## 3 Improved Honey Badger Algorithm
### Simulation Experiments and Results Analysis
#### 3.3.1 Function Selection and Parameter Setting
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Algorithm** & **Function Optimum** & **Function Worst** & **Function Average** & **Standard Deviation** & **Time Elapsed** \\ \hline \multirow{10}{*}{F1} & IHBA & **0** & **0** & **0** & **0** & 0.2688 \\  & HBA & \(2.84\times 10^{-209}\) & \(3.10\times 10^{-217}\) & \(8.32\times 10^{-208}\) & **0** & 0.2778 \\  & BOA & \(1.64\times 10^{-14}\) & \(2.02\times 10^{-14}\) & \(1.81\times 10^{-14}\) & \(1.01\times 10^{-15}\) & 0.0942 \\  & PSO & \(9.18\times 10^{-8}\) & \(2.07\times 10^{-10}\) & \(2.31\times 10^{-6}\) & 5.89 & 0.0549 \\  & SCA & \(2.21\times 10^{-6}\) & \(1.47\) & \(1.21\times 10^{-1}\) & \(3.51\times 10^{-1}\) & 0.1147 \\  & SSA & \(6.28\times 10^{-9}\) & \(2.11\times 10^{-8}\) & \(1.21\times 10^{-8}\) & \(3.14\times 10^{-9}\) & 0.1259 \\  & WOA & \(1.20\times 10^{-167}\) & \(1.20\times 10^{-151}\) & \(1.10\times 10^{-152}\) & \(2.80\times 10^{-152}\) & 0.05088 \\  & DA & \(4.45\times 10^{2}\) & \(2.37\times 10^{3}\) & \(1.04\times 10^{3}\) & \(4.36\times 10^{2}\) & 18.927 \\ \hline \multirow{10}{*}{F2} & IHBA & **0** & **0** & **0** & 0.2622 \\  & HBA & \(6.02\times 10^{-106}\) & \(3.99\times 10^{-108}\) & \(8.54\times 10^{-105}\) & \(1.69\times 10^{-105}\) & 0.2938 \\  & BOA & \(9.89\times 10^{-12}\) & \(1.22\times 10^{-11}\) & \(1.10\times 10^{-11}\) & \(6.09\times 10^{-13}\) & 0.1013 \\  & PSO & \(9.41\) & \(2.23\times 10^{1}\) & \(1.50\times 10^{1}\) & 3.10 & 0.0584 \\  & SCA & \(1.26\times 10^{-4}\) & \(7.81\times 10^{-9}\) & \(1.26\times 10^{-4}\) & \(4.15\times 10^{-4}\) & 0.1166 \\  & SSA & \(7.17\times 10^{-3}\) & \(3.25\) & \(8.28\times 10^{-1}\) & \(8.28\times 10^{-1}\) & 0.1258 \\  & WOA & \(3.70\times 10^{-115}\) & \(1.20\times 10^{-100}\) & \(3.80\times 10^{-102}\) & \(2.10\times 10^{-101}\) & 0.0530 \\  & DA & \(2.89\times 10^{-1}\) & \(2.17\times 10^{1}\) & \(1.12\times 10^{1}\) & 4.89 & 21.807 \\ \hline \multirow{10}{*}{F3} & IHBA & **0** & **0** & **0** & **0** & 0.4797 \\  & HBA & \(6.65\times 10^{-200}\) & \(2.77\times 10^{-209}\) & \(2.00\times 10^{-198}\) & **0** & 0.5254 \\  & BOA & \(1.63\times 10^{-14}\) & \(2.09\times 10^{-14}\) & \(1.82\times 10^{-14}\) & \(1.05\times 10^{-15}\) & 0.4253 \\  & PSO & \(8.36\times 10^{1}\) & \(2.78\times 10^{2}\) & \(1.74\times 10^{2}\) & \(4.75\times 10^{1}\) & 0.2191 \\  & SCA & \(1.69\times 10^{2}\) & \(1.10\times 10^{4}\) & \(3.48\times 10^{3}\) & \(2.93\times 10^{3}\) & 0.2765 \\  & SSA & \(7.27\times 10^{1}\) & \(6.78\times 10^{2}\) & \(2.67\times 10^{2}\) & \(1.50\times 10^{2}\) & 0.2956 \\  & WOA & \(4.86\times 10^{3}\) & \(4.38\times 10^{4}\) & \(2.17\times 10^{4}\) & \(9.53\times 10^{3}\) & 0.2192 \\  & DA & \(2.57\times 10^{3}\) & \(2.12\times 10^{4}\) & \(1.15\times 10^{4}\) & \(5.54\times 10^{3}\) & 22.809 \\ \hline \multirow{10}{*}{F4} & IHBA & **0** & **0** & **0** & **0** & 0.2321 \\  & HBA & \(1.43\times 10^{-102}\) & \(5.14\times 10^{-107}\) & \(2.96\times 10^{-101}\) & \(5.68\times 10^{-102}\) & 0.2428 \\  & BOA & \(1.10\times 10^{-11}\) & \(1.38\times 10^{-11}\) & \(1.22\times 10^{-11}\) & \(6.47\times 10^{-13}\) & 0.0959 \\  & PSO & \(1.99\) & \(2.88\times 10^{2}\) & \(2.43\) & \(2.22\times 10^{-1}\) & 0.0570 \\  & SCA & \(1.59\) & \(3.95\times 10^{1}\) & \(1.91\times 10^{1}\) & \(1.05\times 10^{1}\) & 0.1125 \\  & SSA & \(2.93\) & \(1.55\times 10^{1}\) & \(8.70\) & 3.45 & 0.1282 \\  & WOA & \(5.40\times 10^{-2}\) & \(8.95\times 10^{1}\) & \(3.70\times 10^{1}\) & \(3.04\times 10^{1}\) & 0.0561 \\  & DA & \(1.38\times 10^{1}\) & \(3.58\times 10^{1}\) & \(2.25\times 10^{1}\) & 5.99 & 16.682 \\ \hline \multirow{10}{*}{F5} & IHBA & **\(\mathbf{2.66\times 10^{1}}\)** & \(\mathbf{2.56\times 10^{1}}\)** & \(\mathbf{2.73\times 10^{1}}\)** & \(\mathbf{1.13\times 10^{-3}}\)** & 0.2752 \\  & HBA & \(2.88\times 10^{1}\) & \(2.84\times 10^{1}\) & \(2.89\times 10^{1}\) & \(1.20\times 10^{-1}\) & 0.2806 \\  & BOA & \(2.89\times 10^{1}\) & \(2.90\times 10^{1}\) & \(2.89\times 10^{1}\) & \(3.00\times 10^{-2}\) & 0.1355 \\  & PSO & \(2.16\times 10^{3}\) & \(1.48\times 10^{4}\) & \(6.07\times 10^{3}\) & \(2.92\times 10^{3}\) & 0.0751 \\  & SCA & \(2.77\times 10^{1}\) & \(8.24\times 10^{3}\) & \(5.47\times 10^{2}\) & \(1.59\times 10^{3}\) & 0.1328 \\  & SSA & \(1.81\times 10^{1}\) & \(1.79\times 10^{3}\) & \(2.41\times 10^{2}\) & \(4.20\times 10^{2}\) & 0.1484 \\  & WOA & \(2.84\times 10^{1}\) & \(2.90\times 10^{1}\) & \(2.88\times 10^{1}\) & \(1.21\times 10^It can be seen from Table 3 that, compared with other traditional swarm intelligence optimization algorithms, the performance of the IHBA algorithm on the four unimodal functions F1 to F4 is much higher than that of other traditional swarm intelligence algorithms, and its optimization has reached the optimal value, its optimization stability is  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Algorithm** & **Function Optimum** & **Function Worst** & **Function Average** & **Standard Deviation** & **Time Elapsed** \\ \hline \multirow{5}{*}{F7} & WOA & \(1.11\times 10^{-2}\) & \(3.69\times 10^{-1}\) & \(9.47\times 10^{-2}\) & \(9.76\times 10^{-2}\) & \(0.0515\) \\  & DA & \(2.89\times 10^{2}\) & \(3.76\times 10^{3}\) & \(1.09\times 10^{3}\) & \(6.41\times 10^{3}\) & \(18.836\) \\ \hline \multirow{5}{*}{F7} & IHBA & \(6.82\times 10^{-7}\) & \(1.88\times 10^{-4}\) & \(5.71\times 10^{-5}\) & \(4.54\times 10^{-5}\) & \(0.2389\) \\  & HBA & \(2.81\times 10^{-4}\) & \(3.26\times 10^{-5}\) & \(1.81\times 10^{-3}\) & \(3.54\times 10^{-4}\) & \(0.2285\) \\  & BOA & \(2.28\times 10^{-4}\) & \(1.11\times 10^{-3}\) & \(6.57\times 10^{-4}\) & \(2.33\times 10^{-4}\) & \(0.2854\) \\  & PSO & \(2.77\times 10^{1}\) & \(1.10\times 10^{2}\) & \(5.93\times 10^{1}\) & \(2.36\times 10^{1}\) & \(0.1543\) \\  & SCA & \(3.46\times 10^{-3}\) & \(2.11\times 10^{-1}\) & \(4.06\times 10^{-2}\) & \(4.64\times 10^{-2}\) & \(0.2094\) \\  & SSA & \(4.46\times 10^{-2}\) & \(2.13\times 10^{-1}\) & \(1.09\times 10^{-1}\) & \(4.30\times 10^{-2}\) & \(0.2251\) \\  & WOA & \(1.17\times 10^{-4}\) & \(1.19\times 10^{-2}\) & \(2.22\times 10^{-3}\) & \(2.84\times 10^{-3}\) & \(0.1478\) \\  & DA & \(1.15\times 10^{-1}\) & \(6.20\times 10^{-1}\) & \(2.83\times 10^{-1}\) & \(1.32\times 10^{-1}\) & \(16.723\) \\ \hline \multirow{5}{*}{F8} & IHBA & \(0\) & \(0\) & \(0\) & \(0\) & \(0.7173\) \\  & HBA & \(0\) & \(0\) & \(0\) & \(0\) & \(0.7798\) \\  & BOA & \(0.00\)E+00 & \(2.04\times 10^{2}\) & \(3.16\times 10^{1}\) & \(7.20\times 10^{-1}\) & \(0.1235\) \\  & PSO & \(1.70\times 10^{2}\) & \(2.70\times 10^{2}\) & \(2.17\times 10^{2}\) & \(2.89\times 10^{1}\) & \(0.0756\) \\  & SCA & \(3.25\times 10^{-5}\) & \(1.44\times 10^{2}\) & \(2.25\times 10^{1}\) & \(4.13\times 10^{1}\) & \(0.1237\) \\  & SSA & \(2.29\times 10^{1}\) & \(8.86\times 10^{1}\) & \(6.10\times 10^{1}\) & \(1.83\times 10^{1}\) & \(0.1409\) \\  & WOA & \(0\) & \(0\) & \(0\) & \(0\) & \(0.0570\) \\  & DA & \(8.69\times 10^{1}\) & \(2.40\times 10^{2}\) & \(1.58\times 10^{2}\) & \(3.86\times 10^{1}\) & \(18.460\) \\ \hline \multirow{5}{*}{F9} & IHBA & \(8.88\times 10^{-16}\) & \(8.88\times 10^{-16}\) & \(8.88\times 10^{-16}\) & \(0\) & \(0.2738\) \\  & HBA & \(8.88\times 10^{-16}\) & \(4.44\times 10^{-15}\) & \(2.90\times 10^{-15}\) & \(1.79\times 10^{-15}\) & \(0.3914\) \\  & BOA & \(1.13\times 10^{-11}\) & \(1.46\times 10^{-11}\) & \(1.29\times 10^{-11}\) & \(9.03\times 10^{-13}\) & \(0.1133\) \\  & PSO & \(3.59\) & \(5.37\) & \(4.39\) & \(3.66\times 10^{-1}\) & \(0.0780\) \\  & SCA & \(4.91\times 10^{-4}\) & \(2.03\times 10^{-1}\) & \(1.34\times 10^{-1}\) & \(8.86\) & \(0.1382\) \\  & SSA & \(2.18\times 10^{-5}\) & \(2.96\) & \(1.93\) & \(7.33\times 10^{-1}\) & \(0.1437\) \\  & WOA & \(8.88\times 10^{-16}\) & \(7.99\times 10^{-15}\) & \(4.20\times 10^{-15}\) & \(2.07\times 10^{-15}\) & \(0.0593\) \\  & DA & \(0\) & \(1.18\times 10^{-1}\) & \(5.24\times 10^{-3}\) & \(2.24\times 10^{-2}\) & \(0.0753\) \\ \hline \multirow{5}{*}{F10} & IHBA & \(0\) & \(0\) & \(0\) & \(0\) & \(0.2535\) \\  & HBA & \(0\) & \(0\) & \(0\) & \(0\) & \(0.3989\) \\  & BOA & \(0\) & \(6.44\times 10^{-15}\) & \(1.64\times 10^{-15}\) & \(1.79\times 10^{-15}\) & \(0.1459\) \\  & PSO & \(3.35\times 10^{-1}\) & \(7.95\times 10^{-1}\) & \(5.27\times 10^{-1}\) & \(1.21\times 10^{-1}\) & \(0.0890\) \\  & SCA & \(6.15\times 10^{-5}\) & \(7.24\times 10^{-1}\) & \(3.08\times 10^{-1}\) & \(2.14\times 10^{-1}\) & \(0.1446\) \\  & SSA & \(3.30\times 10^{-8}\) & \(4.44\times 10^{-2}\) & \(1.00\times 10^{-2}\) & \(1.07\times 10^{-2}\) & \(0.1597\) \\  & WOA & \(5.06\) & \(1.17\) & \(8.60\) & \(1.89\) & \(18.383\) \\  & DA & \(3.19\) & \(2.82\times 10^{1}\) & \(1.26\times 10^{1}\) & \(6.57\) & \(19.235\) \\ \hline \multirow{5}{*}{F11} & IHBA & \(6.91\times 10^{-3}\) & \(2.63\times 10^{-3}\) & \(1.18\times 10^{-2}\) & \(1.06\times 10^{-2}\) & \(0.5501\) \\  & HBA & \(7.09\times 10^{-1}\) & \(3.28\times 10^{-1}\) & \(1.18\times 10^{1}\) & \(2.06\times 10^{-1}\) & \(0.6714\) \\  & BOA & \(4.01\times 10^{-1}\) & \(1.00\) & \(6.61\times 10^{-1}\) & \(1.51\times 10^{-1}\) & \(0.8 good, and there is no phenomenon that the individual optimization value deviates from the theoretical value in 30 experiments.