## 4 Experimentation, Performance Evaluation, and Discussion
### Results and Discussion
The remaining algorithms, GA, DE, and IWO, outperformed the HFA-K-means in one dataset, namely S1, Birch1, and DIM002, respectively. HFA-K-means had the minimum average clustering results compared with the classical metaheuristic algorithms. This shows that the proposed HFA-K-means demonstrates superior performance over all the other competing metaheuristic algorithms. Table 8 compares the HFA-K-means with other hybrid algorithms, namely ISOS-K-means, PSODE, FADE, and IWODE. From the table, HFA-K-means also shows the best optimal solutions in 14 datasets, namely, A1, A2, Birch2, Birch3, Bridge, D31, DIM1024, Housec5, Housec8, Letter, Finland, S3, T4.8k, and Yeast. PSODE recorded a better performance in S1, S2, and S4, while FADE performed better on the A3, Birch1, and DIM002 datasets. The minimum average clustering result across the 20 datasets was recorded by HFA-K-means followed by FADE, ISOSK-means, PSODE, and IWODE. This indicates that HFA-K-means has performance superiority compared with other competing hybrid metaheuristic algorithms. The HFA-K-means algorithm was also compared with three other FA-based hybrid metaheuristic algorithms, FAPSO, FADE, and FATLBO, on seven high-dimensional datasets, as shown in Table 8. From the results, the HFA-K-means recorded superior performance in five of the seven datasets, namely, Birch2, Birch3, Bridge, Housec5, and Housec8. FAPSO demonstrated better performance in the Birch 1 and Letter datasets. HFA-K-means again recorded the smallest average clustering solution across the seven datasets, followed by FAPSO. Based on this, it can be stated that on the basis of comparison of all the FA-based hybrid metaheuristic algorithms, it is evident that the HFA-K-means had superior performance. Furthermore, in terms of comparison of HFA-K-means with the K-means-based algorithm ISOSK-means, it can be seen from Table 8 that HFA-K-means outperformed its counterpart in all except one of the datasets, namely, DIM002. This shows that the improvement in the K-means contributes substantially to the superior performances recorded by the HFA-K-means algorithm. In Figure 3, the performance gain in the computation time using the CLT-based K-means in the proposed hybrid algorithm is clearly demonstrated against the regular hybrid of FA and K-means. The HFA-K-means recorded a lower computation time to achieve convergence than its standard FA-K-means counterpart in all 20 datasets. clusions about the performance claims of the proposed algorithm reported earlier in the previous section. The report of the Friedman rank-sum test for the HFA-K-means and the two classical algorithms tested across the 20 datasets for the 20 algorithm runs is presented in Table 10. The report shows that the HFA-K-means had the best performance having the lowest rank value of 1 and highest rank value of 1.5 compared to FA and K-Means. The FA recorded a minimum rank value of 1.53 and a maximum rank value of 2.0, while the K-means had its minimum and maximum rank values as 3.0. An additional post hoc test was performed on the Friedman rank-sum test using the Wilcoxon signed-rank test to verify the significant differences between the algorithms. The Wilcoxon signed-rank test presents \(p\) values for determining the significant differences between the competing algorithms. The \(p\)-values were tested against the significant value of 0.05, meaning that if the \(p\)-value is larger than 0.05, there is no significant difference between the two algorithms. The results of the Wilcoxon signed-rank test presented in Table 11 clearly show significant differences in the performance of the representative algorithms. From the report, it can be clearly stated that HFA-K-means achieved a significant performance improvement in clustering high-dimensional datasets over the classical K-means algorithm in all the datasets and over the FA in 11 of the 20 datasets.