# Multi-Strategy Hybrid Whale Optimization Algorithm Improvement
## 4 Simulation Experiments and Comparative Analysis
### [PERSON]'s Rank-Sum Test Analysis
It is worth discussing the performance of MHWOA in the hybrid function and composition function. Like the medium dimension, MHWOA still shows the characteristics of large standard deviation when solving the F7 function of high dimension, but compared with the PSO-sono, which also performs well on this function, the average accuracy of MHWOA is 1.2% higher. However, when solving the F8 function, there is a problem of insufficient accuracy and a standard deviation. Obviously, combined with the discussion of the dimension of 10, MHWOA is not an algorithm for solving the hybrid function problem, and its performance in this aspect will be weak. The performance of MHWOA on the F10 function with dimension 20 is consistent with that of the F11 function with dimension 10. The difference between the two lies in the different values of the function N, which also indicates that the value of N will affect the calculation results of MHWOA. All in all, MHWOA ranks first in 10 out of 12 test functions in 20 dimensions, which still demonstrates its accuracy and stability. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & **Criteria** & **MHWOA** & **PSO-Sono** & **IGWO** & **CSCFA** & **ABA** \\ \hline F1 & Mean & **22,027.87** & 60,495.86 & 69,748.8 & 35,959.05 & 95,670.96 \\  & Std & **8099.099** & 18,903.63 & 28,574.15 & 6643.091 & 18,266.18 \\  & Rank & **1** & 3 & 4 & 2 & 5 \\ \hline F2 & Mean & **479.3199** & 617.213 & 607.8362 & 679.0989 & 2860.194 \\  & Std & **22.03253** & 76.63501 & 81.6858 & 64.65435 & 1380.128 \\  & Rank & **1** & 3 & 2 & 4 & 5 \\ \hline F3 & Mean & **628.0799** & 629.2805 & 681.3455 & 656.5687 & 673.1567 \\  & Std & 13.73115 & 17.63624 & **8.68169** & 11.04099 & 11.31018 \\  & Rank & **1** & 2 & 5 & 3 & 4 \\ \hline F4 & Mean & **870.2611** & 939.0913 & 919.5266 & 897.6036 & 936.9259 \\  & Std & **11.75017** & 12.49051 & 31.22034 & 19.37081 & 44.78866 \\  & Rank & **1** & 4 & 3 & 2 & 5 \\ \hline F5 & Mean & **1830.013** & 2840.376 & 3068.016 & 2775.691 & 4323.632 \\  & Std & **265.0278** & 629.7914 & 658.6148 & 561.3822 & 1550.754 \\  & Rank & **1** & 3 & 4 & 2 & 5 \\ \hline F6 & Mean & **6454.376** & 12,630,942 & 685,439.9 & 1,376,244 & 1.65 \(\times\) 10\({}^{9}\) \\  & Std & **4418.096** & 7,033,967 & 449,857.1 & 1,098,830 & 1.55 \(\times\) 10\({}^{9}\) \\  & Rank & **1** & 4 & 2 & 3 & 5 \\ \hline F7 & Mean & **2107.023** & 2132.643 & 2344.392 & 2189.896 & 2325.244 \\  & Std & 32.38123 & **13.68462** & 160.2177 & 34.25982 & 118.7654 \\  & Rank & **1** & 2 & 5 & 3 & 4 \\ \hline F8 & Mean & 2305.656 & **2245.256** & 2659.981 & 2275.204 & 2712.805 \\  & Std & 107.7911 & 98.15996 & 129.5854 & **43.817** & 173.8798 \\  & Rank & 3 & **1** & 4 & 2 & 5 \\ \hline F9 & Mean & **2486.654** & 2521.35 & 2611.125 & 2623.621 & 3013.765 \\  & Std & **2.761597** & 10.21709 & 57.66229 & 34.88416 & 323.719 \\  & Rank & **1** & 2 & 3 & 4 & 5 \\ \hline F10 & Mean & 3005.218 & **2509.646** & 6075.863 & 4858.347 & 5618.618 \\  & Std & 611.4207 & **5.358794** & 635.9783 & 1398.893 & 993.6781 \\  & Rank & 2 & **1** & 5 & 3 & 4 \\ \hline F11 & Mean & **2974.534** & 4386.09 & 3389.189 & 5091.03 & 9812.307 \\  & Std & **45.44418** & 726.5114 & 163.8954 & 1679.959 & 2402.044 \\  & Rank & **1** & 3 & 2 & 4 & 5 \\ \hline F12 & Mean & **3001.978** & 3017.543 & 3363.352 & 3188.788 & 3963.649 \\  & Std & **40.36912** & 43.98265 & 129.134 & 104.411 & 309.5008 \\  & Rank & **1** & 2 & 4 & 3 & 5 \\ \hline \hline \end{tabular} Note: Bold indicates the optimal value in the same function test.  
\end{table} 
Table 9: Data comparison of MHWOA and variants of swarm intelligence algorithms on the test function of dimension 20.