## 3 IWOA Simulation Experiments and Result Analysis
### IWOA Result Analysis  
#### 3.2.1 Sensitivity Analysis of Adaptive Inertia Weights  
The population size of the IWOA algorithm was set to 30, with maximum iteration counts of 10, 15, and 20, respectively. The target function was the Sphere function, with the calculation formula given by  
\[f(x)=\sum_{i=1}^{N}x_{i}^{2} \tag{28}\]  
where \(f(x)\) is the fitness value, and \(x_{i}\) represents the position of an individual whale.  
The convergence curves under different inertia weights for the same number of iterations are shown in Figure 5. From Figure 5, it can be observed that when \(w_{\text{max}}\) = 0.9 and \(w_{\text{min}}\) = 0.2, IWOA achieved the fastest convergence speed, effectively controlling the time complexity of the IWOA algorithm and improving its convergence rate.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Function** & **Expression** & **Dimension** & **Search Range** & **Optimal Value** & **Type** \\ \hline \(F_{1}\) & \(f_{1}(x)=\sum\limits_{i=1}^{n}x_{i}^{2}\) & 30 & \([-100,100]\) & 0 & Unimodal \\ \(F_{2}\) & \(f_{2}(x)=\sum\limits_{i=1}^{n}|x_{i}|+\sum\limits_{i=1}^{n}|x_{i}|\) & 30 & \([-10,10]\) & 0 & Unimodal \\ \(F_{3}\) & \(f_{3}(x)=\sum\limits_{i=1}^{n}\left(\sum\limits_{i=1}^{i}x_{i}\right)^{2}\) & 30 & \([-100,100]\) & 0 & Unimodal \\ \(F_{4}\) & \(f_{4}(x)=\max_{i}\{|x_{i}|.1\leq i\leq n\}\) & 30 & \([-100,100]\) & 0 & Unimodal \\ \(F_{5}\) & \(f_{5}(x)=\sum\limits_{i=1}^{n}x_{i}^{4}+\text{random}(0,1)\) & 30 & \([-1.28,1.28]\) & 0 & Multimodal \\ \(F_{6}\) & \(f_{6}(x)=\sum\limits_{i=1}^{n}[x_{i}^{2}-10\cos(2\pi x_{i})+10]\) & 30 & \([-5.12,5.12]\) & 0 & Multimodal \\ \(F_{7}\) & \(f_{7}(x)=-20\exp\left(-0.2\sqrt{1}\frac{1}{n\sum\limits_{i=1}^{n}x_{i}^{2}} \right)-\exp\left[\frac{1}{n\sum\limits_{i=1}^{n}\cos(2\pi x_{i})}\right]+20+e\) & 30 & \([-32,32]\) & \(8.8818\times 10^{16}\) & Multimodal \\ \(F_{8}\) & \(f_{8}(x)=\frac{1}{4000}\sum\limits_{i=1}^{n}x_{i}^{2}-\sum\limits_{i=1}^{n} \cos\left(\frac{x_{i}}{\sqrt{i}}\right)+1\) & 30 & \([-600,600]\) & 0 & Multimodal \\ \hline \hline \end{tabular} Note: \(c_{1}\) and \(c_{2}\) are acceleration constants that control the step size of particles in PSO optimization; \(P\) is the scaling factor, affecting the step size of solutions in the search space; FADs is the vortex effect probability, enhancing the algorithm’s global optimization capability; BF is the jump factor, controlling the global and local optimization abilities of individuals; \(\text{BE}_{\text{max}}\) and \(\text{BE}_{\text{min}}\) represent the maximum and minimum values of predation efficiency.  
\end{table}
Table 2: Benchmark functions.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameter Settings** \\ \hline WOA & \(a_{\text{max}}=2\), \(a_{\text{min}}=0\) \\ IWOA & \(a_{\text{max}}=2\), \(a_{\text{min}}=0\), \(w_{\text{max}}=0.8\), \(w_{\text{min}}=0.1\) \\ PSO & \(w_{\text{max}}=0.9\), \(w_{\text{min}}=0.2\), \(c_{1}\)= \(c_{2}=2\) \\ SSA & — \\ SBOA & — \\ MPA & \(p=0.5\), \(\text{FADs}=0.2\) \\ PKO & BF = 8, \(\text{PE}_{\text{max}}\)= 0.5, \(\text{PE}_{\text{min}}=0\) \\ \hline \hline \end{tabular} Note: \(c_{1}\) and \(c_{2}\) are acceleration constants that control the step size of particles in PSO optimization; \(P\) is the scaling factor, affecting the step size of solutions in the search space; FADs is the vortex effect probability, enhancing the algorithm’s global optimization capability; BF is the jump factor, controlling the global and local optimization abilities of individuals; \(\text{BE}_{\text{max}}\) and \(\text{BE}_{\text{min}}\) represent the maximum and minimum values of predation efficiency.  
\end{table}
Table 3: Parameter settings for each algorithm.