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

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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.

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Acknowledgements

The authors are grateful to the anonymous reviewers and the editor for their suggestions in improving the quality of the paper.

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Authors and Affiliations

  1. Department of Basic Engineering Science, Faculty of Engineering, El-Menoufia University, Shebin El-Kom, Egypt

    R. M. Rizk-Allah

  2. Department of Mathematical Science, Faculty of Science, Princess Nora Bent AbdulRahman University, Al Riyadh, Saudi Arabia

    Mahmoud A. Abo-Sinna

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  1. R. M. Rizk-Allah
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  2. Mahmoud A. Abo-Sinna
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Correspondence to R. M. Rizk-Allah.

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Rizk-Allah, R.M., Abo-Sinna, M.A. Integrating reference point, Kuhn–Tucker conditions and neural network approach for multi-objective and multi-level programming problems. OPSEARCH 54, 663–683 (2017). https://doi.org/10.1007/s12597-017-0299-4

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