# IDEINFO: An Improved Vector-Weighted Optimization Algorithm
## 4 Discussion
### Wilcoxon Rank Sum Test  
In the above simulation experiment, the mean and standard deviation alone cannot fully verify the superiority of the IDEINFO algorithm. To ensure the fairness and validity of the algorithm, it is necessary to conduct a statistical test. In this paper, we use the Wilcoxon rank sum test to verify whether the results of each IDEINFO experiment are statistically significantly different from other algorithms. The rank sum test was performed at the 5% significance level, and at \(p<5\%\), it can be considered as rejecting the H0 hypothesis, \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**F** & **Index** & **IDEINFO** & **INFO** & **SSA** & **GWO** & **WOA** & **INFO1** & **INFO2** \\ \hline \multirow{4}{*}{F1} & Best & **0** & \(6.7057\times 10^{-28}\) & **0** & \(2.7058\times 10^{-36}\) & \(1.3810\times 10^{-115}\) & \(4.2970\times 10^{-28}\) & **0** \\ \cline{2-7}  & Mean & **0** & \(2.8115\times 10^{-27}\) & \(6.4300\times 10^{-23}\) & \(1.0693\times 10^{-34}\) & \(2.5704\times 10^{-102}\) & \(2.8729\times 10^{-27}\) & **0** \\ \cline{2-7}  & Std & **0** & \(6.8192\times 10^{-28}\) & \(7.2766\times 10^{-19}\) & \(1.0672^{-34}\) & \(2.1129\times 10^{-101}\) & \(6.3544\times 10^{-28}\) & **0** \\ \hline \multirow{4}{*}{F2} & Best & **0** & \(1.2106\times 10^{-53}\) & **0** & \(6.3897\times 10^{-21}\) & \(9569.1641\) & \(9.2088\times 10^{-54}\) & **0** \\ \cline{2-7}  & Mean & **0** & \(7.8038\times 10^{-52}\) & \(4.2017\times 10^{-34}\) & \(1.4629\times 10^{-14}\) & \(20.730.2593\) & \(7.6727\times 10^{-52}\) & **0** \\ \cline{2-7}  & Std & **0** & \(7.0452\times 10^{-52}\) & \(5.9418\times 10^{-33}\) & \(5.7738\times 10^{-14}\) & \(2569.6795\) & \(8.3436\times 10^{-52}\) & **0** \\ \hline \multirow{4}{*}{F3} & Best & **0** & \(3.4184\times 10^{-29}\) & 0 & \(2.9501\times 10^{-16}\) & \(0.00011002\) & \(5.7132\times 10^{-29}\) & **0** \\ \cline{2-7}  & Mean & **0** & \(5.7937\times 10^{-28}\) & \(1.1195\times 10^{-20}\) & \(1.7655\times 10^{-14}\) & \(32.8655\) & \(5.2304\times 10^{-28}\) & **0** \\ \cline{2-7}  & Std & **0** & \(3.4028\times 10^{-28}\) & \(1.4256\times 10^{-19}\) & \(3.4399\times 10^{-14}\) & \(28.2881\) & \(2.51\times 10^{-28}\) & **0** \\ \hline \multirow{4}{*}{F4} & Best & **4.6904\(\times\) 10\({}^{-15}\)** & \(16.9501\) & \(2.2361\times 10^{-11}\) & \(25.0954\) & \(26.1798\) & \(16.5694\) & \(3.1549\times 10^{-14}\) \\ \cline{2-7}  & Mean & **1.5759\(\times\) 10\({}^{-8}\)** & \(19.4498\) & \(2.5536\times 10^{-5}\) & \(26.7773\) & \(27.1942\) & \(19.4832\) & \(1.5887\times 10^{-8}\) \\ \cline{2-7}  & Std & **3.6914\(\times\) 10\({}^{-8}\)** & \(0.7041\) & \(6.0245\times 10^{-5}\) & \(0.7764\) & \(0.5283\) & \(0.7499\) & \(6.1874\times 10^{-8}\) \\ \hline \multirow{4}{*}{F5} & Best & **1.2326\(\times\) 10\({}^{-32}\)** & \(2.6038\times 10^{-20}\) & \(4.009\times 10^{-11}\) & \(1.2798\times 10^{-5}\) & \(0.0092902\) & \(1.1449\times 10^{-19}\) & \(1.5407\times 10^{-32}\) \\ \cline{2-7}  & Mean & **3.2376\(\times\) 10\({}^{-31}\)** & \(2.0788\times 10^{-13}\) & \(1.2121\times 10^{-7}\) & \(0.6228\) & \(0.068798\) & \(1.9366\times 10^{-14}\) & \(7.0196\times 10^{-33}\) \\ \cline{2-7}  & Std & **5.1236\(\times\) 10\({}^{-31}\)** & \(1.0668\times 10^{-12}\) & \(3.522\times 10^{-7}\) & \(0.42264\) & \(0.078427\) & \(6.2517\times 10^{-14}\) & \(1.1262\times 10^{-30}\) \\ \hline \multirow{4}{*}{F6} & Best & **6.2313\(\times\) 10\({}^{-7}\)** & \(5.1252\times 10^{-5}\) & \(1.4029\times 10^{-0}\) & \(0.00013678\) & \(4.3456\times 10^{-5}\) & \(6.7265\times 10^{-0}\) & \(7.2831\times 10^{-6}\) \\ \cline{2-7}  & Mean & \(7.2422\times 10^{-5}\) & \(0.00077635\) & \(0.00077635\) & \(0.00075583\) & \(0.0015206\) & \(0.0008433\) & \(\bf{6.5934\times 10^{-5}}\) \\ \cline{2-7}  & Std & 5.6658\(\times\) 10\({}^{-5}\) & \(0.00066449\) & \(0.00066449\) & \(0.00044961\) & \(0.0016606\) & \(0.00073516\) & \(\bf{4.0882\times 10^{-5}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results for six high-latitude single-target benchmark test functions.