## 2 Related Work
### Equilibrium Optimizer Algorithm  
Heuristic algorithms are proposed relative to optimization algorithms. Scholars have proposed heuristic algorithms such as Bat Algorithm (BA) [39], Differential Evolution algorithm (DE) [40], Particle Swarm optimization algorithm (PSO) [41], and Whale Optimization Algorithm (WOA) [42; 43]. These algorithms have improved the ability to search for optimal solutions. EO is a physics-based heuristic optimization algorithm for dynamic source and sink models proposed by [PERSON] in 2020, which has the advantages of good optimization and fast convergence [44]. The heuristic algorithm has also been improved by adding many strategies. [PERSON] presents a Levy flight black edge regeneration black algorithm (LEBH) to speed up the convergence rate of BH [45]. [PERSON] applies the compact strategy to the snake optimization algorithm (SO). The compact snake optimization algorithm (cSO) is proposed, which effectively reduces the use of memory resources [46]. [PERSON] proposes the adaptive Bat algorithm (ABA), which can dynamically and adaptively adjust the flight speed and direction, significantly improving the global convergence accuracy of the BA [47]. [PERSON] applies the adaptive optimization strategy to the PSO (APSO). The problem of slow convergence of PSO and ease of falling into the local optimal land was effectively solved. [48]. [PERSON] and [PERSON] also apply adaptive strategy to WOA (ANWOA) and DE (ADE), respectively, and the convergence speed and optimization accuracy of the original algorithm can be effectively improved [49; 50]. The adaptive strategy can dynamically adjust the parameters of the algorithm and change the direction and speed of particle motion in the algorithm so that it can easily solve the problem that the algorithm is prone to local optimization and improve the accuracy of the global optimization. Thus, the adaptive strategy is applied to EO to improve the optimization ability and convergence speed of EO. The main of inspiration for the EO is the simple mixing of well-defined dynamic mass balance phenomena on the control volume. The first-order ordinary differential equation for the mass balance equation is given by Equation (1) [44]. \[V\frac{dC}{dt}=QC_{eq}-QC+G \tag{1}\]\(V\frac{dC}{dt}\) is the rate of mass change in the control volume, and \(C\) is the concentration inside the control volume. When \(V\frac{dC}{dt}\) is equal to zero, the solution reaches a steady state. \(Q\) is the volumetric flow rate into and out of the control volume, and \(C_{eq}\) represents the concentration at an equilibrium state. \(G\) is the mass generation rate inside the control volume. By solving for Equation (1) [44], through the arrangement and combination of Equation (1) [44], \(\frac{dC}{dt}\) can be converted into a function of \(\frac{Q}{\mathcal{V}}\). \(\lambda=\frac{Q}{\mathcal{V}}\) is introduced into the formula as the flow rate, and \(C\) can be expressed in the form of another Equation (2) [44]. \(F\) is the coefficient of the exponential term, which can be calculated by Equation (3) [44]. \[C=C_{eq}+\big{(}C_{0}-C_{eq}\big{)}F+(1-F)\frac{G}{\lambda V} \tag{2}\]  
\[F=exp[-\lambda(t-t_{0})] \tag{3}\]  
\(\lambda\) is the mobility rate, and \(C_{0}\) is the initial concentration of the control volume at the initial time \(t_{0}\). The three parts of Equation (2) [44] can represent the three update rules in the inspired EO. The first is the equilibrium concentration, and the second is related to the concentration difference and represents the search mechanism. The third represents the part of the optimal solution. Applying Equation (2) [44] to the EO, \(C\) represents the solution obtained in the current iteration, and \(C_{eq}\) represents the optimal solution in the current generation. Thus, the EO continuously updates the positions of the particles through iterative search and searches for the optimal solution through a combination of local search and global search. The principle and process of the EO are shown below.