# Hybrid Strategy Improved Beetle Antennae Search Algorithm and Application
## 4 Simulation Experiment and Analysis  
### Algorithm Data Comparison  
To quantitatively evaluate the performance of the Hybrid Strategy Improved Beetle Antennae Search (HSBAS) algorithm, the study conducted simulation experiments on ten selected standard test functions, as shown in Table 1. Among the selected test functions, \(f_{1}\)\(\sim\)\(f_{3}\) belong to the single-peak function, which has only a single extreme point in the definition domain, and the use of such functions to evaluate the algorithm can test its convergence rate and optimization search accuracy, thus reflecting the optimization performance level of the algorithm. Moreover, \(f_{4}\)\(\sim\)\(f_{7}\) belongs to the multi-peak function, and \(f_{8}\)\(\sim\)\(f_{11}\) belong to the fixed-dimension multi-peak function, with multiple extreme points, usually used to evaluate the algorithm's performance in the global search ability and avoid premature convergence. The simulation experiments were conducted on a computer with 64-bit Windows operating system, Intel(r) Core (TM) i7-10870H CPU @ 2.20 GHz 2.21 GHz processor (Intel, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Test Function Name** & **Dimension** & **Search Area** & **Theoretical Optimality** \\ \hline \(f_{1}\) & Sphere & 30 & [\(-\)100,100] & 0 \\ \(f_{2}\) & Schwefel 2.22 & 30 & [\(-\)10,10] & 0 \\ \(f_{3}\) & Rosenbrock & 30 & [\(-\)5,5] & 0 \\ \(f_{4}\) & Rastrigin & 30 & [\(-\)5.12,5.12] & 0 \\ \(f_{5}\) & Penalized & 30 & [\(-\)50,50] & 0 \\ \(f_{6}\) & Ackley’s & 30 & [\(-\)32,32] & 0 \\ \(f_{7}\) & Generalized Penalized & 30 & [\(-\)32,32] & 0 \\ \(f_{8}\) & Six-Hump Camel-Back & 2 & [\(-\)5,5] & \(-\)1.0316 \\ \(f_{9}\) & Goldstein–Price & 2 & [\(-\)2,2] & 3 \\ \(f_{10}\) & Hartman & 3 & [1,3] & \(-\)3.86 \\ \(f_{11}\) & Shekel’s Family & 4 & [0,10] & \(-\)10.5365 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Eleven benchmark test functions. Santa Clara, CA, USA), 16 G RAM (LC Power, Willich, Germany), and the algorithms were implemented using software MATLAB R2016b. A single execution was run 1000 times, and each algorithm ran 30 experiments independently for each test function. Set the species dimension to 30 for PSO and GA and set the species dimension to 1 for BAS and HSBAS. Their means and standard deviations were recorded separately, as shown in Table 2.  
The superiority of HSBAS is verified compared to other algorithms widely used in engineering structure optimization. The HSBAS algorithm shows better stability and optimization search ability in optimizing high-dimensional functions and achieves better optimal function values than the BAS algorithm. Compared with PSO and GA algorithms, HSBAS performs better on nine optimization functions and only shows sub-optimal performance on \(f_{4}\) and \(f_{5}\). [PERSON]'s ranking test results show that HSBAS is ranked first, PSO is ranked second, GA is ranked third, and BAS is fourth. The results indicate that the HSBAS algorithm effectively improves its performance in high-dimensional function optimization by improving the algorithm structure and parameter settings, overcoming