## 5 Results and Discussion of Findings
### Comparative Analysis of Selected Features for All Methods  
The basis of solving feature selection problems using the binary optimization method is to reduce the number of features used for classification purposes. This is necessary to eliminate the bottleneck which is often associated with high-dimensional datasets on classifiers. Another benefit of reducing the number of features is to ensure that only relevant ones are used for the classification operation. In this subsection, we evaluate BEOSA and BIEOSA and compare their performance with that of BWOA, BPSO, BFSO, BGWOA, BDMO and BSNDO. Table 4 compares the number of features selected for each algorithm across four different population sizes, namely, 25, 50, 75 and 100. An interesting performance result was observed when the algorithms were compared based on their average number of selected features. For example, the BPSO outputs a value of 1 for the number of selected features for all population sizes and for all datasets considered during our experiments. While this showed some measure of abnormality in the process of feature selection in the algorithm, we observed more standard performance for all the remaining methods. As an example, consider the outcome of some low-dimensional datasets such as the BreastEW, CongressEW, Exactly and Exactly2. The BEOSA and BIEOSA yielded similar results to all the other methods. For BWOA, BGWO, BDMO, BSNDO, BEOSA and BIEOSA, the average numbers of features (on population sizes yielding this average performance) were 17.0 (25), 16.9 (100), 5.5 (50), 3.0 (25), 7.3 (25) and 5.9 (75), respectively. The CongressEW showed 8.9 (100), 10.1 (25), 2.4 (50), 2.4 (50), 5.3 (100) and 4.6 (50) for the same BWOA, BGWO, BDMO, BSNDO, BEOSA and BIEOSA methods. Similarly, the Exactly dataset reported values of 6.2 (50), 8.5 (25), 3.0 (25), 2.2 (25), 4.2 (25) and 2.5 (75), while Exactly2 gave 7.0 (75), 8.3 (100), 3.5 (100), 2.0 (25), 1.7 (100) and 2.5 (25) on the same methods, respectively. These results show that in most cases, population sizes of 25-50 were sufficient to produce the desired results. Even population-intensive algorithms such as BEOSA and BIEOSA demonstrated that their best average feature selection counts could be obtained using a population size range of 25-75. High-dimensional datasets like Lung, Prostate, Leukemia and Colon, and moderate-dimensional datasets like the PenglungEW, showed how superior the BEOSA and BIEOSA methods were. For instance, the average feature selection numbers in the Lung dataset were 1692.5 (100), 2151.1 (75), 820.3 (50), 2098.4 (25), 403.9 (100) and 685.3 (75) for BWOA, BGWO, BDMO, BSNDO, BEOSA and BIEOSA respectively. Clearly, the BEOSA algorithm yielded the best performance, i.e., 403.9 using 100 as the population size. Additionally, the results obtained for the Prostate dataset showed that the BDMO, BSNDO, BEOSA and BIEOSA methods were able to yield average numbers of selected features of 1402.8 (100), 1478.4 (25), 682.2 (100) and 1141.5 (25), while the BEOSA provided the best performance with a population size of 100. A very impressive result was obtained for BEOSA and BIEOSA on the Leukemia dataset; the BWOA, BGWO, BDMO, BSNDO, BEOSA and BIEOSA algorithms yielded 1708.3 (25), 2320.4 (75), 999.7 (75), 928.5 (25), 50.3 (25) and 589.7 (75), respectively, for the average number of selected features. BEOSA produced an optimal number of 50.3 for selected features with a population size of 25. Moreover, the BIEOSA variant also yielded 589.7 as the average feature size with a population size of 75. Furthermore, the performance of the BWOA, BGVO, BGWO, BDMO, BSNDO, BEOSA and BIEOSA algorithms on the PenglungEW dataset showed values of 170.0 (75), 4.0 (50), 193.0 (50), 23.9 (100), 124.0 (100), 35.0 (75) and 24.0 (25), respectively, as the average number of selected features. Accordingly, BEOSA and BIEOSA performed well using population sizes of 75 and 25, respectively.