An Interactive Decomposition Algorithm for Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters Using TOPSIS Method

This paper extended TOPSIS (Technique for Order Preference by Similarity Ideal Solution) method for solving Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters in the righthand side of the constraints (TL-LSLMOP-SP)rhs of block angular structure. In order to obtain a compromise ( satisfactory) solution to the (TL-LSLMOP-SP)rhs of block angular structure using the proposed TOPSIS method, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions of the two levels. In every level, as the measure of ―Closeness‖ dp-metric is used, a k-dimensional objective space is reduced to two –dimentional objective space by a first-order compromise procedure. The membership functions of fuzzy set theory is used to represent the satisfaction level for both criteria. A single-objective programming problem is obtained by using the max-min operator for the second –order compromise operaion. A decomposition algorithm for generating a compromise ( satisfactory) solution through TOPSIS approach is provided where the first level decision maker (FLDM) is asked to specify the relative importance of the objectives. Finally, an illustrative numerical example is given to clarify the main results developed in the paper.