Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

Azza Hassan Amer

Abstract


Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

Keywords


geometric programming; -constraint method; fuzzy programming; duality theorem; bi-level programming; Pareto optimal solution.

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DOI: http://dx.doi.org/10.18187/pjsor.v13i4.1698

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Title

Implementation of the - Constraint Method in Special Class of Multi-objective Fuzzy Bi-Level Nonlinear Problems

Keywords

geometric programming; -constraint method; fuzzy programming; duality theorem; bi-level programming; Pareto optimal solution.

Description

Geometric programming problem is a powerful tool for solving some special type nonlinear programming problems. In the last few years we have seen a very rapid development on solving multiobjective geometric programming problem. A few mathematical programming methods namely fuzzy programming, goal programming and weighting methods have been applied in the recent past to find the compromise solution. In this paper, -constraint method has been applied in bi-level multiobjective geometric programming problem to find the Pareto optimal solution at each level. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem at eash level. Here, we have developed a new algorithm for fuzzy programming technique to solve bi-level multiobjective geometric programming problems to find an optimal compromise solution. Finally the solution procedure of the fuzzy technique is illustrated by a numerical example

Date

2017-12-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 13 No. 4, 2017



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810