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

Author

Listed:
  • Mahmoud A. Abo-Sinna

    (Menoufia University)

  • Rizk M. Rizk-Allah

    (Menoufia University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:55:y:2018:i:2:d:10.1007_s12597-018-0337-x
    DOI: 10.1007/s12597-018-0337-x
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    References listed on IDEAS

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    1. 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.
    2. Abo-Sinna, Mahmoud A. & Hussein, Mohammad L., 1994. "An algorithm for decomposing the parametric space in multiobjective dynamic programming problems," European Journal of Operational Research, Elsevier, vol. 73(3), pages 532-538, March.
    3. Abo-Sinna, Mahmoud A. & Hussein, Mohammad L., 1995. "An algorithm for generating efficient solutions of multiobjective dynamic programming problems," European Journal of Operational Research, Elsevier, vol. 80(1), pages 156-165, January.
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