A compromise decision-making model based on VIKOR for multi-objective large-scale nonlinear programming problems with a block angular structure under uncertainty


1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, P.O. Box 3419759811, Iran

2 Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, P.O. Box 18151-159, Iran


This paper proposes a model on the basis of VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methodology as a compromised method to solve the Multi-Objective Large-Scale Nonlinear Programming (MOLSNLP) problems with block angular structure involving fuzzy coeffcients. The proposed method is introduced for solving large scale nonlinear programming in fuzzy environment for rst time. The problem involves fuzzy coeffients in both objective functions and constraints. In this method, an aggregating function developed from LP- metric is based on the particular measure of closeness" to the ideal" solution. The solution process is composed of two steps: First, the decomposition algorithm is utilized to reduce the q-dimensional objective space into a one-dimensional space. Then a multi-objective identical crisp non-linear programming is derived from each fuzzy non-linear model for solving the problem. Second, for nding the nal solution, a single-objective large-scale nonlinear programming problem is solved. In order to justify the proposed method, an illustrative example is presented and followed by description of the sensitivity analysis.