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The Parallel Variable Neighborhood Search for the p-Median Problem

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Abstract

The Variable Neighborhood Search (VNS) is a recent metaheuristic that combines series of random and improving local searches based on systematically changed neighborhoods. When a local minimum is reached, a shake procedure performs a random search. This determines a new starting point for running an improving search. The use of interchange moves provides a simple implementation of the VNS algorithm for the p-Median Problem. Several strategies for the parallelization of the VNS are considered and coded in C using OpenMP. They are compared in a shared memory machine with large instances.

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References

  • Beasley, J.E. (1985). “A Note on Solving Large p-Median Problems.” European Journal of Operational Research 21, 270–273.

    Google Scholar 

  • Erlenkotter, D. (1978). “A Dual-Based Procedure for Uncapacitated Facility Location.” Operations Research 26, 992–1009.

    Google Scholar 

  • Glover, F. (1989). “Tabu Search—Part I.” ORSA Journal on Computing 1, 190–206.

    Google Scholar 

  • Glover, F. (1990). “Tabu Search—Part II.” ORSA Journal on Computing 2, 4–32.

    Google Scholar 

  • Hanjoul, P. and D. Peeters. (1985). “A Comparison of Two Dual-Based Procedures for Solving the p-Median Problem.” European Journal of Operational Research 20, 387–396.

    Google Scholar 

  • Hansen, P. and N. Mladenovic. (1997). “Variable Neighborhood Search for the p-Median.” In Les Cahiers du GERAD G-97-39. Montreal, Canada.

  • Hansen, P. and N. Mladenovic. (1999). “An Introduction to Variable Neighborhood Search.” In S. Voss et al. (eds.), Proceedings of the 2nd International Conference on Metaheuristics—MIC97. Dordrecht: Kluwer.

    Google Scholar 

  • Hansen, P. and N. Mladenovic. (2000). “Variable Neighborhood Search: A Chapter of Handbook of Applied Optimization.” In Les Cahiers du GERAD G-2000-3. Montreal, Canada.

  • Hansen, P., N. Mladenovic, and D. Pérez-Brito. (2001). “Variable Neighborhood Decomposition Search.” Journal of Heuristics 7(3), 335–350.

    Google Scholar 

  • Holland, J.H. (1975). Adaptation in Natural and Artificial Systems. Ann Arbor, Michigan: The University of Michigan Press.

    Google Scholar 

  • Kariv, O. and S.L. Hakimi. (1969). “An Algorithmic Approach to Network Location Problems; Part 2. The p-Medians.” SIAM Journal on Applied Mathematics 37, 539–560.

    Google Scholar 

  • Kirkpatrick, S., C.D. Gelatt, and M.P. Vecchi. (1983). “Optimization by Simulated Annealing.” Science 220, 671–666.

    Google Scholar 

  • Kuehn, A.A. and M.J. Hamburger. (1963). “A Heuristic Program for LocatingWarehouses.” Management Science 9(4), 643–666.

    Google Scholar 

  • Maranzana, F.E. (1964). “On the Location of Supply Points to Minimize Transportation Costs.” Operations Research Quarterly 12, 138–139.

    Google Scholar 

  • Mladenovic, N. (1995). “A Variable Neighborhood Algorithm—A New Metaheuristic for Combinatorial Optimization.” Presented at Optimization Days, Montreal.

  • Mladenovic, N., J.A. Moreno-Pérez, and J. Marcos Moreno-Vega. (1996). “A Chain-Interchange Heuristic Method.” Yugoslav J. Oper. Res. 6, 41–54.

    Google Scholar 

  • OpenMP: A Proposed Industry Standard API for Shared Memory Programming. White Paper, Oct. 1997. (http://www.openmp.org/openmp/mp-documents/paper/paper.html).

  • Teitz, M.B. and P. Bart. (1968). “Heuristic Methods for Estimating the Generalized Vertex Median of a Weighted Graph.” Operations Research 16(5), 955–961.

    Google Scholar 

  • TSPLIB (1995). http://www.iwr.uni-heidelberg.de/iwr/comopt/software/TSPLIB95/.

  • Voss, S. (1996). “A Reverse Elimination Approach for the p-Median Problem.” Studies in Locational Analysis 8, 49–58.

    Google Scholar 

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García-López, F., Melián-Batista, B., Moreno-Pérez, J.A. et al. The Parallel Variable Neighborhood Search for the p-Median Problem. Journal of Heuristics 8, 375–388 (2002). https://doi.org/10.1023/A:1015013919497

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