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Abstrakty
When dealing with multicriteria problems, the aggregation of multiple outcomes plays an essential role in finding a solution, as it reflects the decision-maker's preference relation. The Ordered Weighted Averaging (OWA) operator provides a exible preference model that generalizes many objective functions. It also ensures the impartiality and allow to obtain equitable solutions, which is vital when the criteria represent evaluations of independent individuals. These features make the OWA operator very useful in many fields, one of which is location analysis. However, in general the OWA aggregation makes the problem nonlinear and hinder its computational complexity. Therefore, problems with the OWA operator need to be devised in an efficient way. The paper introduces new general formulations for OWA optimization and proposes for them some simple valid inequalities to improve efficiency. A hybrid structure of proposed models makes the number of binary variables problem type dependent and may reduce it signicantly. Computational results show that for certain problem types, some of which are very useful in practical applications, the hybrid models perform much better than previous general models from literature.
Rocznik
Tom
Strony
22--30
Opis fizyczny
Bibliogr. 17 poz., tab.
Twórcy
autor
- National Institute of Telecommunications, Szachowa st 1, 04-894 Warsaw, Poland
Bibliografia
- [1] R. R. Yager, “On ordered weighted averaging aggregation operators in multicriteria decisionmaking”, IEEE Trans. on Systems, Man, and Cybernet., vol. 18, no. 1, pp. 183–190, 1988.
- [2] R. R. Yager, J. Kacprzyk, and G. Beliakov, Eds., Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice, vol. 265 of Studies in Fuzziness and Soft Computing. Springer, 2011.
- [3] W. Ogryczak, T. Śliwiński, and A. Wierzbicki, “Fair resource allocation schemes and network dimensioning problems”, J. Telecommun.& Inform. Technol., no. 3, pp. 34–42, 2003.
- [4] M. Köppen, K. Yoshida, M. Tsuru, and Y. Oie, “Annealing heuristic for fair wireless channel allocation by exponential ordered-ordered weighted averaging operator maximization”, in Proc. 11th Ann. Int. Symp. on Applications and the Internet SAINT 2011, Munich, Germany, 2011, pp. 538–543.
- [5] R. R. Yager, “Constrained OWA aggregation”, Fuzzy Sets and Syst., vol. 81, no. 1, pp. 89–101, 1996.
- [6] W. Ogryczak and T. Śliwiński, “On solving linear programs with the ordered weighted averaging objective”, Eur. J. of Operat. Res., vol. 148, no. 1, pp. 80–91, 2003.
- 7] W. Ogryczak and A. Tamir, “Minimizing the sum of the k largest functions in linear time”, Inform. Process. Lett., vol. 85, no. 3, pp. 117–122, 2003.
- [8] W. Ogryczak, “On the distribution approach to location problems”, Comp. & Indust. Engin., vol. 37, no. 3, pp. 595–612, 1999.
- [9] S. Nickel and J. Puerto, Location Theory: A Unified Approach. Berlin: Springer, 2005.
- [10] N. Boland, P. Domínguez-Marín, S. Nickel, and J. Puerto, “Exact procedures for solving the discrete ordered median problem”, Comp. & Operat. Res., vol. 33, no. 11, pp. 3270–3300, 2006.
- [11] A. Marín, S. Nickel, J. Puerto, and S. Velten, “A flexible model and efficient solution strategies for discrete location problems”, Discr. Appl. Mathem., vol. 157, no. 5, pp. 1128–1145, 2009.
- [12] A. Marín, S. Nickel, and S. Velten, “An extended covering model for flexible discrete and equity location problems”, Mathem. Methods of Operat. Res., vol. 71, no. 1, pp. 125–163, 2010.
- [13] W. Ogryczak and P. Olender, “Ordered median problem with demand distribution weights”, Optimization Lett., vol. 10, no. 5, pp. 1071–1086, 2016.
- [14] W. Ogryczak and P. Olender, “On MILP models for the OWA optimization”, J. Telecommun. & Inform. Technol., no. 2, pp. 5–12, 2012.
- [15] P. B. Mirchandani and R. L. Francis, Discrete Location Theory. New York: Wiley, 1990.
- [16] P. Domínguez-Marín, The Discrete Ordered Median Problem: Models and Solution Methods. Springer, 2003.
- [17] IBM, IBM ILOG CPLEX Optimization Studio [Online]. Available: http://www-03.ibm.com/software/products/en/ibmilogcpleoptistud/.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-326e0efd-5fd9-4f93-ac36-8495f15d954e