## 3 Results and Analysis
### Simulation Experiment and Result Analysis
#### 3.3.5 Comparison with Other Algorithms  
The above experiments verify that the stability and optimization ability of the AFS-MMSBAS algorithm are better than the two basic algorithms with respect to high-dimensional  
Figure 6: D = 200, functions \(f_{1}\sim f_{11}\) convergence performance. (**a**) Comparison of convergence of three algorithms for function \(f_{1}\); (**b**) Comparison of convergence of three algorithms for function \(f_{2}\); (**c**) Comparison of convergence of three algorithms for function \(f_{3}\); (**d**) Comparison of convergence of three algorithms for function \(f_{4}\); (**e**) Comparison of convergence of three algorithms for function \(f_{5}\); (**f**) Comparison of convergence of three algorithms for function \(f_{6}\); (**f**) Comparison of convergence of three algorithms for function \(f_{7}\); (**h**) Comparison of convergence of three algorithms for function \(f_{8}\); (**i**) Comparison of convergence of three algorithms for function \(f_{9}\); (**j**) Comparison of convergence of three algorithms for function \(f_{10}\); (**k**) Comparison of convergence of three algorithms for function \(f_{11}\).  
problems. This section compares the AFS-MMSBAS algorithm with other related algorithms, an Adaptive Dual-Strategy AFS algorithm based on the PSO algorithm (ADSAFS-PSO) [16], and an Adaptive AFSA utilizing Gene Exchange (AAFSA-GE) [17]. The unimodal function \(f_{1}\), noise function \(f_{4}\), multimodal functions \(f_{5}\) and \(f_{8}\), non-partitioned function \(f_{10}\), and step function \(f_{11}\) are selected as test functions. The parameter settings are as follows: population 50, crowding factor 0.75, attempt number = 5, dimensions D = 10 and D = 200, and iterations 800. The other relevant parameters of the AFS-MMABAS algorithm are the same as those in Section 3.3.1, and the other parameters of the PSOEM-FSA and AAFSA-GE algorithms are the same as those in the references. Each algorithm runs independently 10 times. The experimental results are shown in Table 6, including the average, standard deviation, the maximum and minimum of the optimization results, and the average running time of the algorithm.  
As seen from the table, at low dimensions, the three algorithms can converge to the minimum value for functions \(f_{5}\) and \(f_{11}\), but the ADSAFS-PSO algorithm is more stable. Moreover, the average value and standard deviation index obtained by the ADSAFS-PSO algorithm are also better than the other two algorithms. In general, the AAFSA-GE algorithm has the best optimization accuracy and stability at low dimensions, while the AFS-MMSBAS and ADSAFS-PSO algorithms perform similarly. However, at high dimensions, the average, standard deviation, and maximum index obtained by the AFS-MMSBAS algorithm are superior to the other two algorithms. Therefore, the AFS-MMSBAS algorithm has more advantages than the other algorithms. However, although the AFS-MMSBAS algorithm has good optimization performance for most test functions, it has poor optimization performance for f11 functions. This shows that the algorithm is not suitable for the optimization of step functions.  
In addition, the running time of the AFS-MMSBAS algorithm is the shortest.