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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; m_heidary@ind.iust.ac.ir
Mohammad Kazem Sayadi
Affiliation:
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir
Kamran Shahanaghi
Affiliation:
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran; m_heidary@ind.iust.ac.ir
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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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