Aluminium is a noncorrosive, lightweight material used to fabricate parts for the aerospace, automobile, and construction industries. Due to the low-temperature resistance, more heat is generated. At the same time, in machining, tremendous efforts are taken to keep friction and chatter to a minimum and to attain better quality and perfect output, and also more attention is required while selecting the machining process parameters. Spindle speed, rate of feed, radial and axial depth of cut, and radial rake angle of the tool are the parameters utilized to machine aluminium 6063 using the HSS tool on CNC milling to estimate spindle and worktable vibration using a prediction model. In this study, the design of the experiment of the response surface methodology approach is used to create a second-order statistical equation for experimentation with the Design-Expert v12 software. The performance characteristics are analyzed using the ANOVA method. The spindle speed achieved the lowest vibration between 2000 and 3000 rpm. Next, axial and radial depths were the most vibration-affecting parameter compared to the rate of feed and radial rake angle of the tool. To find the best feasible response, the nondominant sorting genetic algorithm II (NSGA II) approach was trained and tested using MATLAB software. Using a Pareto-optimal technique, the optimum worktable vibration ranged from 0.00284 to 0.00165 mm/s2, whereas the spindle vibration ranged from 0.02404 to 0.01336 mm/s2. The predicted values were found to be in an excellent argument when Pareto-optimal solutions are used.