# Multi-Strategy Hybrid Whale Optimization Algorithm Improvement
## 4 Simulation Experiments and Comparative Analysis
### [PERSON]'s Rank-Sum Test Analysis
Among them, the standard deviation of CSCFA is 37.19% smaller than that of MHWOA when calculating F5, which means MHWOA is not more stable than CSCFA when solving shifted and full rotated Levy function. But comparing their average results, even if MHWOA fluctuates up and down within the standard deviation interval, its floating maximum value is significantly smaller than the floating minimum value of CSCFA, which also indicates that its calculation accuracy is at least 8.13% higher than that of CSCFA. When calculating F7, the standard deviation of PSO-sono is 17.01% smaller than that of MHWOA. Since the difference between the two is only 1.833, and the mean values of the two are 2035.583 and 2029.43, respectively, the difference in the mean value is insignificant. However, for PSO-sono, it is 2044.52. Therefore, it can be considered that the excellence of MHWOA solution accuracy can better cover the small gap of standard deviation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Function** & **Criteria** & **MHWOA** & **PSO-Sono** & **IGWO** & **CSCFA** & **ABA** \\ \hline F1 & Mean & **394.515** & 8588.389 & 11,980.6 & 3334.689 & 42,899.14 \\  & Std & **191.6905** & 2794.111 & 6932.151 & 937.8051 & 14,269.27 \\  & Rank & **1** & 3 & 4 & 2 & 5 \\ \hline F2 & Mean & **421.0541** & 422.4502 & 460.0775 & 476.9043 & 1600.122 \\  & Std & **29.32472** & 33.34969 & 46.58404 & 17.34312 & 540.1802 \\  & Rank & **1** & 2 & 4 & 3 & 5 \\ \hline F3 & Mean & **602.9408** & 606.5202 & 664.4814 & 632.1304 & 661.2621 \\  & Std & **2.772699** & 5.611721 & 10.83572 & 14.87866 & 6.910817 \\  & Rank & **1** & 2 & 5 & 4 & 3 \\ \hline F4 & Mean & **820.3956** & 833.1857 & 826.4405 & 829.6341 & 844.973 \\  & Std & **5.050952** & 12.10409 & 7.25452 & 11.734 & 20.50375 \\  & Rank & **1** & 4 & 2 & 3 & 5 \\ \hline F5 & Mean & **1004.252** & 1068.793 & 1446.053 & 1224.959 & 1810.676 \\  & Std & 76.77896 & 223.1835 & 148.0199 & **48.22638** & 363.7131 \\  & Rank & **1** & 2 & 4 & 3 & 5 \\ \hline F6 & Mean & 5432.739 & 13,434.49 & 4975.174 & **4291.356** & 3942.571 \\  & Std & **1295.119** & 7457.195 & 2878.547 & 2652.357 & 8808.860 \\  & Rank & 3 & 4 & 2 & **1** & 5 \\ \hline F7 & Mean & **2029.43** & 2035.583 & 2152.745 & 2064.995 & 2190.097 \\  & Std & 10.77383 & **8.940873** & 65.96419 & 11.83191 & 40.71099 \\  & Rank & **1** & 2 & 4 & 3 & 5 \\ \hline F8 & Mean & **2222.802** & 2225.729 & 2322.416 & 2228.746 & 2407.507 \\  & Std & **2.809444** & 6.390807 & 92.41293 & 2.170908 & 170.8406 \\  & Rank & **1** & 2 & 4 & 3 & 5 \\ \hline F9 & Mean & **2529.303** & 2544.15 & 2618.021 & 2620.703 & 2716.683 \\  & Std & **0.040414** & 23.77512 & 52.02896 & 56.32707 & 35.29841 \\  & Rank & **1** & 2 & 3 & 4 & 5 \\ \hline F10 & Mean & **2500.653** & 2527.122 & 2758.924 & 2525.796 & 2694.194 \\  & Std & **0.082673** & 58.2044 & 306.3824 & 55.88422 & 199.7621 \\  & Rank & **1** & 3 & 5 & 2 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Data comparison of MHWOA and variants of swarm intelligence algorithms on the test function of dimension 10. After solving all kinds of problems in medium dimensions, in order to further test the performance of the algorithm in high dimensions, it is necessary to set the dimension to 20 for further testing which shows in Table 9.  
Consistent with the test results when the dimension is 10, MHWOA still has great advantages in solving 20-dimensional unimodal functions and basic functions. When solving the unimodal function, the maximum improvement is 76.97%, and the minimum improvement is 38.74%. When solving basic functions, the maximum improvement is 83.24%, and the minimum improvement is 0.19%. Even though the standard deviation is 58.16% larger than that of IGWO in calculating F3, the difference of 5.05 is very small in the calculation of the optimal mean. The maximum value of MHWOA in F3 is 641.81, the minimum value of IGWO is 672.67, and the accuracy of MHWOA is 4.58% higher than that of IGWO. Figure 8: Convergence comparison for CEC2022 with dimension 10.