## 3 Proposed RBAVO-DE for GS
### The Complete RBAVO-DE Algorithm
### Results of Comparing the Proposed RBAVO-DE with Various Meta-Heuristic Algorithms

The proposed RBAVO-DE approach with the SVM and \(k\)-NN models was compared with other recent meta-heuristic methods executed under the same conditions to show its superiority over its counterparts. The proposed RBAVO-DE algorithm was compared with binary variants of several optimizers, including BABC, BSSA, BPSO, BBA, BGWO, BWOA, BBSA, BGOA, BHHO, BASO, and BHGSO. #### 4.4.1 Results Employing the \(k\)-NN Model

Table 4 shows the results of the proposed RBAVO-DE algorithm and other optimization techniques employing the \(k\)-NN model, based on accuracy metrics compared under similar conditions. The experimental outcomes reveal that the proposed RBAVO-DE achieved the most promising outcomes in four benchmarks. It is noteworthy that all competitive methods, including the proposed RBAVO-DE employing the \(k\)-NN model, produced comparable outcomes across eighteen benchmarks. The rest of the metrics for the \(k\)-NN model are shown in Appendix A.1. In terms of the average fitness values, the proposed RBAVO-DE algorithm demonstrated higher efficiency compared to its counterparts using the \(k\)-NN model under similar conditions. The RBAVO-DE algorithm yielded the lowest fitness results and the most competitive STDE across all benchmarks. Also, all utilized benchmarks are high-dimensional, demonstrating that the proposed RBAVO-DE can run effectively on all benchmarks regardless of size. The RBAVO-DE algorithm shows promise by effectively balancing exploitation and exploration of the search space, avoiding becoming trapped in local optima during iterations. Unlikemany other algorithms that tend to become trapped, it demonstrated the ability to escape such traps. Regarding the mean results for the genes selected by the proposed RBAVO-DE algorithm and its counterparts employing \(k\)-NN, the proposed RBAVO-DE algorithm surpassed the other methods across all benchmarks concerning the number of chosen genes. Furthermore, the RBAVO-DE's capacity to identify significant genes is due to its effective exploration of possible areas while enhancing accuracy. In terms of the mean precision of the proposed RBAVO-DE algorithm and its counterparts with \(k\)-NN, the proposed RBAVO-DE outperformed alternative approaches for three of the twenty-two datasets. For nineteen datasets, BWOA achieved similar results, while BABC, BPSO, BGWO, BGOA, and BHHO obtained results similar to those of the proposed RBAVO-DE. BASO and BHGSO, which produced the same outcomes as the proposed RBAVO-DE on seventeen datasets, ranked fourth. Ultimately, BBA ranked lowest among all approaches, producing similar outcomes to the proposed RBAVO-DE for fifteen datasets. Regarding the mean recall of the proposed RBAVO-DE and its counterparts employing \(k\)-NN, RBAVO-DE outperformed the alternative approaches for three of the twenty-two datasets. On the other hand, BSSA, BABC, BPSO, BGWO, BWOA, BGOA, and BBSA produced the same outcomes as RBAVO-DE for 19 datasets, while BHHO achieved similar results for 18 datasets. BHGSO, which obtained the same outcomes as the proposed RBAVO-DE for seventeen datasets, ranked fourth. Ultimately, BASO and BBA ranked lowest among all approaches, producing similar results to RBAVO-DE for sixteen datasets. With regard to the mean F1-score of the proposed RBAVO-DE and its counterparts employing \(k\)-NN, the proposed RBAVO-DE outperformed the alternative approaches for three of the twenty-two datasets. In contrast, for eighteen datasets, BSSA, BABC, BPSO, BGWO, BGOA, and BBSA produced the same outcomes as RBAVO-DE, while BWOA and BHHO produced comparable outcomes for seventeen datasets. BASO and BHGSO, which obtained the same outcomes for 16 datasets as the proposed RBAVO-DE, ranked fourth. Ultimately, BBA ranked lowest among all approaches, producing similar outcomes to the proposed RBAVO-DE for fourteen datasets.