# 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
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Test**}} & \multirow{2}{*}{**Indicators**} & \multirow{2}{*}{**PSO**} & \multirow{2}{*}{**BOA**} & \multirow{2}{*}{**HPSOBOA**} & \multirow{2}{*}{**SCA**} & \multirow{2}{*}{**GWO**} & \multirow{2}{*}{**COOT**} & \multirow{2}{*}{**BES**} & \multirow{2}{*}{**HBES**} \\ \multicolumn{1}{c}{**Function**} & & & & & & & & & \\ \hline \multirow{3}{*}{\(F_{12}\)} & mean & 0.7678 & 0.4866 & 0.0019 & \(1.06\times 10^{3}\) & 0.0398 & 0.2583 & \(5.79\times 10^{-30}\) & \(5.18\times 10^{-20}\) \\  & std & 0.6487 & 0.1274 & 0.0014 & \(5.83\times 10^{3}\) & 0.0170 & 0.6319 & \(3.68\times 10^{-19}\) & \(1.02\times 10^{-18}\) \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{13}\)} & mean & 0.0015 & 2.777 & 0.911 & 788.27 & 0.6138 & 0.4766 & 2.8705 & 0.0059 \\  & std & 0.0044 & 0.2658 & 0.7025 & 180.74 & 0.2386 & 0.4419 & 0.4485 & 0.0144 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{14}\)} & mean & 1.5131 & 1.1505 & 3.1745 & 1.9508 & 4.2161 & 0.9980 & 5.3268 & 2.5651 \\  & std & 1.1153 & 0.3866 & 2.7582 & 1.0009 & 3.7155 & \(2.3\times 10^{-13}\) & 5.2344 & 3.2754 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{15}\)} & mean & \(5.85\times 10^{-4}\) & \(3.72\times 10^{-4}\) & 0.0015 & 0.0011 & 0.0044 & \(7.02\times 10^{-4}\) & \(3.68\times 10^{-4}\) & \(3.07\times 10^{-4}\) \\  & std & \(4.37\times 10^{-4}\) & \(5.26\times 10^{-5}\) & \(7.9226\times\) & \(3.807\times 10^{-4}\) & 0.008 & \(2.59\times 10^{-4}\) & \(2.22\times 10^{-4}\) & \(3.42\times 10^{-5}\) \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{16}\)} & mean & \(-1.0316\) & \(-1.0316\) & \(-0.6435\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) & \(-1.0316\) \\  & std & \(2.61\times 10^{-16}\) & \(5.6\times 10^{-5}\) & 0.0972 & \(6.1034\times\) & \(2.14\times 10^{-8}\) & \(3.31\times 10^{-12}\) & \(1.48\times 10^{-7}\) & \(1.53\times 10^{-9}\) \\  & SR(\%) & 100 & 64 & 0 & 78 & 100 & 100 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{17}\)} & mean & 0.3979 & 0.4514 & 0.3979 & 0.4010 & 0.3979 & 0.3979 & 0.3979 & 0.3979 \\  & std & 0 & 0.0078 & \(4.39\times 10^{-6}\) & 0.0032 & \(3.79\times 10^{-6}\) & 0.0012 & \(4.71\times 10^{-7}\) & \(2.28\times 10^{-4}\) \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{18}\)} & mean & 3 & 3.5621 & 28.0966 & 3.0002 & 3 & 3 & 3 & 3 \\  & std & \(1.37\times 10^{-15}\) & \(3.6640\) & 5.8650 & \(3.02\times 10^{-4}\) & \(3.74\times 10^{-5}\) & \(1.83\times 10^{-12}\) & \(6.085\times\) & \(7.4587\times 10^{-18}\) \\  & SR(\%) & 100 & 0 & 0 & 0 & 92 & 100 & 100 & 100 \\ \hline \multirow{3}{*}{\(F_{19}\)} & mean & \(-3.8628\) & \(-3.8568\) & \(-3.1973\) & \(-3.8543\) & \(-3.8615\) & \(-3.8628\) & \(-3.8628\) & \(-3.8628\) \\  & std & \(1.3\times 10^{-15}\) & 0.0089 & 0.0094 & 0.0027 & 0.0023 & \(1.89\times 10^{-11}\) & \(1.34\times 10^{-15}\) & \(2.34\times 10^{-15}\) \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{20}\)} & mean & \(-3.2649\) & \(-3.0238\) & \(-2.0792\) & \(-2.8994\) & \(-3.2738\) & \(-3.2958\) & \(-3.2602\) & \(-3.2673\) \\  & std & 0.06 & 0.1649 & \(8.97\times 10^{-16}\) & 0.3445 & 0.0675 & 0.0498 & 0.06 & 0.04 \\  & SR(\%) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{3}{*}{\(F_{21}\)} & mean & \(-5.4891\) & \(-6.9961\) & \(-1.6612\) & \(-2.4205\) & \(-9.3193\) & \(-9.0522\) & \(-7.505\) & \(-10.1513\) \\  & std & \(3.2346\) & \(1.7411\) & \(0.0272\) & 1.9668 & 1.9313 & 2.5766 & 2.5702 & \(3.48\times 10^{-5}\) \\  & SR(\%) & 32 & 0 & 0 & 0 & 0 & 78 & 48 & 94 \\ \hline \multirow{3}{*}{\(F_{22}\)} & mean & \(-7.1406\) & \(-7.4507\) & \(-1.6867\) & \(-3.5481\) & \(-10.0364\) & \In order to further compare the convergence speed and convergence accuracy of each algorithm, the curve of the optimization seeking process of the test function is observed, as shown below.