# 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

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topHeydari, 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 -

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