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

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.