# Improved Binary Grey Wolf Optimization Approaches for Feature Selection Optimization
## 1 Introduction
This combination aims to overcome the GWO stuck-in-local-optima problem that might occur by leveraging the PSO-wide search space exploration ability on the solutions obtained by GWO. The three proposed approaches are all named Improved Binary Grey Wolf Optimization (IBGWO) and each of them is abbreviated to IBGWO and appended to the approach number. The proposed work in this paper adds significant extensions to the work proposed in [19]. The FS optimization problem considered in this paper is a binary problem since the features are represented as a bit string of 0's and 1's to reflect the non-selected and selected features, respectively [20; 21]. Transfer functions (TFs) are the mechanisms that are used to transform continuous solutions into binaries [22]. Two types of TF, namely, S-shaped and V-shaped, are used in this work. The three proposed hybrid approaches are based on the binary versions of both PSO and GWO to resolve the FS optimization problem. Each of the three proposed approaches combines GWO with PSO by applying GWO followed by PSO and then each approach manipulates the solutions obtained by both algorithms in a different way. The first approach is named IBGWO2 and it performs peer-to-peer (P2P) comparisons between the PSO solutions and the corresponding GWO solutions and keeps the fittest solutions for the next iteration. The second approach is named IBGWO3 and it ranks all the solutions that are obtained from both GWO and PSO and keeps the fittest solutions from both algorithms together. The third approach is named IBGWO4. It is like IBGWO3 in ranking all the solutions that are obtained from both GWO and PSO and it adds the initially generated solutions to select the optimal solutions from these three populations, i.e., those obtained by GWO, PSO, and the initial population. The performances of the three approaches were evaluated and compared with each other in addition to making comparisons with the original binary PSO (BPSO), binary GWO (BGWO), and other state-of-the-art metaheuristics used for FS optimization in the literature. The comparisons were performed using nine high-dimensional, cancer-related human gene expression datasets. The evaluations were performed in terms of a set of evaluation metrics, namely, average classification accuracy, average number of selected features, average fitness values, average computational time, and computational complexity. The results showed that the proposed S-shaped optimizer, IBGWO3-S, achieved more than 0.9 average classification accuracy while selecting the fewest number of features in most of the datasets. The proposed V-shaped optimizer named IBGWO4-V achieved more than 0.95 average classification accuracy while also selecting the fewest number of features in most of the datasets. The results also confirmed the superiority of the proposed IBGWO4-V approach when compared with the original BGWO and BPSO. Moreover, the results confirmed the superiority of the proposed IBGWO4-V approach over other state-of-the-art metaheuristics selected from the literature in most of the datasets. Finally, the computational complexity analysis of the three proposed approaches showed that the best approach in terms of classification accuracy, fitness value, and number of selected features had the highest computational complexity. This paper is organized as follows. Related works are discussed in Section 2. Section 3 introduces GWO, PSO, and their binary versions. The details of the proposed approaches are provided in Section 4. The evaluation metrics are described in Section 5. The datasets and experimental setup are presented in Section 6. The evaluation results are discussed in Section 7. A discussion of the evaluation results is summarized in Section 8. Conclusions and future work directions are presented in Section 9. Finally, Appendix A lists all abbreviations used throughout the paper.