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

Majeed Heydari; Mohammad Kazem Sayadi; Kamran Shahanaghi

RAIRO - Operations Research (2010)

  • Volume: 44, Issue: 2, page 139-152
  • ISSN: 0399-0559

Abstract

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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.

How to cite

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Heydari, Majeed, Kazem Sayadi, Mohammad, and Shahanaghi, Kamran. "Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems." RAIRO - Operations Research 44.2 (2010): 139-152. <http://eudml.org/doc/250844>.

@article{Heydari2010,
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. },
author = {Heydari, Majeed, Kazem Sayadi, Mohammad, Shahanaghi, Kamran},
journal = {RAIRO - Operations Research},
keywords = {Large-scale systems; multi-criteria decision making; nonlinear programming; compromise programming; ideal solution; VIKOR method; nonlinear programming},
language = {eng},
month = {4},
number = {2},
pages = {139-152},
publisher = {EDP Sciences},
title = {Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems},
url = {http://eudml.org/doc/250844},
volume = {44},
year = {2010},
}

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
DA - 2010/4//
PB - EDP Sciences
VL - 44
IS - 2
SP - 139
EP - 152
AB - 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.
LA - eng
KW - Large-scale systems; multi-criteria decision making; nonlinear programming; compromise programming; ideal solution; VIKOR method; nonlinear programming
UR - http://eudml.org/doc/250844
ER -

References

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