70 60 50 40 30 20 10 8 7 6 5 4 3 2 1 0100 200300 400500 600700 800900 1,000 (a) 80 90 70 60 50 40 30 20 10 0100 200300 400500 600700 800900 1,000 (c) WOA APSO 8 9 7 6 5 4 3 2 1 0100 200300 400500 600700 800900 1,000 (d) GWA SMA USMA FIGURE 5. Representative benchmark functions showing convergence graphs of (a) F2, (b) F4, (c) F12, and (d) F21. TABLE 3. Analysis of mean fitness value using Kruskal-Wallis and Wilcoxon statistical methods. MEAN FITNESS VALUE ALGORITHM A ALGORITHM B TEST WOA APSO USMA GWO SMA Kruskal 6.3078 Wilcoxon 5.0396 Kruskal 12.8491 Wilcoxon 10.6947 Kruskal 12.9609 Wilcoxon 11.6287 Kruskal 6.7852 Wilcoxon 4.5677 STATISTICS p VALUE 0.012 2.63E-06 0.0003 APSO 2.58E-06 0.0003 2.56E-06 0.0091 SMA 2.55E-06 USMA GWO TABLE 4. Analysis of best fitness value using Kruskal- Wallis and Wilcoxon statistical methods. BEST FITNESS VALUE ALGORITHM A ALGORITHM B TEST WOA Kruskal 5.0497 Wilcoxon 5.0446 STATISTICS p VALUE 0.0246 2.52E-06 Kruskal 12.0805 0.0005 Wilcoxon 12.0685 2.76E-06 Kruskal 10.7161 Wilcoxon 10.7054 Kruskal 4.5723 Wilcoxon 4.5677 0.001 2.26E-06 0.0324 8.33E-06 0100 200300 400500 600700 800900 1,000 (b) DECEMBER 2023 IEEE ROBOTICS & AUTOMATION MAGAZINE 37