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.

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://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] M.A. Abo Sinna and A.H. Amer, Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems, Appl. Math. Comput. 162 (2005) 243-256. | Zbl

[2] V.J. Bowman, 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] G. Buyukozkan and O. Feyzioglu, Evaluation of suppliers' environmental management performances by a fuzzy compromise ranking technique. J. Multiple-Valued Logic and Soft Computing 14 (2008) 309-323.

[4] M.T. Chu, J. Shyu, G.H. Tzeng and R. Khosla, Comparison among three analytical methods for knowledge communities group-decision analysis. Expert Syst. Appl. 33 (2007) 1011-1024.

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

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

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

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

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

[10] Y.J. Lai, T.Y. Liu and C.L. Hwang, TOPSIS for MODM. Eur. J. Oper. Res. 76 (1994) 486-500. | Zbl

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

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

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

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

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

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

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

[18] L.I. Tong, C.C. Chen and C.H. Wang, Optimization of multi-response processes using the VIKOR method. Adv. Manuf. Tech. 31 (2007) 1049-1057.

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

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

Cited by Sources: