A New Compromise Solution Model Based on Dantzig-Wolfe Decomposition for Solving Belief Multi-Objective Nonlinear Programming Problems with Block Angular Structure

Abstract

This paper presents an integrated model based on a compromised solution method to solve fuzzy belief multi-objective large-scale nonlinear programming (FBMOLSNLP) problem with block angular structure. A new method is proposed to transfer each belief decision-making problem into some fuzzy problems. Furthermore, we propose a new compromise method of decisionmaking as one of the most e±cient methods based on the particular measure of closeness to the ideal solution to aggregate multi-objective decision-making (MODM) problems into a single problem. The decomposition algorithm based on Dantzig–Wolfe is utilized to reduce the largedimensional objective space into a two-dimensional space. Then, Zimmerman method is applied to transfer each bi-objective to a single-objective. Moreover, TOPSIS and VIKOR are utilized as two independent solution methods to aggregate each multi-objective sub-problem. Finally, a new single-objective nonlinear programming problem is solved to ̄nd the ̄nal solution. To justify the proposed model, two illustrative examples are provided, and the results of three decision methods are compromised.

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