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

Behnam Vahdani (), Meghdad Salimi and Seyed Meysam Mousavi
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Behnam Vahdani: Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Meghdad Salimi: Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Seyed Meysam Mousavi: #x2020;Department of Industrial Engineering, Faculty of Engineering, Shahed University, Tehran, Iran

International Journal of Information Technology & Decision Making (IJITDM), 2017, vol. 16, issue 02, 333-387

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 decision-making as one of the most efficient 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 large-dimensional 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 find the final solution. To justify the proposed model, two illustrative examples are provided, and the results of three decision methods are compromised.

Keywords: Multi-criteria decision-making (MCDM); multi-objective decision-making (MODM); TOPSIS; VIKOR; belief structure; large-scale; block angular structure (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0219622017500043

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