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Decomposition of parametric space for bi-objective optimization problem using neural network approach

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Abstract

A new gradient-based neural network approach is proposed for solving nonlinear programming problems (NLPPs) and bi-objective optimization problems (BOOPs). The most prominent feature of the proposed approach is that it can converge rapidly to the equilibrium point (optimal solution), for an arbitrary initial point. The proposed approach is affirmed to be stable in the sense of Lyapunov and it is capable for obtaining the optimal solution in solving both NLPPs and BOOPs tasks. Further, BOOP is converted into an equivalent optimization problem by the mean of the weighted sum method, where the Pareto optimal solutions are obtained by using different weights. Also the decomposition of parametric space for BOOP is analyzed in details based on the stability set of the first kind. The experiments results also affirmed that the proposed approach is a promising approach and has an effective performance.

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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, Menoufia University, Shibin El-Kom, Egypt

    Mahmoud A. Abo-Sinna & Rizk M. Rizk-Allah

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

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Abo-Sinna, M.A., Rizk-Allah, R.M. Decomposition of parametric space for bi-objective optimization problem using neural network approach. OPSEARCH 55, 502–531 (2018). https://doi.org/10.1007/s12597-018-0337-x

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