## 2 Materials and Methods  
Aluminum is one of the most important metals used in various industries and products, such as appliances, aviation, automotives, etc. [31]. Its chemical and mechanical properties include high ductility, high malleability, high corrosion resistance, a highly reflective surface, a low density, and its ability to be alloyed with other materials, such as zinc, copper, and magnesium. Hence, the prediction of the surface finishing would assist engineers in identifying suitable settings based on the applications. Al6061 is aluminum alloyed with magnesium and silicon as the main constituents, precipitated and hardened.  
In order to investigate the link between input variable factors that identify the machine setup and output achievement or surface roughness, 30 tests were conducted. The training and testing datasets came from full-scale datasets that were made accessible and documented in the paper by [PERSON] et al. [32]. In this experiment, Al6061 material was milled using a variety of cutting dimensions and axial depths of cut, and the Press o-firm Mitutoyo surface roughness tester was employed to measure each testing result. The measurements of the surface roughness were performed 3 times and the average was taken for all 30 samples This study employed the response surface methodology to design the template used for the experiment, and, in this design, there is room for the repeatability of the samples, which permits a good optimization analysis. This study uses the response surface methodology (RSM) and the least square approximation approach to predict the surface roughness for the end-milling of an aluminum alloy machining process. The influence of numerous factors on surface roughness was examined using ANOVA, and the accuracy of the RSM forecast method was compared to that of the least square approximation forecast method. For illustration, Figure 4 shows two of 30 experimental samples of surface aluminum blocks machined at two different input settings. The 30 experimental data corresponding to the testing configurations are shown in Table 1.  
\begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{\#} & **Spindle Speed** & **Feed Rate** & **Axial Depth** & **Radial Depth** \\  & **(rpm)** & **(mm/min)** & **(mm)** & **(mm)** \\ \hline  
\end{tabular}
\end{table}
Table 1: Experimental data.  
In the present paper, the surface roughness prediction has been performed using 6 modeling approaches: ANN, ANFIS, ANN-PSO, ANN-GA, ANFIS-PSO, and ANFIS-GA. The data have been obtained from a separate study conducted by [PERSON] et al. (2018). The mathematical expression and mathematical models (least square approximation method and response surface methodology) have been developed to predict the surface roughness on aluminum block Al6061 alloys. These Al6061 blocks were machined on an end-milling CNC using a high-speed stainless-steel tool and minimum quantity lubrication, with results gauged using a Mitutoyo surface roughness tester and a Press o-film. This experimental study used the spindle speed, feed rate, cutting axial depth, and radial depth as controllable variables to forecast the surface finish. The obtained data have been employed to train and validate the 6 models developed using ready-made artificial intelligence models on the Matlab interface. The 6 emerging results derived from the models were compared. The best model has been considered to predict the surface roughness. Parametric analysis was performed to identify the best model layout for the system under consideration through the investigation of several configurations.