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Integrating reference point, Kuhn–Tucker conditions and neural network approach for multi-objective and multi-level programming problems

Author

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  • R. M. Rizk-Allah

    (El-Menoufia University)

  • Mahmoud A. Abo-Sinna

    (Princess Nora Bent AbdulRahman University)

Abstract

In this paper, a neural network approach is constructed to solve multi-objective programming problem (MOPP) and multi-level programming problem (MLPP). The main idea is to convert the MOPP and the MLPP into an equivalent convex optimization problem. A neural network approach is then constructed for solving the obtained convex programming problem. Based on employing Lyapunov theory, the proposed neural network approach is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the MOPP and the MLPP. The simulation results also demonstrate that the proposed neural network is feasible and efficient.

Suggested Citation

  • R. M. Rizk-Allah & Mahmoud A. Abo-Sinna, 2017. "Integrating reference point, Kuhn–Tucker conditions and neural network approach for multi-objective and multi-level programming problems," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 663-683, December.
    • Handle: RePEc:spr:opsear:v:54:y:2017:i:4:d:10.1007_s12597-017-0299-4
    DOI: 10.1007/s12597-017-0299-4
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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.
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    Cited by:

    1. Mahmoud A. Abo-Sinna & Rizk M. Rizk-Allah, 2018. "Decomposition of parametric space for bi-objective optimization problem using neural network approach," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 502-531, June.
    2. Rizk M. Rizk-Allah & Mahmoud A. Abo-Sinna, 2021. "A comparative study of two optimization approaches for solving bi-level multi-objective linear fractional programming problem," OPSEARCH, Springer;Operational Research Society of India, vol. 58(2), pages 374-402, June.

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