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To provide a multiple objective solution we used Pareto analysis.
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By introducing multiple objectives the solutions obtained should possess better properties and also have better defined parameters.
Its methodological procedure can easily be incorporated into multiple objective programming formulations with interactive solution process.
Multiple objective optimization (MOO) models and solution methods are commonly used for multi-criteria decision making in real-life engineering and management applications.
According to the MMDP, the following equation can be obtained: mu_{D} left( {x_{text{m}}^ right) = hbox{max} mu_{D} left( x right) = hbox{max} bigcaplimits_{i = 1}^{m} {mu_{i} left( {f_{i} } right)} (17 The optimal (x_{text{m}}^) that has the maximum membership degree of the fuzzy decision set is the optimum solution to the multiple objective functions f i.
For solving MOPs, one of the most important problems that should be addressed is how to distinguish the quality of solutions consisting of multiple objective values.
Since we deal with multiple objective functions, there is no best single solution in the HM.
The solution obtained by combining the multiple objective functions to a single-objective function depends on the relative importance of the objective functions (f_{1} left( x right),{text{and}},f_{2} left( x right).) So, while setting the weights for combining the objectives, only the relative importance of the objectives should be considered and not the relative magnitude of the function values.
The results obtained from the integrated module show that GA with FEM can lead to a near optimal solution for both single as well multiple objective functions.
Since the solution algorithm of the FFP can transform multiple objective functions to equivalent constraints, it makes the FFP straightforward to deal with importance of multiple objectives.
The results obtained from the integrated module show that IMPGA with FEM can lead to a global optimal solution for both single as well as multiple objective functions.
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