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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Behnam Vahdani & Meghdad Salimi & Seyed Meysam Mousavi, 2017. "A New Compromise Solution Model Based on Dantzig–Wolfe Decomposition for Solving Belief Multi-Objective Nonlinear Programming Problems with Block Angular Structure," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(02), pages 333-387, March.
    • Handle: RePEc:wsi:ijitdm:v:16:y:2017:i:02:n:s0219622017500043
    DOI: 10.1142/S0219622017500043
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    References listed on IDEAS

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    1. Lai, Young-Jou & Liu, Ting-Yun & Hwang, Ching-Lai, 1994. "TOPSIS for MODM," European Journal of Operational Research, Elsevier, vol. 76(3), pages 486-500, August.
    2. Wang, Reay-Chen & Liang, Tien-Fu, 2005. "Applying possibilistic linear programming to aggregate production planning," International Journal of Production Economics, Elsevier, vol. 98(3), pages 328-341, December.
    3. Yang, Jian-Bo, 2001. "Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties," European Journal of Operational Research, Elsevier, vol. 131(1), pages 31-61, May.
    4. Gang Kou & Yanqun Lu & Yi Peng & Yong Shi, 2012. "Evaluation Of Classification Algorithms Using Mcdm And Rank Correlation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 197-225.
    5. Xu, Dong-Ling & Yang, Jian-Bo & Wang, Ying-Ming, 2006. "The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1914-1943, November.
    6. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    7. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    8. Wang, Ying-Ming & Yang, Jian-Bo & Xu, Dong-Ling, 2006. "Environmental impact assessment using the evidential reasoning approach," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1885-1913, November.
    9. de Sá, Elisangela Martins & de Camargo, Ricardo Saraiva & de Miranda, Gilberto, 2013. "An improved Benders decomposition algorithm for the tree of hubs location problem," European Journal of Operational Research, Elsevier, vol. 226(2), pages 185-202.
    10. Fu, Chao & Yang, Shan-Lin, 2010. "The group consensus based evidential reasoning approach for multiple attributive group decision analysis," European Journal of Operational Research, Elsevier, vol. 206(3), pages 601-608, November.
    11. Sakawa, Masatoshi & Sawada, Kazuya & Inuiguchi, Masahiro, 1995. "A fuzzy satisficing method for large-scale linear programming problems with block angular structure," European Journal of Operational Research, Elsevier, vol. 81(2), pages 399-409, March.
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