## 2 Related Work
### Equilibrium Optimizer Algorithm
The initial concentration is constructed based on the number and dimensional of the particle swarm. The particle swarm is initialized as in Equation (4) [44]. \[C_{i}^{0}=C_{min}+randi(C_{max}-C_{min}),i=1,2,\ldots,n \tag{4}\]  
\(C_{i}^{0}\) represents the initial concentration of the \(i\)th particle, and it also represents the initial position of the \(i\)th particle. \(C_{max}\) and \(C_{min}\) denote the minimum and maximum values of the range. \(n\) represents the number of particle groups, and \(randi\) is a random number in the range of [0, 1]. In each iteration, each particle randomly selects a particle in the equilibrium state pool with the same probability to update its concentration. The equilibrium state pool is defined by the following Equation (5) [44]. \[C_{eq,pool}=\big{\{}C_{eq1},C_{eq2},C_{eq3},C_{eq4},C_{eq5}\big{\}} \tag{5}\]  
\(C_{eq1}\), \(C_{eq2}\), \(C_{eq3}\), and \(C_{eq4}\) are the best four solutions obtained throughout the current iteration. \(C_{eq5}\) represents the average position of the four solutions. To optimize the search ability, two parameters \(a_{1}\) and \(a_{2}\) are introduced to improve Equation (3) [44] to better balance the local and global search. The improved equation is given in Equation(6) [44], where \(t\) is defined as a function of iteration (Iter) and it decreases as the number of iterations increases, as shown in Equation (7) [44]. \[F=-a_{1}sign(r-0.5)\Big{(}e^{-\lambda t}-1\Big{)} \tag{6}\]  
\[t=\bigg{(}1-\frac{Iter}{MaxIter}\bigg{)}^{a_{2}\frac{Iter}{MaxIter}} \tag{7}\]  
\(r\) and \(\lambda\) are random variables in the range of [0, 1]. The \(a_{1}\) in Equation (6) [44] represents the control exploration capability. The larger \(a_{1}\) becomes, the greater the exploration capacity and the weaker the exploitation capacity. The \(a_{2}\) in Equation (7) [44] represents the managed exploration capacity. The larger the \(a_{2}\), the greater the exploitation capacity and the weaker the exploration capacity. \(sign(r-0.5)\) affects the direction of exploration and development. Generation rate (\(G\)) is one of the most important terms in EO, providing precise solutions by improving the development phase. G is described as a first-order exponential decay process, which is used in many engineering applications, as shown in Equation (8) [44]. \[G=G_{0}e^{-k(t-t_{0})} \tag{8}\]  
\(G_{0}\) is the initial value and \(k\) is the attenuation constant. To better adapt to the iteration of the algorithm, the exponential term of Equation (8) [44] is adopted. The generation speed control parameter \(G\cdot GP\) is defined as Equation (9) [44]. \(G\) is the mass generation rate, defined as Equation (10) [44]. Combined with Equation (8) [44], G is defined in EO as shown in Equation (11) [44], which can provide an exact solution by improving the development phase. \[G\cdot GP=\left\{ \begin{array}{ll}0.5r_{1}&r_{2}\geq GP\\ 0&r_{2}\leq GP\end{array} \right. \tag{9}\]  
\[G_{0}=G\cdot GP\big{(}C_{eq}-\lambda C\big{)} \tag{10}\]  
\[G=G_{0}F \tag{11}\]  
\(GP=0.5\) gives an ideal balance of local and global search capabilities. In summary, the rules for updating the particle positions in the EO are given in Equation (12) [44]. \[C=C_{eq}+\big{(}C-C_{eq}\big{)}.F+\frac{G}{\lambda V}(1-F) \tag{12}\]  
Equation (12) [44] is divided into three terms, the first term being the equilibrium concentration. The second and third terms indicate the change in concentration. The second term can use the concentration difference to search globally to find the best solution. The third part can make the solution more precise when the solution is found. This provides better global and local search based on the difference of symbols of the second and third terms. Algorithm 1 is the pseudo-code for the EO.