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
Highlights
Various mathematical programming methods have been formulated to solve many real world problems
This special class is represented in geometric programming problem (GPP) which is a powerful tool for solving some special type nonlinear programming problems
The corresponding fuzzy programming technique of the multiobjective geometric programming problems (MOGPP) is applied in two levels to give an optimal compromise solution
Summary
Various mathematical programming methods have been formulated to solve many real world problems. In the above BLMOGPP from (2.1)-(2.6) there are (M + N) number of minimization type objective functions, (m + n) number of inequality type constraints and L = p + q number of strictly positive decision variables Both upper level problem (2.1) – (2.3) and lower level problem (2.4) – (2.6) is considered as a vector minimum problem. The present ULMOGPP (2.1) – (2.3) can be redefined as a single objective geometric programming Problem (GPP) by using - constraint method as:. The dual form of GPP plays an important role in solving complex types of single and multiobjective optimization problems.
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