## 4 Performance Analysis  
Since numerous factors are required to be optimized, the reliability analysis ought to be performed prior to array antenna pattern synthesis. According to [PERSON]'s \"No Free Lunch\" (NFL) theorem [28], there is no algorithm that can solve all issues of all sectors worldwide. To confirm the efficacy of the IWOA method, four well-known test functions are selected, which are also utilized as benchmark functions for GA and PSO optimization techniques. The benchmark functions are listed in Table 1. To validate the IWOA algorithm's efficiency, four well-known test functions are chosen, which are also used as benchmark functions for optimization strategies such as GA and PSO. Table 1 displays the benchmark functions. The GA, PSO, DE, IWO, MOA, standard WOA algorithms, and IWOA algorithms were simulated and compared in 30 dimensions using the aforementioned four standard test functions. The computed \(f(x)\) can be defined as the fitness value of the solution. In the procedure described, the population size is set to 40 and the maximum number of iterations is 500. Table 2 illustrates the parameters of several algorithms. Additionally, tests were performed 30 times separately to prevent random deviation.The population size in the above algorithm is set to the same 40, and the maximum number of iterations is 500. The parameters of different algorithms are shown in Table 2. Furthermore, tests are independently repeated 30 times to avoid random deviation. Table 3 presents the results of thirty different tests computed by various methods. Ideal value, average value, and variance are the three statistical indicators, which are used to evaluate the optimization accuracy, average accuracy, and robustness of the algorithm in turn. The best results are indicated in bold for each function. The aforementioned three indicators of IWOA algorithm are obviously superior to other algorithms. Therefore, compared with other algorithms, IWOA has the optimal overall performance in solving the solution problem of the above four test functions, as shown in Table 3. As a result, compared with other algorithms, IWOA has the most satisfying overall performance in solving these four test functions listed above. Correspondingly, Figure 4a-d show the convergence curves of different algorithms in the process of solving the above test functions. It can be seen that the IWOA has a faster convergence and better solution result. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function Name** & **Expression** & **Search Space** & **Dim** & \(\mathbf{F_{min}}\) \\ \hline Sphere & \(F_{1}=\sum_{i=1}^{d}x_{i}^{2}\) & \([-10,10]\) & 30 & 0 \\ Rosenbrock & \(F_{2}=\sum_{i=1}^{d-1}[100(x_{i+1}-x_{i}^{2})^{2}+1-x_{i}^{2}]\) & \([-30,30]\) & 30 & 0 \\ Quartic & \(F_{3}=\sum_{i=1}^{d}x_{i}^{4}+random[0,1)\) & \([-1.28,1.28]\) & 30 & 0 + random noise \\ Ackley & \(F_{4}=20+e-20\exp[-0.2\sqrt{\frac{1}{2}\sum_{i=1}^{d}x_{i}^{2}}]-\) & \([-32,32]\) & 30 & 0 \\  & \(\exp[\frac{1}{d}\sum_{i=1}^{d}\cos(2\pi x_{i})]\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: This is a wide table. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Values of the Parameters** \\ \hline GA [13] & \(P_{c}=0.8,P_{m}=0.08\) \\ PSO [29] & \(C1=1.5,C2=2.0\) \\ DE [15] & \(F=0.5,CR=0.1\) \\ IWO [30] & \(\sigma_{initial}=0.05,\sigma_{final}=0.01\) \\ MOA [20] & \(male=20,female=20,g=0.8\sigma_{1}=1,\alpha_{2}=1.5,\beta=2,d=5,\lambda=1\) \\ WOA [26] & \(b=1,r=[0,1],l=[-1,1],p=[0,1]\) \\ IWOA & \(l=[-1,1],p=[0,1],r=[0,1]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter setups of different algorithms. However, the performance of the IWOA algorithm in sidelobe suppression optimization problem needs further evaluation. Figure 4: Simulation experiment results.