## 6 Conclusions  
Though there has been a lot of research on CMS design issues, there have been few studies on taking Cell Formation and a dynamic flexible architecture into consideration. This study created a novel method that uses a number of flexibility parameters to direct the formation of cells. The proposed method was created to address complex, multiobjective design problems in CMS on a big scale. It incorporated a Genetic Algorithm (GA), an encoding function technique, and machine layout cell designs that maximize performance outcomes in order to obtain Cell Formation. The machines and their components were introduced as a matrix. In GA runs, a number of chromosomal evolution and selection throughput adjustment techniques were used. In order to determine the best Cell Formation and machine layout, Genetic Algorithms (GAs) were used. The machines were programmed for each Cell Formation. This approach is distinctive in a number of ways, particularly when flexibility is viewed as an expression of the trade-off between machine usage and the number of exceptional features, i.e., in terms of Cell Formation dimensions Cell Formation based on any required flexibility ranging from 0.1 to 0.8, resolving issues in real-world case studies. The effectiveness of the established approach was demonstrated through the resolution of a Pakistani automotive real-world case study. It is concluded that the proposed GA based on the machine encoding technique optimizes the design of CMS and improves the group efficiency to 72.81 (average value) compared with other metaheuristics algorithms, as shown in Table 15.  
Additionally, it would be beneficial to investigate whether the current production processes can accommodate a new part throughout cell manufacturing operations. When admitting additional parts, logistics and cell reorganization costs should be taken into  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Problem Set**} & **Problem** & **Clustering** & **Genetic** & **Hybrid** & **Genetic Pro-** & **Evolutionary** & **Proposed** \\  & **Size** & **Algorithm** & **Algorithm** & **Algorithm** & **germming** & **Algorithm** & **Algorithm** \\  & **(M \(\times\) P)** & **(M.ST)** & **(GA)** & **(HA)** & **(GP)** & **(EA)** & **Algorithm** \\ \hline
1 & \(5\times 7\) & - & - & 73.68 & - & 73.68 & **74.58** \\
2 & \(6\times 8\) & - & 76.92 & 76.92 & - & 76.92 & **79.44** \\
3 & \(7\times 11\) & - & 46.88 & 53.13 & - & 53.13 & **61.95** \\
4 & \(8\times 12\) & - & - & 68.3 & - & 68.3 & 68.56 \\
5 & \(8\times 20\) & 58.72 & 58.32 & 58.70 & 58.33 & - & **59.45** \\
6 & \(10\times 10\) & 70.59 & 70.59 & 70.59 & - & 70.59 & **74.33** \\
7 & \(10\times 15\) & 91.00 & 91.00 & 92.00 & 91.00 & 92.00 & 89.56 \\
8 & \(10\times 20\) & - & - & - & - & 90.00 & 90.23 \\
9 & \(14\times 24\) & - & 67.44 & 70.50 & - & 69.33 & **78.60** \\
10 & \(20\times 20\) & - & 37.12 & 42.96 & - & 43.20 & **51.45** \\ \hline \hline \end{tabular}
\end{table}
Table 15: Performance metric group efficiency comparison with other methods.  
account in the objective functions, and a new strategy should be designed to deal with the optimization model's high level of complexity.  
Conceptualization, X.W.; methodology, M.R.; software, Q.S.K.; validation, M.A. and F.M.A.; formal analysis, W.L.; investigation, W.L. and M.A.; data curation, F.M.A.; writing--original draft preparation, M.R.; writing--review and editing, Q.S.K. and M.R.; supervision, X.W.; funding acquisition, M.A. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Researchers Supporting Project Number (RSP2023R274) King Saud University, Riyadh, Saudi Arabia.  
Not applicable.  
The data used in this study are available from the corresponding author upon reasonable request. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.