Extended VIKOR as a new method for solving Multiple Objective Large-Scale Nonlinear Programming problems
Department of Industrial Engineering, Iran University of Science and Technology, Narmak, Tehran,
Accepted: 9 October 2009
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.
Mathematics Subject Classification: 90C06 / 90C30 / 90V29
Key words: Large-scale systems / multi-criteria decision making / nonlinear programming / compromise programming / ideal solution / VIKOR method
© EDP Sciences, ROADEF, SMAI, 2010