Abstract
The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems. The proposed approach minimizes the weighted objective function comes from multi-objective geometric programming problem subject to constraints which constructed by using Kuhn-Tucker Conditions. A new nonlinear problem formed by this approach is solved iteratively. The solution of this approach gives the Pareto optimal solution for the multi-objective posynomial geometric programming problem. To demonstrate the performance of this approach, a problem which was solved with a weighted mean method by Ojha and Biswal (2010) is used. The comparison of solutions between two methods shows that similar results are obtained. In this manner, the proposed approach can be used as an alternative of weighted mean method.
Highlights
The aim of this study is to present an alternative approach for solving the multi-objective posynomial geometric programming problems
Geometric Programming Problem (GPP) is a special type of nonlinear programming that often used in the applications for production planning, personal allocation, distribution, risk managements, chemical process designs and other engineer design situations
The solution to the GPP follows the opposite method with respect to the classical optimization technique and it depends on the technique of first finding the weight values and calculating the optimum value for the objective function, finding the values of the decision variables
Summary
Geometric Programming Problem (GPP) is a special type of nonlinear programming that often used in the applications for production planning, personal allocation, distribution, risk managements, chemical process designs and other engineer design situations. GPP is a special technique that is developed in order to find the optimum values of posynomial and signomial functions. In the classical optimization technique, a system of nonlinear equations is generally faced after taking partial derivatives for each variable and equalizing them to zero
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