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Extended VIKOR as a new method for solving multiple objective large-scale nonlinear programming problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 2, pp. 139-152

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The VIKOR method was introduced as a Multi-Attribute Decision Making (MADM) method to solve discrete decision-making problems with incommensurable and conflicting criteria. This method focuses on ranking and selecting from a set of alternatives based on the particular measure of “closeness” to the “ideal” solution. The multi-criteria measure for compromise ranking is developed from the l-p metric used as an aggregating function in a compromise programming method. In this paper, the VIKOR method is extended to solve Multi-Objective Large-Scale Non-Linear Programming (MOLSNLP) problems with block angular structure. In the proposed approach, the Y-dimensional objective space is reduced into a one-dimensional space by applying the Dantzig-Wolfe decomposition algorithm as well as extending the concepts of VIKOR method for decision-making in continues environment. Finally, a numerical example is given to illustrate and clarify the main results developed in this paper.

DOI : 10.1051/ro/2010011
Classification : 90C06, 90C30, 90V29
Keywords: large-scale systems, multi-criteria decision making, nonlinear programming, compromise programming, ideal solution, VIKOR method 
@article{RO_2010__44_2_139_0,
     author = {Heydari, Majeed and Kazem Sayadi, Mohammad and Shahanaghi, Kamran},
     title = {Extended {VIKOR} as a new method for solving multiple objective large-scale nonlinear programming problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {139--152},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {2},
     year = {2010},
     doi = {10.1051/ro/2010011},
     mrnumber = {2666486},
     zbl = {1190.90187},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2010011/}
}
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AU  - Heydari, Majeed
AU  - Kazem Sayadi, Mohammad
AU  - Shahanaghi, Kamran
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PB  - EDP-Sciences
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%A Kazem Sayadi, Mohammad
%A Shahanaghi, Kamran
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%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2010
%P 139-152
%V 44
%N 2
%I EDP-Sciences
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%R 10.1051/ro/2010011
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%F RO_2010__44_2_139_0
Heydari, Majeed; Kazem Sayadi, Mohammad; Shahanaghi, Kamran. Extended VIKOR as a new method for solving multiple objective large-scale nonlinear programming problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 44 (2010) no. 2, pp. 139-152. doi: 10.1051/ro/2010011

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