## 3 Improved Sparrow Search Algorithm
### Improved Sparrow Search Algorithm
Figure 6 is the design flow chart of the multi-objective antenna based on MISSA-BP. The specific steps are as follows:

Figure 5: Structure of BP neural network model. Step 1. Determining the size parameters and length range of the antenna. Step 2. Latin hypercube sampling (LHS) is used for uniform sampling within the length range of the antenna, and the parameter set \(P\) is obtained. Step 3. Substituting \(P\) into HFSS simulation software to obtain result set \(R\). Step 4. Building the neural network model using \(P\) and \(R\). Step 5. Using MISSA to optimize the parameters of the neural network, the surrogate model \(M\) of MISSA-BP is obtained. Step 6. Combine \(M\) and the MOPSO algorithm to design the multi-objective antenna. Step 7. If the iteration is not completed, continue to step 5. Otherwise, end the optimization and output the non-dominated solution set. ## 5 Simulation and Verification

### Verification of MISSA

To verify the accuracy and efficiency of the MISSA, PSO, GWO, WOA, and the original SSA were added to the test to compare with it. The specific information of the ten classic benchmark functions is shown in Table 1. The first five are unimodal, and the last five are multimodal. The experiments were carried out in the same simulation environment. The computer used is an Intel Core i7-10700 processor, 2.90 GHz, 16G RAM, Windows 10 system, and the simulation software is MATLAB R2020b and Ansys HFSS 2021 R1. Figure 6: Flow chart of antenna design based on MISSA-BP. PSO parameter setting: \(c1=1.6\), \(c2=1.4\), \(w=0.75\); GWO parameter setting: optimal solution a is between \([0,2]\); WOA parameter setting: \(a=0\), \(b=1\); SSA and MISSA parameter setting: \(ST=0.85\), \(PD=0.18\), \(SD=0.18\). At the same time, the upper iteration limit of all algorithms is \(T=500\), and the number of the population is \(N=30\). The five algorithms are tested on every function for 30 cycles to avoid randomness, and the corresponding results are taken. Table 2 records the relevant indicators corresponding to the algorithm. From Table 2, we know that in the solution of unimodal functions F1, F2 and F3, MISSA is the only one that can obtain the optimal solution, and the standard deviation of the F1 and F2 functions is also 0. When solving the function F1, only MISSA and SSA reach the optimal solution. Regarding the solution of unimodal functions F4 and F5, the average value and standard deviation of MISSA are obviously improved compared with other algorithms. MISSA is the best among the five algorithms for solving unimodal functions. In the last five multimodal functions, for the solution of F6 and F7, the accuracy and stability of MISSA and SSA are the same as the results. Still, in the resolution of F8, F9, and F10, the three indicators of MISSA are the best among the comparison algorithms. To directly see the changes in the convergent speed and accuracy of various algorithms, the average fitness convergence of the five algorithms when solving ten benchmark functions is plotted. Figure 7 distinctly displays that when the optimization test is performed for ten benchmark functions, MISSA can achieve the desired effect relatively quickly and perform well.