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Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems

Published online by Cambridge University Press:  27 April 2010

Majeed Heydari ,
Mohammad Kazem Sayadi  and
Kamran Shahanaghi
Majeed Heydari
Affiliation:
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; [email protected]
Mohammad Kazem Sayadi
Affiliation:
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; [email protected]
Kamran Shahanaghi
Affiliation:
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; [email protected]
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Abstract

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 systemsmulti-criteria decision makingnonlinear programmingcompromise programmingideal solutionVIKOR method
Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 2 , April 2010 , pp. 139 - 152
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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References

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.
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.
Buyukozkan, G. and Feyzioglu, O., Evaluation of suppliers' environmental management performances by a fuzzy compromise ranking technique. J. Multiple-Valued Logic and Soft Computing 14 (2008) 309–323.
Chu, M.T., Shyu, J., Tzeng, G.H. and Khosla, R., Comparison among three analytical methods for knowledge communities group-decision analysis. Expert Syst. Appl. 33 (2007) 1011–1024. CrossRef
G. Dantzig, Linear Programming and Extensions. Princeton University Press, Princeton (1963).
Dantzig, G. and Wolfe, P., The decomposition algorithm for linear programming. Econometrical 29 (1961) 767–778. CrossRef
Geoffrion, M., Elements of large scale mathematical programming: Part II: Synthesis of algorithms and bibliography. Manage. Sci. 16 (1970) 676–691. CrossRef
Ho, J.K. and Sundarraj, R.P., An advanced implementation of the Dantzig-Wolf decomposition algorithm for linear programming. Math. Program. 20 (1981) 303–326. CrossRef
Ho, J.K. and Sundarraj, R.P., Computational experience with advanced implementation of decomposition algorithm for linear programming. Math. Program. 27 (1983) 283–290. CrossRef
Lai, Y.J., Liu, T.Y. and Hwang, C.L., TOPSIS for MODM. Eur. J. Oper. Res. 76 (1994) 486–500. CrossRef
L.S. Lasdon, Optimization theory for large systems. Macmillan, New York, USA (1970).
S. Opricovic, Multi-criteria optimization of civil engineering systems, Faculty of Civil engineering, Belgrade (1998).
Opricovic, S., A fuzzy compromise solution for multi-criteria problems. Int. J. Unc. Fuzz. Knowl. Based Syst. 15 (2007) 363–380. CrossRef
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.
Opricovic, S. and Tzeng, G.H., Extended VIKOR method in comparison with outranking methods. Eur. J. Oper. Res. 178 (2007) 514–529. CrossRef
M. Sakawa, Large Scale Interactive Multi-objective Programming Decomposition Approaches. Physica-Verlag, New York (2000).
Sayadi, M.K., Heydari, M. and Shahanaghi, K., Extension of VIKOR method for decision making problem with interval numbers. Appl. Math. Model. 33 (2009) 2257–2262. CrossRef
Tong, L.I., Chen, C.C. and Wang, C.H., Optimization of multi-response processes using the VIKOR method. Adv. Manuf. Tech. 31 (2007) 1049–1057. CrossRef
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.
H.J. Zimmermann, Fuzzy sets,decision making and expert systems. Kluwer Academic Publishers, Boston, USA (1987).