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

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.

Untitled

“…The bi-level programming (BLP) problem is considered a useful optimization problems in which there are independent decision makers (DM s ) and the feasible region of the upper-level (UL) problem is determined implicitly by the solution set of the lower-level (LL) problem. In the past few decades, the BLP problem has been covered the theoretical and computational points [1][2][3][4][5][6][7][8][9][10][11] and has been applied indifferent fields such as finance budget, transport network design [12], supply chain management [13], principal-agent problem [14] engineering design [15], price control and electricity markets.…”

Untitled

“…In the past few decades, the BLP problem has been covered the theoretical and computational points [1][2][3][4][5][6][7][8][9][10][11] and has been applied indifferent fields such as finance budget, transport network design [12], supply chain management [13], principal-agent problem [14] engineering design [15], price control and electricity markets.…”