# Improved Binary Grey Wolf Optimization Approaches for Feature Selection Optimization
## 8 Discussion  
In this section, the strong and weak points of each of the three proposed approaches are discussed. In general, hybrid metaheuristics are classified into two levels in terms of design issues: low-level and high-level [23]. Low-level hybridization means that one optimizer is embedded inside another optimizer, while high-level hybridization means that one optimizer is performed after applying another optimizer. The three proposed approaches can be classified as high-level optimizers. In general, such hybridization adds more computational complexity, which is considered one of the limitations of such hybrid approaches. In each iteration of IBGWO2, a P2P comparison was performed between each individual obtained from applying the BGWO optimizer and its corresponding individual obtained after applying BGWO and then BPSO. This P2P comparison was not applied collectively to all individuals in both populations. Therefore, the best solution among both populations could have been missed. The previously mentioned limitation of IBGWO2 was overcome in IBGWO3 by applying the ranking process across all individuals in both populations obtained by BGWO and \begin{table}
\begin{tabular}{l c c c c} \hline \hline  & IBGWO1 & IBGWO2 & IBGWO3 & IBGWO4 \\ \hline Total number of iterations & T & T & T & T \\ \hline GWO loop estimated iterations & T \(\times\) P & T \(\times\) P & T \(\times\) P & T \(\times\) P \\ \hline PSO loop estimated iterations & T \(\times\) P & T \(\times\) P & T \(\times\) P & T \(\times\) P \\ \hline P2P comparison loop estimated iterations & N/A & T \(\times\) P & N/A & N/A \\ \hline Ranking process & N/A & N/A & T \(\times\) P or T \(\times\) P\({}^{2}\) & T \(\times\) P or T \(\times\) P\({}^{2}\) \\ \hline Total estimated loops & 2 \(\times\) T \(\times\) P & 3 \(\times\) T \(\times\) P & 3 \(\times\) T \(\times\) P or 3 \(\times\) T \(\times\) P\({}^{2}\) & 3 \(\times\) T \(\times\) P or 3 \(\times\) T \(\times\) P\({}^{2}\) \\ \hline Big-O notation & O(T \(\times\) P) & O(T \(\times\) P) & O(T \(\times\) P) or O(T \(\times\) P\({}^{2}\)) & O(T \(\times\) P) or O(T \(\times\) P\({}^{2}\)) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Computational complexity of the proposed approaches. BGWO followed by BPSO. A further enhancement of IBGWO3 was achieved with IBGWO4. This enhancement considered the initial population obtained from every previous iteration in addition to the two populations obtained by BGWO and BGWO followed by BPSO. This clarified the reason why IBGWO4 generally provided better evaluation results than IBGWO3 and IBGWO2. However, the complexity of the ranking process increased when IBGWO4 or IBGWO3 was applied compared with IBGWO2. Since a high-dimensional dataset was used in the evaluation of the three proposed approaches, the authors would like to discuss the suitability of each of the three approaches as the dimensionality of the dataset increased. As previously mentioned, IBGWO4 provided the best general performance, followed by IBGWO3 and IBGWO2, at the expense of computational complexity. Therefore, IBGWO4 can be used to provide the best classification accuracy with the least number of selected features for datasets with very high dimensionality of features. IBGWO4 will be suitable for this type of dataset provided that the computational complexity is not a concern or the target system is not time-constrained. However, if the computational complexity of analyzing this dataset type has priority over the classification accuracy and fitness values, IBGWO2 or IBGWO3 will be better to apply relative to IBGWO4. Selecting IBGWO2 or IBGWO3 will depend on the required classification accuracy and fitness values. IBGWO2 will provide the lowest classification accuracy and fitness values at the lowest computational complexity compared with the other two approaches. An extensive numerical analysis needs to be implemented to provide insights into the relation between the performance of each of the three proposed approaches and the degree of dimensionality of the different datasets.