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.

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://archive.numdam.org/articles/10.1051/ro/2010011/} }

TY - JOUR AU - Heydari, Majeed AU - Kazem Sayadi, Mohammad AU - Shahanaghi, Kamran TI - Extended VIKOR as a new method for solving multiple objective large-scale nonlinear programming problems JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2010 SP - 139 EP - 152 VL - 44 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2010011/ DO - 10.1051/ro/2010011 LA - en ID - RO_2010__44_2_139_0 ER -

%0 Journal Article %A Heydari, Majeed %A Kazem Sayadi, Mohammad %A Shahanaghi, Kamran %T Extended VIKOR as a new method for solving multiple objective large-scale nonlinear programming problems %J RAIRO - Operations Research - Recherche Opérationnelle %D 2010 %P 139-152 %V 44 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2010011/ %R 10.1051/ro/2010011 %G en %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, Volume 44 (2010) no. 2, pp. 139-152. doi : 10.1051/ro/2010011. http://archive.numdam.org/articles/10.1051/ro/2010011/

[1] Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems, Appl. Math. Comput. 162 (2005) 243-256. | Zbl

and ,[2] On the relationship of the Tchebycheff norm and the efficient frontier of multiple criteria objectives, Lect. Notes Econ. Math. 135 (1976) 76-85. | Zbl

,[3] Evaluation of suppliers' environmental management performances by a fuzzy compromise ranking technique. J. Multiple-Valued Logic and Soft Computing 14 (2008) 309-323.

and ,[4] Comparison among three analytical methods for knowledge communities group-decision analysis. Expert Syst. Appl. 33 (2007) 1011-1024.

, , and ,[5] Linear Programming and Extensions. Princeton University Press, Princeton (1963). | Zbl

,[6] The decomposition algorithm for linear programming. Econometrical 29 (1961) 767-778. | Zbl

and ,[7] Elements of large scale mathematical programming: Part II: Synthesis of algorithms and bibliography. Manage. Sci. 16 (1970) 676-691. | Zbl

,[8] An advanced implementation of the Dantzig-Wolf decomposition algorithm for linear programming. Math. Program. 20 (1981) 303-326. | Zbl

and ,[9] Computational experience with advanced implementation of decomposition algorithm for linear programming. Math. Program. 27 (1983) 283-290. | Zbl

and ,[10] TOPSIS for MODM. Eur. J. Oper. Res. 76 (1994) 486-500. | Zbl

, and ,[11] Optimization theory for large systems. Macmillan, New York, USA (1970). | Zbl

,[12] Multi-criteria optimization of civil engineering systems, Faculty of Civil engineering, Belgrade (1998).

,[13] A fuzzy compromise solution for multi-criteria problems. Int. J. Unc. Fuzz. Knowl. Based Syst. 15 (2007) 363-380.

,[14] Compromise solution by MCDM methods; a comparative analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 156 (2004) 445-455. | Zbl

and ,[15] Extended VIKOR method in comparison with outranking methods. Eur. J. Oper. Res. 178 (2007) 514-529. | Zbl

and ,[16] Large Scale Interactive Multi-objective Programming Decomposition Approaches. Physica-Verlag, New York (2000).

,[17] Extension of VIKOR method for decision making problem with interval numbers. Appl. Math. Model. 33 (2009) 2257-2262. | Zbl

, and ,[18] Optimization of multi-response processes using the VIKOR method. Adv. Manuf. Tech. 31 (2007) 1049-1057.

, and ,[19] Compromise programming, in Multiple Criteria Decision Making edited by J.L. Cochrane, M. Zeleny. University of South Carolina, SC (1973) pp. 262-300.

,[20] Fuzzy sets,decision making and expert systems. Kluwer Academic Publishers, Boston, USA (1987).

,*Cited by Sources: *