SOLVING MULTI-OBJECTIVE GEOMETRIC PROGRAMMING PROBLEMS WITH WEIGHTED SUM, FUZZY GEOMETRIC PROGRAMMING, −CONSTRAINED AND NEUROSOPHIC GEOEMETRIC PROGRAMMING METHODS

Abstract

In this project, we discussed multi objective geometric programming problems by covering some basic concepts as well as different solution methods. Methods like weighted sum, -constraint, fuzzy geoemetric programming and Neutrosophic geometric programming methods were applied for solving multi-objective geometric programming optimization problems. First, a multi objective geometric programming problems is transformed into a single-objective geometric programming optimization problem by using weighted sum, -constraint, fuzzy and neutrosophic geometric programming methods. Then the transformed single-objective geometric programming optimization problem was solved by arthemetic geometric inequality or geometric programming method. Illustrative examples were presented to show the effectiveness of the proposed methods and the results so obtained by weighted sum method has been compared with fuzzy and neutrosophic geometric programming methods. From the result we concluded that FGP method obtained the sum of two objective functions are 65.6, NGP method obtained 65.35 and weighted sum 64.807 which is the sum of two objective functions. This implies that weighted sum method is the most appropriate to solve MOGPP than other listed methods because the result obtained is too minimum relatively to others and neutrosophic method is the second best method according to the result obtained. We can recommend that all problems solved by weighted sum method can not solved by other problems but problems solved by FGP, NGP and epsilon constrained can also be solved by weighted sum method. This is due to the degree of difficulty being negative. so all transformed MOGPP to SOGPP can not be solved by GP method if degree of difficulty is negative it requires further investigation and also as the degree of difficulty increases it is difficult to solve.