## 4 Simulation
### Simulation on ISSA Performance
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test Functions** & **Algorithm** & **Best Value** & **Worst Value** & **Average Value** \\ \hline \multirow{8}{*}{F5} & SSA & \(0.0000\times 10^{0}\) & \(3.0119\times 10^{-124}\) & \(3.0119\times 10^{-125}\) \\  & ISSA & \(0.0000\times 10^{0}\) & \(0.0000\times 10^{0}\) & \(0.0000\times 10^{0}\) \\  & PSO & \(6.2717\times 10^{1}\) & \(1.7519\times 10^{2}\) & \(1.2573\times 10^{2}\) \\  & Chimp & \(1.7803\times 10^{0}\) & \(2.2152\times 10^{1}\) & \(9.1301\times 10^{0}\) \\  & GWO & \(1.4177\times 10^{-11}\) & \(4.5254\times 10^{-9}\) & \(1.0949\times 10^{-9}\) \\  & WOA & \(5.0206\times 10^{2}\) & \(2.9749\times 10^{2}\) & \(4.3256\times 10^{2}\) \\ \hline \multirow{8}{*}{F6} & SSA & \(8.8818\times 10^{-16}\) & \(8.8818\times 10^{-16}\) & \(8.8818\times 10^{-16}\) \\  & ISSA & \(8.8818\times 10^{-16}\) & \(8.8818\times 10^{-16}\) & \(8.8818\times 10^{-16}\) \\  & PSO & \(1.0527\times 10^{0}\) & \(3.0465\times 10^{0}\) & \(2.2359\times 10^{0}\) \\  & Chimp & \(1.9961\times 10^{1}\) & \(1.9964\times 10^{1}\) & \(1.9963\times 10^{1}\) \\  & GWO & \(5.0626\times 10^{-14}\) & \(7.5495\times 10^{-14}\) & \(6.1995\times 10^{-14}\) \\  & WOA & \(8.8818\times 10^{-16}\) & \(7.9936\times 10^{-15}\) & \(4.0856\times 10^{-15}\) \\ \hline \multirow{8}{*}{F7} & SSA & \(1.4742\times 10^{-6}\) & \(1.4673\times 10^{-2}\) & \(5.0658\times 10^{-3}\) \\  & ISSA & \(5.7401\times 10^{-5}\) & \(2.4232\times 10^{-2}\) & \(3.3781\times 10^{-3}\) \\ \cline{1-1}  & PSO & \(2.1128\times 10^{-1}\) & \(9.0880\times 10^{-1}\) & \(4.6949\times 10^{-1}\) \\ \cline{1-1}  & Chimp & \(2.6782\times 10^{0}\) & \(2.9905\times 10^{0}\) & \(2.8295\times 10^{0}\) \\ \cline{1-1}  & GWO & \(3.0732\times 10^{-1}\) & \(7.2904\times 10^{-1}\) & \(5.0930\times 10^{-1}\) \\ \cline{1-1}  & WOA & \(1.2416\times 10^{-1}\) & \(9.4357\times 10^{-1}\) & \(3.1349\times 10^{-1}\) \\ \hline \multirow{8}{*}{F8} & SSA & \(3.1419\times 10^{-4}\) & \(1.2254\times 10^{-3}\) & \(5.2091\times 10^{-4}\) \\  & ISSA & \(3.0750\times 1 Figure 3 shows the changes in the fitness values of six optimization algorithms when one is finding the optimal values of eight test functions with increasing iterations. It can be seen from the diagrams that ISSA demonstrates a superior optimization capability in all test functions, with faster convergence and higher solution precision. For instance, in unimodal functions F1, F2, and F4, ISSA's convergence rate is significantly higher than that of other algorithms, with values matching the theoretical ones, thus showing the highest solution precision. Compared to SSA, which has the second highest solution precision, ISSA's precision is greater by more than 100 orders of magnitude. In multimodal functions F3, F5, F6, F7, and F8, ISSA performs best when comparing optimal, worst, and average values. In F3, the ISSA algorithm demonstrates a rapid initial decline, stabilizing after approximately 50 iterations, indicating an exceptionally fast convergence rate. In comparison, both the SSA and PSO algorithms also stabilize after around 50 iterations, but their convergence speed and precision values are slightly inferior to those of ISSA. In F5, the final convergence value of ISSA is the lowest among all the algorithms, indicating that there is a more optimal solution. The final convergence values of PSO and GWO are slightly higher than those of ISSA and SSA, but they are still at a relatively good level. WOA and Chimp exhibit significant fluctuations throughout the entire iteration process, resulting in lower final precision values. In F6, neither Chimp nor PSO found the ideal solution, with ISSA showing more than 15 times greater precision. In F6, ISSA and SSA have the same average value of \(8.8818\times 10^{-16}\), but ISSA converges faster. In F7 and F8, the ISSA solution still exhibits the highest accuracy. Notably, in F7, the Chimp algorithm does not produce an exact solution.