## 3 Experimental Verification Using Benchmark Test Functions
### Comparative Analysis  
Tables 1 and 2 show the comparative analysis between the IRSA and other MH algorithms for unimodal, multimodal, and fixed-dimension functions. For unimodal and multimodal functions, each algorithm was evaluated considering population size and iterations of 50 and 500, respectively. For statistical analysis, each algorithm ran 30 times to compute the best value, average value, worst value, and standard deviations [52]. The IRSA showed a great ability to find the optimum value on 16 out of 23 test functions, which represented nearly 70%, and it ranked second among five other test functions. The convergence curves are depicted in Figure 4. These results demonstrate the positive effects of the improvisations in the form of improved global convergence, enhanced optimization accuracy, and increased stability. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Fun** & **Measure** & **IRSA** & **RSA** & **BMO** & **PSO** & **GWO** & **AOA** & **DGCO** \\ \hline
**F1** & **Best** & 0 & 0 & 6.030e-129 & 32.4203 & 4.7922e-35 & 6.706e-284 & 1.238e-21 \\ \hline  & **Worst** & 0 & 0 & 1.961e-121 & 63.6854 & 8.0427e-33 & 1.2838e-114 & 2.1218e-19 \\ \hline  & **Average** & **0** & **0** & 2.712e-122 & 43.2608 & 1.4545e-33 & 1.2838e-115 & 4.7446e-20 \\ \hline  & **STD** & 0 & 0 & 6.153e-122 & 9.48589 & 2.4625e-33 & 4.0598e-115 & 7.9075e-20 \\ \hline
**F2** & **Best** & 0 & 0 & 1.393e-67 & 2.35817 & 1.7406e-20 & 0 & 3.7704e-14 \\ \hline  & **Worst** & 0 & 0 & 7.383e-65 & 5.32663 & 9.4593e-20 & 0 & 4.68526e-13 \\ \hline  & **Average** & **0** & **0** & 1.841e-65 & 3.31147 & 4.5301e-20 & **0** & 1.10333e-13 \\ \hline  & **STD** & 0 & 0 & 2.663e-65 & 0.89717 & 2.2708e-20 & 0 & 1.29549e-13 \\ \hline
**F3** & **Best** & 0 & 0 & 4.0313e-92 & 5.5826e+03 & 4.5340e-04 & 0.0286 & 0.0025 \\ \hline  & **Worst** & 0 & 0 & 2.9026e-76 & 9.1971e+03 & 0.0201 & 0.5838 & 25.4054 \\ \hline  & **Average** & **0** & **0** & 1.1183e-76 & 7.8891e+03 & 0.0074 & 0.1907 & 5.7823 \\ \hline  & **STD** & 0 & 0 & 1.5330e-76 & 1.3842e+03 & 0.0074 & 0.2277 & 10.9998 \\ \hline
**F4** & **Best** & 0 & 0 & 7.3742e-58 & 5.43665 & 7.5397e-09 & 4.6289e-88 & 4.97610e-06 \\ \hline  & **Worst** & 0 & 0 & 2.5295e-52 & 14.1279 & 4.4114e-08 & 0.05287 & 0.000247 \\ \hline  & **Average** & **0** & **0** & 4.1512e-53 & 8.305702 & 1.8813e-08 & 0.024560 & 5.9520e-05 \\ \hline  & **STD** & 0 & 0 & 8.765e-53 & 2.59027 & 1.274e-08 & 0.02222 & 7.3133e-05 \\ \hline F5 & **Best** & 45.4705 & 48.9824 & 48.9417 & 5.7675e+03 & 46.1950 & 48.6070 & 46.1974 \\ \hline  & **Worst** & 47.7889 & 48.9903 & 48.9984 & 1.0132e+04 & 47.8430 & 48.9439 & 47.8660 \\ \hline  & **Average** & **46.4656** & 48.9883 & 48.9721 & 8.1573e+03 & 47.0300 & 48.7869 & 47.0569 \\ \hline  & **STD** & 0.6506 & 0.0032 & 0.0173 & 2.0349e+03 & 0.8086 & 0.1402 & 0.5917 \\ \hline
**F6** & **Best** & 1.58 & 11.97 & 11.39 & 150.00 & 2.25 & 6.43 & 3.48 \\ \hline  & **Worst** & 2.67 & 12.25 & 12.44 & 284.60 & 2.89 & 7.44 & 5.78 \\ \hline  & **Average** & **2.37** & 12.22 & 11.935 & 214.76 & 2.5 & 6.90 & 4.67 \\ \hline  & **STD** & 0.25 & 0.0878 & 0.4067 & 47.02 & 0.27 & 0.34 & 0.66 \\ \hline F7 & **Best** & 7.6084e-06 & 2.6639e-05 & 1.5133e-04 & 0.1347 & 4.8839e-04 & 1.6821e-07 & 0.0014 \\ \hline  & **Worst** & 2.8963e-05 & 6.7811e-05 & 3.8440e-04 & 0.2985 & 0.0037 & 5.2418e-05 & 0.0154 \\ \hline  & **Average** & 8.7740e-05 & **9.0710e-05** & 4.1659e-04 & 0.2155 & 0.0022 & 2.3443e-05 & 0.0071 \\ \hline  & **STD** & 9.3116e-05 & 5.2933e-05 & 2.3023e-04 & 0.0592 & 0.0012 & 2.0923e-05 & 0.0055 \\ \hline \end{tabular}
\end{table} 
Table 1: Results for unimodal and multimodal functions for 50 dimensions, 500 iterations.