## 2 Basic Knowledge  
### Artificial Electric Field Algorithm  
The artificial electric field algorithm (AEFA) is a novel meta-heuristic optimization algorithm to simulate the mutual motion of charged particles in an electrostatic field. In order to simplify the operation, the AEFA only considers the attractive force between particles, ignoring the repulsive force between charged particles to ensure that particles with a large charge can attract the nearby particles with a low charge. Each charged particle represents a feasible solution in the search space. The fitness value of each solution is determined by the charge of each charged particle. The higher the charge of the particles, the closer the feasible solutions are to the optimal solution. The motion principle of the charged particles is shown in Figure 1. Each circle represents a charged particle, and the size of the circle represents the amount of charge. The charged particle \(Q_{1}\) is attracted to the other three charged particles and finally forms a resultant force \(F\) and acceleration in this direction. It can be seen that \(Q_{4}\) has the largest amount of charge and has the greatest attraction to \(Q_{1}\), so the direction of the resultant force on \(Q_{1}\) is closer to the direction of attraction of \(Q_{4}\) to \(Q_{1}\). Therefore, in the iteration process of the AEFA, the charged particles with a small charge in the search space will move to the charged particles with a high charge, so that the algorithm converges to the optimal solution [41]. Figure 1: A schematic diagram of the force on the charged particles. The mathematical model of the AEFA can be described by Equations (1) and (2) [42]. \[V_{i}^{t+1}=rand\times V_{i}^{t}+a_{i}^{t} \tag{1}\]  
\[X_{i}^{t+1}=X_{i}^{t}+V_{i}^{t} \tag{2}\]  
where \(rand\) is a random number in the interval \([0,\ 1]\); \(V_{i}^{t+1}\) represents the velocity of the \(i\)-th charged particle at the \((t+1)\)-th iteration; \(X_{i}^{t+1}\) represents the position of the \(i\)-th charged particle at the \((t+1)\)-th iteration; and \(a_{i}^{t}\) represents the acceleration of the \(i\)-th charged particle at the \(t\)-th iteration. According to [PERSON]'s second law, when the particle is subjected to the electric field force, the expression of acceleration is described as follows. \[a_{i}^{t}=\frac{Q_{i}^{t}\times E_{i}^{t}}{m_{i}^{t}} \tag{3}\]  
At the \(t\)-th iteration, the electric field intensity of the \(i\)-th particle is  
\[E_{i}^{t}=\frac{F_{i}^{t}}{Q_{i}^{t}} \tag{4}\]  
The resultant force of the charged particle in the solution space is  
\[F_{i}^{t}=\sum_{j=1,j\
eq i}^{N}rand\times F_{ij}^{t} \tag{5}\]  
The resultant force is calculated according to the Coulomb force on the particle. The Coulomb force on the charged particle is modeled as follows. \[F_{ij}^{t}=K^{t}\times\frac{Q_{i}^{t}\times Q_{j}^{t}\times\left(X_{best}^{t}- X_{i}^{t}\right)}{R_{ij}^{t}+\varepsilon} \tag{6}\]  
\[R_{ij}=\left\|X_{i}(t),X_{j}(t)\right\|_{2} \tag{7}\]  
\[K^{t}=K_{0}\times exp\left(-\alpha\times\frac{iteration}{Maxiteration}\right) \tag{8}\]  
In Equation (6), \(F_{ij}^{t}\) represents the Coulomb force of charged particle \(i\) and charged particle \(j\) at the \(t\)-th iteration; \(K^{t}\) is the Coulomb constant; \(X_{best}^{t}\) represents the optimal individual at the \(t\)-th iteration; \(R_{ij}\) represents the distance between charged particle \(i\) and charged particle \(j\); \(\varepsilon\) is a very small positive number. In Equation (8), \(K_{0}=500;\alpha=30\); \(iteration\) represents the current number of iterations; \(Maxiteration\) represents the maximum number of iterations. The change in the Coulomb constant makes the algorithm perform a global search in the early iteration and turn to a local search in the later iteration. The \(K^{t}\) iteration process is shown in Figure 1:0  
The charge of all particles in the first-generation population is the same (set to 1).