## 4 Conclusions  
The purpose of this study was to minimize machinability indices CF, SR, and CT while performing the turning of Hastelloy X. Three levels of turning process parameters namely  
Figure 6: (**a**–**c**) Normal Probability plot (**d**–**f**) summary report.  
cutting speed (\(v_{\text{c}}\)), feed rate \(f\), and machining environment were considered for performing the experiments under L27 orthogonal array basis. Further, the MFO algorithm was used to identify the optimal set of turning process parameters to minimize the machinability indices individually and simultaneously. Three case studies were carried out for this purpose. The conclusion drawn from these case studies is given below.  
1. From the case study 1 (minimization of machinability indices individually), as compared to other algorithms such as GHO, GA, PSO, and GWO, the MFO algorithm yielded the minimum values of CF = 127.1 N, SR = 1.78 \(\upmu\)m, and CT = 33.19 \({}^{\circ}\)C for the optimal set of turning process parameters such as \(v_{\text{c}}\) = 124 m/min, \(f\) = 0.05 mm/rev, and cryogenic environment. The range of reduction in CF, SR, and CT values based on the MFO algorithm was 4-8 %, 1-23%, and 3-57%, respectively, compared with other algorithms.
2. The simultaneous minimization of dual machinability indices with three combinations were performed using the MFO algorithm in case study 2. The results were compared with the results obtained from other algorithms. Based on the hypervolume indicator identified from the Pareto analyses, again the MFO outperformed others, and the corresponding optimal set of input parameters were identified.
3. In case study 3, the simultaneous minimization of all three machinability indices was carried out using the MFO algorithm. The performance of MFO algorithm was compared with other algorithms using the quality indicators namely Diversity, Inverted Generational Distance, and Hyper Volume. From the analyses, the best results were obtained as CF = 171.13 N, SR = 2.35 \(\upmu\)m and CT = 72.28 \({}^{\circ}\)C form the MFO algorithm for the inputs of \(v_{\text{c}}\) = 93 m/min, \(f\) = 0.05 mm/rev and cryogenic environment.  
Based on the results of all three case studies, the MFO algorithm effectively predicted the optimal set of turning process parameters in view of minimizing the machinability indices individually and simultaneously when compared with other algorithms. Further, the other machinability indices such as tool life and machining cost will also be considered in addition to the existing indices as the future work.  
Conceptualization, V.S.; Methodology, V.S., J.S. and Y.N.; Experimental design, V.S. and J.S.; Experimental setup, V.S.; Measurements, V.S., S.K.M. and Y.N.; Investigation, L.N., S.K.M. and Y.N.; Resources, L.N., S.K.M. and Y.N.; Visualization, V.S., L.N., S.K.M. and S.S.; Writing--Original Draft Preparation, V.S.; J.S., L.N., S.K.M., Y.N., S.S., E.A.N., J.P.D. and H.M.A.M.H.; Writing--Review & Editing, V.S., J.S., L.N., S.K.M., Y.N. and S.S.; Supervision, J.S. and V.S.; Project administration, V.S. and J.S.; Funding acquisition, J.S. and S.S. All authors have read and agreed to the published version of the manuscript.  
This research has received funding from King Saud University through Researchers Supporting Project number (RSP-2021/164), King Saud University, Riyadh, Saudi Arabia. Moreover, this is part of the project was financially supported by Fundamental Research Fund of Shandong University under the funding code No. 2019 HW040. the Future for Young Scholars of Shandong University, China under the funding code No. 31360082064026.  
Not applicable.  
The authors extend their appreciation to King Saud University for funding this work through Researchers Supporting Project number (RSP-2021/164), King Saud University, Riyadh, Saudi Arabia.  
The authors declare no conflict of interest.