# A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization
## 4 Experimental Design and Analysis
### Performance Evaluation
#### 4.2.1 Comparison of Benchmark Test Function Optimization
The results of the optimization experiments are shown in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Test** & **Indicators** & **PSO** & **BOA** & **HFSOBOA** & **SCA** & **GWO** & **COOT** & **BES** & **HBES** \\ \hline \multirow{3}{*}{\(F_{1}\)} & mean & \(1.15\times 10^{5}\) & \(7.71\times 10^{-11}\) & \(1.862\times\) & \multirow{3}{*}{23.2423} & \multirow{3}{*}{\(1.25\times 10^{-27}\)} & \multirow{3}{*}{\(2.07\times 10^{-13}\)} & \multirow{3}{*}{0} & \multirow{3}{*}{0} \\  & std & \(2.57\times 10^{-5}\) & \(6.71\times 10^{-12}\) & 0 & & & & & \\  & SR(\%) & 0 & 0 & 100 & 0 & 0 & 76 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{2}\)} & mean & 0.0063 & \(2.33\times 10^{-8}\) & \(8.62\times 10^{-146}\) & 0.0306 & \(1.07\times 10^{-16}\) & 4.05\(\times 10^{-8}\) & 0 & 0 \\  & std & 0.0124 & \(6.46\times 10^{-9}\) & \(5.59\times 10^{-146}\) & 0.0439 & \(8.79\times 10^{-17}\) & \(2.86\times 10^{-7}\) & 0 & 0 \\  & SR(\%) & 0 & 0 & 100 & 0 & 0 & 0 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{3}\)} & mean & 0.4956 & \(6.2\times 10^{-11}\) & 1.096 \(\times\) & \multirow{3}{*}{92.85} & \multirow{3}{*}{7.28\(\times 10^{-7}\)} & \multirow{3}{*}{2.02\(\times 10^{-10}\)} & \multirow{3}{*}{0} & \multirow{3}{*}{0} \\  & std & 0.2497 & \(7.91\times 10^{-12}\) & 0 & & & & & \\  & SR(\%) & 0 & 0 & 100 & 0 & 0 & 0 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{4}\)} & mean & 0.5364 & \(3.38\times 10^{-8}\) & \(2.52\times 10^{-146}\) & 34.6610 & \(8.15\times 10^{-7}\) & \(4.04\times 10^{-13}\) & 0 & 0 \\  & std & 0.4226 & \(3.38\times 10^{-9}\) & \(1.2\times 10^{-147}\) & 11.1013 & \(9.05\times 10^{-7}\) & 2.66 \(\times 10^{-16}\) & 0 & 0 \\  & SR(\%) & 0 & 0 & 100 & 0 & 0 & 0 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{5}\)} & mean & 42.62 & 28.9069 & 28.776 & 953.3934 & 27.2613 & 44.97 & 19.0639 & 20.4183 \\  & std & 26.64 & 0.0263 & 0.0644 & \(3.37\times 10^{3}\) & 0.7647 & 44.44 & 1.49066 & 0.2718 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{6}\)} & mean & \(1.15\times 10^{-6}\) & 5.4064 & 0.0416 & 40.6717 & 0.6766 & 0.2605 & \(1.34\times 10^{-18}\) & \(2.13\times 10^{-18}\) \\  & std & \(2.04\times 10^{-5}\) & 0.5654 & 0.0318 & 166.8152 & 0.3671 & 0.2008 & \(4.29\times 10^{-18}\) & \(5.05\times 10^{-18}\) \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{7}\)} & mean & 0.0832 & \(2.019\times 10^{-8}\) & \(2.14\times 10^{-5}\) & 112.9 & 0.0022 & 0.0055 & \(3.96\times 10^{-5}\) & \(2.47\times 10^{-4}\) \\  & std & 0.0377 & \(6.81\times 10^{-4}\) & \(1.05\times 10^{-4}\) & 248.6 & 0.0013 & 0.0045 & \(3.77\times 10^{-5}\) & 0.0012 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{8}\)} & mean & \(-2.79\times 10^{3}\) & \(-4.04\times 10^{3}\) & \(-9.745\times\) & \multirow{3}{*}{\(-3.73\times 10^{3}\)} & \multirow{3}{*}{\(-5.97\times 10^{3}\)} & \multirow{3}{*}{\(-7.44\times 10^{3}\)} & \multirow{3}{*}{\(-7.48\times 10^{3}\)} & \multirow{3}{*}{\(-1.24\times 10^{4}\)} \\  & std & 406.595 & 343.2 & \(1.367\times 10^{3}\) & 308.97 & 840.6115 & \(1.05\times 10^{3}\) & \(1.60\times 10^{3}\) & \(1.09\times 10^{3}\) \\ \cline{1-1}  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 78 \\ \hline \multirow{3}{*}{\(F_{9}\)} & mean & 45.8288 & 32.8474 & 0.0643 & 38.6612 & 2.5001 & \(1.04\times 10^{-12}\) & 0 & 0 \\  & std & 14.4283 & 69.8399 & 0.1818 & 34.3327 & 3.299 & \(6.67\times 10^{-12}\) & 0 & 0 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 84 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{10}\)} & mean & 0.0012 & \(2.78\times 10^{-8}\) & \(8.88\times 10^{-16}\) & 14.1827 & \(1.05\times 10^{-13}\) & \(8.39\times 10^{-13}\) & \(8.88\times 10^{-16}\) & \(8.88\times 10^{-16}\) \\  & std & \(5.68\times 10^{-4}\) & \(5.61\times 10^{-9}\) & 0 & 8.9091 & \(1.85\times 10^{-14}\) & \(5.1\times 10^{-12}\) & 0 & 0 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{11}\)} & mean & 43.0227 & \(1.18\times 10^{-11}\) & 0 & 0.9740 & 0.0028 & \(2.4\times 10^{-11}\) & 0 & 0 \\  & std & 6.8557 & \(1.06\times 10^{-11}\) & 0 As can be seen from Table 2, for the single-peak functions, the search results of \(F_{1}\), \(F_{2}\), \(F_{3}\) and \(F_{4}\) show that BES, HBES, and the HPSBOA are better than the other algorithms, and the search success rate reaches 100%, while the remaining single-peak functions of the BES and HBES algorithms are not very different.