approaches: simulated annealing, threshold accepting, and genetic algorithms. Computational results on benchmark instances indicate that the heuristics perform well in terms of the quality of solutions they generate. Furthermore, the simulated annealing-based heuristic implemented with the two-variable exchange neighborhood structure outperforms the other heuristics considered in the paper.
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References
Al-Loughani, I., 1997, Algorithmic approaches for solving the Euclidean distance location-allocation problems, PhD Dissertation, Industrial and System Engineering, Virginia Polytechnic Institute and State University, Blacksburgh, Virginia.
Bazaraa, M.S., Jarvis, J.J., and Sherali, H.D., 1990, Linear Programming and Network Flows. John Wiley and Sons Inc., Singapore.
Brimberg, J. and Love, R.F., 1993, Global convergence of a generalized iterative procedure for the minisum location problem with lp distances, Operations Research 41:1153–1163.
Cooper, L., 1972, The transportation-location problem, Operations Research 20:94–108.
Cooper, L., 1976, An e.cient heuristic algorithm for the transportationlocation problem, Journal of Regional Science 16:309–315.
Dongarra, J., 2006, Performance of various computers using standard linear equations software, Technical Report available online at http:// www.netlib.org/benchmark/performance.ps
Dueck, G. and Scheuer, T., 1990, Threshold accepting: A general purpose optimization algorithm appearing superior to simulated annealing, Journal of Computational Physics 90:161–175.
Eckert, C. and Gottlieb, J., 2002, Direct Representation and Variation Operators for the Fixed Charge Transportation Problem, in: Proceedings of 7th International Conference on Parallel Problem Solving from Nature – PPSN VII, Granada, Spain, pp. 77–87.
Francis R.L., McGinnis, L.F., and White, J.A., 1992, Facility Layout and Location: An Analytical Approach, 2nd edition, Prentice Hall, Upper Saddle River, NJ.
Gottlieb J. and Paulmann, L., 1998, Genetic algorithms for the .xed charge transportation problem, in: Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, pp. 330–335.
Gottlieb, J. and Eckert, C., 2000, A comparison of two representations for the .xed charge transportation problem, in: Proceedings of 6th International Conference on Parallel Problem Solving from Nature– PPSN VI, Berlin, Germany, pp. 345–354.
Gottlieb, J., Julstrom, B., Raidl, G., and Rothlauf, F., 2001, Prüfer numbers: A poor representation of spanning trees for evolutionary search, in: Proceedings of the 2001 Genetic and Evolutionary Computation Conference, San Francisco, California, pp. 343–350.
Hansen, P. and Mladenović, N., 2001, Variable neighborhood search: Principles and applications. European Journal of Operational Research 130:449–467.
Hansen, P., Perreur, J., and Thisse, F., 1980, Location theory, dominance and convexity: Some further results, Operations Research 28:1241– 1250.
Kirkpatrick, S., Gelatt, C.D., and Vecchi, M.P., 1983, Optimization by simulated annealing, Science, 4598:671–680.
Li, Y., Gen, M., and Ida, K., 1998, Fixed charge transportation problem by spanning tree-based genetic algorithm, Beijing Mathematics 4:239–249.
Ohlmann, J.W., and Thomas, B.W., 2006, A compressed annealing approach to the traveling salesman problem with time windows, INFORMS Journal on Computing, forthcoming.
Selim, S., 1979, Biconvex programming and deterministic and stochastic location allocation problems, Ph. D. dissertation, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia.
Sherali, H.D. and Nordai, F.L., 1988, NP-hard, capacitated, balanced pmedian problems on a chain graph with a continuum of link demands, Mathematics of Operations Research 13:32–49.
Sherali, H.D. and Tunçbilek, C.H., 1992, A squared-Euclidean distance location-allocation problem. Naval Research Logistics 39:447–469.
Sherali, H.D. and Adams, W.P., 1999, A reformulation-linearization technique for solving discrete and continuous nonconvex problems, Kluwer Academic Publishers, The Netherlands.
Sherali, H.D., Ramachandran, S., and Kim, S., 1994, A localization and reformulation discrete programming approach for the rectilinear distance location-allocation problem, Discrete Applied Mathematics 49:357–378.
Sherali, H.D., Al-Loughani, I., and Subramanian, S., 2002, Global optimization procedures for the capacitated Euclidean and l p distance multifacility location-allocation problems, Operations Research 50:433–448.
Weiszfeld, E., 1937, Sur le point lequel la somme des distances de n points donné est minimum, Tôhoku Mathematics Journal 43:355–386.
Wesolowsky, G., 1993, The Weber problem: history and perspectives, Location Science 1:5–23.
Yan, S. and Luo, S.C., 1999, Probabilistic local search algorithms for concave cost transportation network problems, European Journal of Operational Research 117:511–521.
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Aras, N., Yumusak, S., Altmel, I.K. (2007). Solving the Capacitated Multi-Facility Weber Problem by Simulated Annealing, Threshold Accepting and Genetic Algorithms. In: Doerner, K.F., Gendreau, M., Greistorfer, P., Gutjahr, W., Hartl, R.F., Reimann, M. (eds) Metaheuristics. Operations Research/Computer Science Interfaces Series, vol 39. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-71921-4_5
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DOI: https://doi.org/10.1007/978-0-387-71921-4_5
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