Extensions of TOPSIS for large scale multi-objective non-linear programming problems with block angular structure

Abstract

This paper focuses on multi-objective large-scale non-linear programming (MOLSNLP) problems with block angular structure. We extend the technique for order preference by similarity ideal solution (TOPSIS) to solve them. Compromise (TOPSIS) control minimizes the measure of distance, provided that the closest solution should have the shortest distance from the positive ideal solution (PIS) as well as the longest distance from the negative ideal solution (NIS). As the measure of ''closeness'' L P -metric is used. Thus, we reduce a q-dimensional objective space to a two-dimensional space by a firstorder compromise procedure. The concept of a membership function of fuzzy set theory is used to represent the satisfaction level for both criteria. Moreover, we derive a single objective large-scale non-linear programming (LSNLP) problem using the max-min operator for the second-order compromise operation. Finally, a numerical illustrative example is given to clarify the main results developed in this paper.

A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

“…After the publication of the Dantzig and Wolfe decomposition method [7], there have been numerous subsequent works on large scale linear and nonlinear programming problems with block angular structure ( [1,6,12]). Abo Sinna et al [4] extended the technique for order preference by similarity ideal solution (TOPSIS) to solve multi-objective large scale non-linear programming problem. Compromise (TOPSIS) control minimizes the measure of distance.…”

“…El-Sawy et al [9] introduced an algorithm for decomposing the parametric space in large scale linear vector optimization problems under fuzzy environment. Recently, notable studies have been done in the area of multi-level and multi-objective large scale programming problems ( [3,4,6,12]). Benzi et al [6] developed and compared multi-level algorithms for solving large scale bound constrained nonlinear problems via interior point methods.…”

“…In large scale programming which closely describes and represents the real world decision situations, various factors of the real system should be reflected in the description of the objective function and constraints. Naturally these objective function and constraints involve many parameters and the experts may assign them different values ( [1,2,3,4]). After the publication of the Dantzig and Wolfe decomposition method [7], there have been numerous subsequent works on large scale linear and nonlinear programming problems with block angular structure ( [1,6,12]).…”

Permutation based decision making under fuzzy environment using Tabu search

“…Xu (2007) defined the notations of the positive ideal fuzzy set and negative ideal fuzzy set, which can be used in fuzzy TOPSIS or other fuzzy MADM methods. Abo-Sinna et al (2008) extended the TOPSIS for large-scale multi-objective non-linear programming problems with block angular structure. Nut and Soner (2008) proposed an integrated approach using AHP and TOPSIS in a fuzzy environment for shipping site selection.…”

A Cloud TOPSIS Method for Multiple Criteria Decision Making with Interval Number

“…TOPSIS method was initially proposed by Hwang and Yoon(1981) [13,14], The basic idea of the TOPSIS method is that the chosen alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest distance from the negative ideal solution (NIS). As various types of uncertainties and imprecision often exist, the information of alternatives are vague, imprecise and uncertain by nature, a variety of more in-depth-study of a new approach emerged, such as those reported in Lai et al [12][13][14][15][16].…”