Abstract
Design and analysis of computationally difficult instances is one of the promising areas in combinatorial optimization. In this paper we present several new classes of benchmarks for the Uncapacitated Facility Location Problem. The first class is polynomially solvable. It has many strong local optima and large mutual pair distances. Two other classes have exponential number of strong local optima. Finally, three last classes have large duality gap and one of them is the most difficult for metaheuristics and the branch and bound method.
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References
V. Beresnev, E. Gimadi, and V. Dement’ev. Extremal standardization problems. Nauka, 1978, (in Russian).
M. Daskin. Network and Discrete Location Problem: Models, Algorithms, and Applications. John Wiley & Sons, 1995.
Z. Drezner (Ed.) Facility Location: A survey of Applications and Methods. Springer Series in Operations Research, Springer, 1995.
M. Hall Jr. Combinatorial Theory. Blaisdell. Waltham. MA, 1967.
D. Erlenkotter. A dual-based procedure for uncapacitated facility location, Operations Research, 26: 992–1009, 1978.
D. Johnson, C. Papadimitriou, and M. Yannakakis. How easy is local search? Journal of Computer and System Sciences, 37: 79–100, 1988.
J. Krarup and P. M. Pruzan. The simple plant location problem: survey and synthesis. European Journal of Operational Research, 12: 36–81, 1983.
D. Krotov. Lower bounds for number of m-quasi groups of order 4 and number of perfect binary codes. Discrete Analysis and Operations Research, 7: 47–53, 2000, (in Russian).
P. Mirchandani and R. Francis (Eds.) Discrete Location Theory. John Wiley & Sons, 1990.
M. Resende and R. Werneck. A hybrid multistart heuristic for the uncapacitated facility location problem, Manuscript, http://www.research.att.com/mgcr/doc/guflp.pdf.
D. Schilling, K. Rosing, and C. ReVelle. Network distance characteristics that affect computational effort in p-median location problems. European Journal of Operational Research, 127: 525–536, 2000.
M. Yannakakis. Computational complexity. E. Aarts and J.K. Lenstra (Eds.) Local Search in Combinatorial Optimization, pages 19–55, Chichester: John Wiley & Sons, 1997.
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Kochetov, Y., Ivanenko, D. (2005). Computationally Difficult Instances for the Uncapacitated Facility Location Problem. In: Ibaraki, T., Nonobe, K., Yagiura, M. (eds) Metaheuristics: Progress as Real Problem Solvers. Operations Research/Computer Science Interfaces Series, vol 32. Springer, Boston, MA. https://doi.org/10.1007/0-387-25383-1_16
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DOI: https://doi.org/10.1007/0-387-25383-1_16
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