Hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear systems with fuzzy parameters |
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Authors: | Mahmoud A Abo-Sinna Azza H Amer Ashraf S Ibrahim |
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Institution: | 1. Department of Basic Engineering Sciences, Faculty of Engineering, El-Menoufiya University, Shebin El-Kom, Egypt;2. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt |
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Abstract: | This paper proposes a decomposition method for hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear programming (MONLP) problems with fuzzy parameters in the objective functions and in the constraints (FMONLP). These fuzzy parameters are characterized by fuzzy numbers. For such problems, the concept of α-Pareto optimality introduced by extending the ordinary Pareto optimality based on the α-level sets of fuzzy numbers. The decomposition method is based on the principle of decompose the original problem into interdependent sub-problems. In this method, the global multi-objective non-linear problem is decomposed into smaller multi-objective sub-problems. The smaller sub-problems, which obtained solved separately by using the weighting method and through an operative procedure. All these solution are coordinates in such a way that an optimal solution for the global problem achieved. In addition, an interactive fuzzy decision-making algorithm for hierarchical generation of α-Pareto optimal solution through the decomposition method is developed. Finally, two numerical examples given to illustrate the results developed in this paper. |
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Keywords: | Fuzzy multi-objective non-linear programming problem Fuzzy set theory α-Pareto optimality Weighting method Decomposition method Interactive decision-making Lagrangian function and Kuhn&ndash Tucker conditions |
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