## 3 Results and Discussion
### Case Study 1  
Cutting force analysis and its minimization plays a crucial role in machining operation and understanding the cutting phenomena of the work material in different environments (dry, wet, and LN\({}_{2}\) machining). Moreover, after machining, the work material must be superior in surface quality [33]. On the other hand, minimizing the machining zone's temperature is necessary to retain the cutting temperature as low as possible. In this case study, the MLRM for minimizing all the machinability indices is developed using Minitab 17. The developed MLRM are given in Equations (1)-(3). **Objective functions 1. **  
\[ \begin{array}{r c c c c}\text{\emph{Minimize}}&\text{\emph{Cutting}}&=212.7-0.244A+703B+20C\\ Force&-&0.00571A^{2}+6289B^{2}-8.11C^{2}\\ &-0.60 AB+0.053 AC-143 BC\\ R^{2}=0.98,&Adj\ R^{2}=0.98\end{array}  \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**S.no**} & **Cutting Speed** & **Feed Rate** & \multirow{2}{*}{**Environment**} & **Cuting Force** & **Surface Roughness** & **Cutting Temperature** \\ \hline \multicolumn{3}{c}{**m/min**} & **mm/rev** & \multicolumn{3}{c}{**Fz (N)**} & **Ra (\(\mu\)m)** & \({}^{\circ}\)**C** \\ \hline
17 & 87 & 0.15 & Wet & 368 & 2.53 & 515 \\ \hline
18 & 124 & 0.15 & Wet & 308 & 2.43 & 565 \\ \hline
19 & 33 & 0.05 & Cryogeic & 228 & 2.65 & 50 \\ \hline
20 & 87 & 0.05 & Cryogeic & 168 & 2.48 & 95 \\ \hline
21 & 124 & 0.05 & Cryogeic & 132 & 2.29 & 110 \\ \hline
22 & 33 & 0.1 & Cryogeic & 275 & 2.2 & 90 \\ \hline
23 & 87 & 0.1 & Cryogeic & 24  
**Objective functions 2. **  
\[ \begin{array}{ll}\text{\emph{Minimize}}&Surface&=3.56-0.008A-9.65B+0.73 \text{C}\\ \text{\emph{Roughness}}&+0.000015A^{2}+19.3B^{2}-0.265\text{C}^{2}\\ &+0.023 AB+0.00028 AC-0.65 BC\\ &R^{2}=0.98,\text{ \emph{Adj}}R^{2}=0.97\\ \end{array}  \tag{2}\]  
**Objective functions 3. **  
\[ \begin{array}{ll}\text{\emph{Minimize}}&\text{\emph{Cutting}}&=-0.083+0.076A+ 2521B+341.21\text{C}\\ \text{\emph{Temperature}}&+0.0033A^{2}-1400B^{2}-118\text{C}^{2}\\ &-1.42 AB-0.16 AC-396.67 BC\\ &R^{2}=0.97,\text{ \emph{Adj}}R^{2}=0.96\\ \end{array}  \tag{3}\]  
Three responses were considered in this section R1, R2 and R3, CF, SR and CT, respectively, as shown in Table 4.  
Figure 4a present the convergence plot for cutting force using the evolutionary algorithms. It is observed that the response is converged in iteration no. 2 using the MFO algorithm. Provided the same response value is converged in iteration no. 3, 10, 61, and 78 based on GA, PSO, GHO, and GWO algorithms, respectively. Further, the response value is very minimum in the MFO algorithm and maximum in GA. The simplicity of the MFO algorithm along with the speed in searching is the prime reason for obtaining the best results in the present work. It is additionally inferred that the CF is very minimum in the LN\({}_{2}\) environment compared to the dry and wet machining environments. The LN\({}_{2}\) nozzle spray droplet acts as cushioning effect of the machining zone and, thus, minimizes the \(v_{\rm c}\)[42]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithms** & **Cutting Speed (m/min)** & **Feed Rate (mm/rev)** & **Environment** & **Machinability Index Value** & **Iteration No.** \\ \hline \multicolumn{5}{c}{Cutting force} \\ \hline MFO & 124 & 0.05 & 3 & 127.10 N & 2 \\ GA & 119.61 & 0.05 & 3 & 139.16 N & 3 \\ GHO & 124 & 0.06 & 3 & 135.27 N & 61 \\ GWO & 121.65 & 0.05 & 3 & 132.85 N & 78 \\ PSO & 123.32 & 0.05 & 3 & 132.77 N & 10 \\ \hline \multicolumn{5}{c}{Surface roughness} \\ \hline MFO & 124 & 0.05 & 3 & 1.78 μm & 1 \\ GA & 86.23 & 0.147 & 3 & 1.88 μm & 3 \\ GHO & 124 & 0.129 & 3 & 1.85 μm & 39 \\ GWO & 134.17 & 0.15 & 3 & 1.81 μm & 79 \\ PSO & 126.32 & 0.052 & 3 & 2.33 μm & 10 \\ \hline \multicolumn{5}{c}{Cutting temperature} \\ \hline MFO & 34.04 & 0.05 & 3 & 33.19 °C & 22 \\ GA & 80.77 & 0.05 & 3 & 78.98 °C & 67 \\ GHO & 36 & 0.05 & 3 & 32.33 °C & 65 \\ GWO & 39.57 & 0.06 & 3 & 48.44 °C & 43 \\ PSO & 33.6 & 0.05 & 3 & 34.11 °C & 26 \\ \hline \hline \end{tabular}
\end{table}