## 3 Advanced AFSA Optimization Method
### Adaptive GSA
 \tag{12}\]  
\(G_{0}\) is the initialized universal gravitation coefficient [35], and \(\theta=20\) is fixed here. \(G_{0}\) is set as a constant number, then the acceleration factor of AFSA_prey, AFSA_swarm, and AFSA_follow can be calculated as:  
\[ \begin{array}{c}F_{i,n\text{k}}^{(j)}=G_{real}\frac{M_{i,n}\cdot M_{i,k}}{R_ {i,n\text{k}}}(x_{i,n}^{(j)}-x_{i,k}^{(j)})\\ G_{real}=G_{0}\cdot e^{-\theta\frac{1}{N}}\\ F_{i,n\text{k}}^{(j)}=\sum\limits_{k\in N,k\
eq n}^{N}d_{j}\cdot F_{i,n\text{k }}^{(i)},d_{j}\sim Normal-Distribution(0,1)\\ a_{i,n}^{(j)}=\frac{F_{i,n}^{(j)}}{M_{i,n}^{(j)}}\end{array}  \tag{13}\]  
As for the whole CTGSA process, both the CT part and the GSA part are of great importance. The identification part of this system is supposed to be optimized according to the real-world situation. There are two basic rules or targets: one is accuracy, and the other is running time. When designing the optimization method for AFSA, the two points mentioned above need to be considered. Therefore, CTGSA is the integration plan after combining these two parts. Among them, the CT part greatly improves the initialization effect of the classifier when the number of samples is limited. It will enable more samples to participate in the formation of weights and preliminary grouping results in the initialization process, not only for those high-grade samples but also for those normal samples. In the process of training, aiming at the weakness of AFSA itself, introducing GSA into the main process of AFSA will make the training process faster and more efficient. Basically, according to Equations (9) and (13), the AFSA_preguing behavior in traditional AFSA is modified. For individual actions in unit time, the original process should be adjusted as follows:  
\[X_{i}^{(t+1)}=X_{i}^{(t)}+[rand()\times v_{i}^{(t)}+a_{i}^{(t)}]\times Weight_{i} \tag{14}\]  
In order to control the convergence speed and increase the practicability, the physical strength transformation model is introduced to illustrate the external force attenuation factor for the AFSA_swarming and the AFSA_following behavior. The physical strength transformation model is designed and implemented according to the regulation based on animals' exercise intensity and the limited upper bound of physical strength in nature. On the one hand, the physical consumption number directly affects the AFSA_swarming behavior and the AFSA_following behavior of the fish itself. At the same time, to make the algorithm converge faster, the most suitable parameter is expected to be used as soon as possible. On the other hand, the AFSA_preguing behavior is regarded as a physical energy maintenance service, so this parameter is not added in the process during updating. For Equations (10) and (11), the new generating field indicates the maximum range of the movement at this stage. Therefore, as for \(range(t)\), if the upper limit of physical strength is set to 100, the lower limit of physical strength should be set to 20 during the training process. The algorithm needs to retain a buffering interval or protection interval until the physical strength number is completely stabilized. A linear transformation model is introduced here. For generation \(t\)-th individuals, the corresponding physical strength value is \(\varphi_{i}^{(t)}\), then we have:  
\[ \begin{array}{c}\varphi_{i}^{(t)}=-\frac{4}{5}\times t+100\\ \varphi_{i}^{(t)}\times range(t)\to range(t+1)\end{array}  \tag{15}\]Obviously, the physical strength number of each individual in one cluster may not decrease at the same time. The main flow of the AFSA algorithm optimized by multiple strategies in this paper is as follows in Figure 5: