## 5 Multiobjective Optimization of Response
### Parametric Optimization  
On the basis of the second-order quadratic mathematical model of the responses developed in the previous sections via Equations (1) and (2), the independent desirability functions d1 and d2 for minimum dimensional deviation and minimum surface irregularity, respectively, were selected. Next, the weighting factor (s) value associated with each response's desirability function was assigned. When the weighting factor has a value of less than one, the desirability function of a response for pursuing the target becomes less sensitive. A weighting factor greater than one has the opposite effect. Therefore, it is typically set to unity, which offers a moderate level of sensitivity [44].  
In the case of multiresponse optimization, it should be noted that a suitable weighting factor must be assigned to each response based on the relative importance of each response. This study assigned (Div) and (Ra) equal weightings (w = 0.5). Furthermore, the default importance value (s = 1) was chosen for all responses, meaning it was equally essential to achieving the goals.  
Minitab's Response Optimizer was used to seek the optimal input combinations that would yield the most acceptable compromise between responses. Table 11 provides a summary of the essential parameters and values for determining the optimal global solution.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter/Response** & **Goal** & **Lower Limit** &
\begin{tabular}{c} **Upper** \\ **Limit** \\ \end{tabular} & **Weight** & **Importance** \\ \hline A & In range & 1.2 & 2.5 & 1 & 1 \\ B & In range & 15 & 55 & 1 & 1 \\ C & In range & 1 & 7 & 1 & 1 \\ Div & Minimize & 0.051695 & 0.089167 & 0.5 & 1 \\ Ra & Minimize & 2.747 & 8.901 & 0.5 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 11: Goals and constraints for inputs and responses.  
Figure 10 is a visual representation of the optimal outcome. The optimization diagram illustrates how each input (columns) affects the desirability of the output (rows). In addition, each cell illustrates how the response varies with specific inputs while other inputs remain constant. The solid red lines represent the optimal configuration, while the blue dashed lines represent the current output value. High and low input parameters are also represented by the numbers \(1\) and \(-1\), respectively.  
The most important part of this graph is located in the middle row, between the high and low rows, as represented by \"cur\" (in red) and written in code. This information offers the ideal parameter settings needed to meet the specified criterion. In this regard, the composite desirability value (shown in blue in the first column from the left) is calculated by adding the individual desirability values of each response. Figure 10 reveals that high values of desirability were attained for each output, resulting in a high composite desirability value. Therefore, optimization was effective in determining the optimal set of parameters. In conclusion, moderate levels of (A) and (B) with high (C) should be used to achieve the optimum combination of (Div) and (Ra) with values of 0.0517 mm and 2.8079 \(\upmu\)m, respectively.