# Improved Brain Storm Optimization Algorithm Based on Flock Decision Mutation Strategy
## 4 Results
### AUV Intelligence Evaluation Application Example  
AUV intelligence evaluation can save test costs and provide guidance direction for enhancement of AUV intelligent capabilities, of which, the key technology is the solution of the combined weight model. In this paper, we drew on the multi-expert combined weight model (MMCW) proposed in [36] for evaluating AUV intelligence and simulation to verify the effectiveness and feasibility of the FDIBSO algorithm. The expression for this combined weight model is as follows. Figure 4: The convergence trajectories for four benchmark functions in 50-dimensional scenarios. \[\text{MinH}=\alpha\sum_{i=1}^{n}k_{i}\ln k_{i}+\beta\sum_{i=1}^{n}\left\{\sum_{j=1 }^{m}w_{cj}\ln\left(\frac{w_{cj}}{w_{ij}}\right)\right\}, \tag{10}\]  
where \(\alpha\) and \(\beta\) are combination coefficients and are both set to 0.5, \(k\) is an n-dimensional variable, \(w_{cj}\) is a function related to the variable \(k\), and \(w_{ij}\) is a constant value. The settings for these parameters refer to reference [36]. This model is relatively complex, thus posing a challenge to the performance of optimization algorithms. In this reference, for the solution of this optimization model, the comparison algorithm uses the differential evolution algorithm (DE), modified differential evolution algorithm (MDE), and GDBSO algorithm, with the same parameter settings as in [36]. These algorithms are relatively old and perform poorly, as can be seen in the experimental section of this article, where the computational performance of several algorithms is low. What is more noteworthy is that the experiments only pertain to four-dimensional variables. Therefore, as the dimensions increase, the problems with the performance of the algorithms become increasingly evident. The lower optimization performance can lead to bias in the computation of weights, which in turn, affects the performance evaluation of different AUV systems. In response to the issues mentioned above, this paper introduces the FDIBSO algorithm, which has higher optimization performance, into the model's solution process to achieve a more accurate assessment of AUV intelligence. In order to examine the performance gap between the FDIBSO algorithm and the comparative algorithms at higher dimensions, this paper employs the Monte Carlo method to generate multiple sets of simulated weights. The experiments limited the number of iterations to 200. The speed at which each algorithm converged was assessed across three conditions with 10, 20, 30, and 50 dimensions, with the results depicted in Figure 5. Additionally, to ensure consistency in experimental testing of the comparative algorithms, the performance of other BSO variants used in the CEC2018 experiments, including ADMBSO and DDGBSO algorithms (the GDBSO algorithm has already been compared), was tested. The results are shown in Figure 6. The mean convergence time required to achieve the optimal solution was calculated and documented in Tables 7 and 8. A \"No\" in the table means the algorithm cannot find a global optimal solution within the given number of iterations. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Algorithm** & **BSO** & **DE** & **MDE** & **GDBSO** & **FDIBSO** \\ \hline Mean (D-10) & 1.65 & 0.24 & 0.13 & 0.22 & 0.33 \\ \hline Mean (D-20) & No & 0.55 & 0.26 & 0.47 & 0.51 \\ \hline Mean (D-30) & No & No & 0.53 & 0.82 & 0.98 \\ \hline Mean (D-50) & No & No & No & 1.44 & 1.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The mean convergence time of each algorithm (unit: seconds). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Algorithm** & **BSO** & **ADMBSO** & **DDGBSO** & **GDBSO** & **FDIBSO** \\ \hline Mean (D-10) & 1.65 & 0.27 & 0.13 & 0.22 & 0.33 \\ \hline Mean (D-20) & No & 0.67 & 0.53 & 0.47 & 0.51 \\ \hline Mean (D-30) & No & 1.03 & 0.77 & 0.82 & 0.98 \\ \hline Mean (D-50) & No & 2.23 & 1.49 & 1.44 & 1.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The mean convergence time of different BSO variants (unit: seconds).