## 5 Conclusions  
In this work, the best ML model suitable to predict the crack dimensions from the given 22 GLCM features extracted from MFL images reported by [PERSON] et al. [12], was determined using the Taguchi L16 orthogonal array experimental design. Out of six ML models, the XGB model is identified as the best suited for the proposed problem. Apart \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Performance Metrics** & **EM** & **MFO** & **GWO** & **DPGWO** \\ \hline \multirow{4}{*}{R\({}^{2}\)} & 0.9970 & 0.9987 & 0.9981 & 0.9992 \\  & 0.9938 & 0.9975 & 0.9966 & 0.9989 \\  & 0.9969 & 0.9993 & 0.9990 & 0.9994 \\ \hline \multirow{4}{*}{RMSE} & 0.101 & 0.066 & 0.078 & 0.050 \\  & 0.032 & 0.020 & 0.023 & 0.014 \\  & 0.208 & 0.099 & 0.126 & 0.089 \\ \hline \multirow{4}{*}{MAE} & 0.0872 & 0.0563 & 0.0568 & 0.0417 \\  & 0.0247 & 0.0147 & 0.0135 & 0.0099 \\  & 0.1922 & 0.0792 & 0.1028 & 0.0727 \\ \hline \multirow{4}{*}{MAPE} & 2.93 & 1.88 & 1.60 & 1.38 \\  & 3.09 & 1.72 & 1.60 & 1.16 \\  & 2.25 & 0.91 & 1.09 & 0.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Comparison of Performance with existing and proposed algorithms. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Variable** & **Samples** & **Mean** & **StDev** & **Variance** & **Minimum** & **Q1** & **Median** & **Q3** & **Maximum** & **Skewness** & **Kurtosis** \\ \hline DPGWO & 12 & 45 & 8.23 & 67.68 & 32.1 & 39.95 & 43.7 & 52.77 & 59.6 & 0.22 & \(-\)0.65 \\ GWO & 12 & 38.4 & 6.98 & 48.75 & 29.6 & 31.62 & 39.25 & 41.38 & 51.8 & 0.57 & \(-\)0.09 \\ MFO & 12 & 108.42 & 15.64 & 244.77 & 89.6 & 95.93 & 103.75 & 126 & 133.7 & 0.42 & \(-\)1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Comparison of computation time of algorithms. Figure 10: Experimental VS Predicted Value of Crack Width Using Different Algorithms. from that, two-filter-based feature selection methods are implemented for prioritizing the features. The performance of the ML models is examined based on the number of features and their combinations. Meta-heuristic algorithms, namely MFO, GWO, and a new variant of GWO called DPGWO, are implemented to identify the number of features and their combinations to achieve better performance of the selected XGB ML model. The proposed method proved that by eliminating 23% of the number of features as compared with the existing method, it was possible to get good performance using the XGB ML model. Also, in this work, it is identified that the features ETR, CST, ID, AC, and IDN are not important features, i.e., these features are eliminated during the prediction of crack dimensions. The effectiveness of the proposed DPGWO is proved by comparing [PERSON]'s Test and performance indicators' values, viz., IGD and SP with MFO and GWO. Also, the proposed method is implemented on the 12-test data set carried out by [PERSON] et al. [12]. As compared to the existing method, the proposed DPGWO performed well in calculating performance metrics like R\({}^{2}\), RMSE, MAE, and MAPE. Approximately 0.2 to 0.5% improvements in R\({}^{2}\) value, 50% to 57% improvement in RMSE value, 52% to 62% improvement in MAE value, and 53% to 63% improvement in MAPE values are reported by using a smaller number of features, i.e., 17 and its combinations, and implementing a new variant of GWO called DPGWO. As a further scope, the wrapper method of features selection along with the multi-regressor concept of ML models may be considered to improve performance. Apart from that, the crack dimensions may be changed from numerical to categorical data type, and ML classifiers can be introduced instead of ML regressors. The proposed DPGWO may be implemented for constrained engineering problems. Conceptualization, M.V.A.W., S.R., R.C., S.K.M. and M.E. ; data curation, M.V.A.W. ; personal analysis, M.V.A.W. ; investigation, M.V.A.W. ; methodology, S.R. and M.E. ; resources, R.C. and S.K.M. ; software, S.R., R.C., S.K.M. and M.E. ; visualization, M.V.A.W. and S.R. ; writing--original draft, M.V.A.W. and S.R. ; writing--review and editing, R.C., S.K.M.