## 3 The Proposed Model
### AFA-Based Parameter Optimization  
At this stage, the AFA model is derived for optimal tuning of the parameters involved in the WELM model. The AFA replicates the behavior of a prey fish swarm and it has been established for rapid searching. Exploration begins with arbitrary result maps for each fish. Fitness is assessed and the fish following techniques are initiated, and each fish follows the other fishes via the optimum outcome. Once the outcome is sub-optimum, a swarming method is initiated. Once the chosen outcome is not linked, the prey method is initiated. This process repeats until the required threshold or termination condition is encountered [21]. The AFA has four functions that have been modeled on the nature of fish in a fish swarm. A primary function is free-moving action: in the environment, a fish  
Figure 2: The structure of ELM.  
travels in a swarm when it is not injured. The next function is prey action, since it uses smell, vision, and other available senses in the body. In AFSA, the area where an artificial fish senses a predator is modeled as a neighborhood via a visual-sized radius. The next function is following action when a fish identifies food; other swarm members follow it to reach the food. The last function is the swarm action, which replicates fishes as each fish continually attempts to be in the swarm and does not leave so it can be protected from the hunter.  
Consider the condition vector of AFS is \((x_{1},\ x_{2},\ldots x_{n})\), where \(x_{1},x_{2},\ldots x_{n}\) denotes the location of the fish. The food in this location of the fish is characterized by \(y=f(x)\), in which \(y\) indicates the objective function value. The distance amongst artificial fish is \(d_{ij}=\left\|X_{i}-X_{j}\right\|\), where \(i\) and \(j\) represent arbitrary fish, Step indicates the maximum step size of artificial fish, and \(a\) denotes the degree of congestion factor.  
Let \(X_{v}\) be the visual location at a particular moment. \(X_{next}\) denotes the novel location. The development process is shown as follows:  
\[X_{v}=X_{i}+Visual\times rand(),i\in[0,\ n] \tag{15}\]  
\[X_{next}=X+\frac{X_{v}-X}{\left\|X_{v}-X\right\|}\times step\times rand() \tag{16}\]  
During the prey model, the behavior of fish is represented as follows:  
\[\textit{prey }(X_{i})=\begin{cases}x_{i}+step\frac{x_{j}-x_{i}}{\left\|x_{j}-x _{i}\right\|}&if\ y_{j}-y_{i}\\ x_{i}+(2 rand-1)\cdot step&else\end{cases} \tag{17}\]  
where _rand_ denotes a random function within \([0,1]\). In the swarming phase, the behavior of the swarm is represented as follows:  
\[\textit{swarm}(X_{i})=\begin{cases}X_{i}+step\frac{x_{j}-x_{i}}{\left\|x_{j}-x _{i}\right\|}&if\frac{y_{v}}{nf}>\delta y_{i}\\ \textit{prey}(X_{i})&else\end{cases} \tag{18}\]  
The next stage is represented in the following (Equation (19)):  
\[follow\ (X_{i})=\begin{cases}X_{i}+step\frac{x_{max}-x_{i}}{\left\|x_{max}-x_{i} \right\|}&if\frac{y\ \max}{nf}>\delta y_{i}\\ \textit{prey}(X_{i})&else\end{cases} \tag{19}\]  
where \(x_{max}\) is the last location that the fish can arrive and \(y_{max}\) is the maximum value of the objective function to guarantee that local and global exploration, and the exploration direction towards the optimum food source are carried out.