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Zbl 1190.90187
Heydari, Majeed; Sayadi, Mohammad Kazem; Shahanaghi, Kamran
Extended VIKOR as a new method for solving multiple objective large-scale nonlinear programming problems. (English)
[J] RAIRO, Oper. Res. 44, No. 2, 139-152 (2010). ISSN 0399-0559; ISSN 1290-3868/e

Summary: 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.

MSC 2000:: *90C29 Multi-objective programming, etc.
90C06 Large-scale problems

Keywords: nonlinear programming; compromise programming; ideal solution

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