## 3 Methodology
### Iajs-Hkrvm Model
#### 3.1.2 Improved Artificial Jellyfish Search Algorithm  
The AJS algorithm is a new swarm intelligence optimization algorithm proposed in 2021 [35]. The algorithm solves the optimization problem by simulating the natural laws of jellyfish movement and foraging behavior in the ocean and swarm. The algorithm-solving process is shown in Equation (4), and the algorithm's schematic diagram is shown in Figure 2. The algorithm determines the motion form of the jellyfish through the time control mechanism and updates the position of the jellyfish according to the food content of the location of the jellyfish. The motion form of the jellyfish includes the movement of the jellyfish following the ocean current, active movement, and passive movement in the jellyfish swarm. When the time control function \(c(t)\geq 0.5\), the position of the jellyfish population changes with the direction of the ocean current movement. When the time control function \(c(t)<0.5\), the jellyfish move in the jellyfish swarm to update their position. When rand (0, 1) > 1 - \(c(t)\), the jellyfish update their positions randomly in the jellyfish swarm according to their spatial range. When rand (0, 1) \(\leq\) 1 - \(c(t)\), the jellyfish update their positions according to the food content of different jellyfish locations in the swarm [35]. \[\left\{ \begin{array}{l}\text{Time control}:c(t)=\big{|}\big{(}1-\frac{t}{T} \big{)}\times(2\times\text{rand}(0,1)-1)\big{|}\\ \text{Ocean motion}\left\{\begin{array}{l}\overrightarrow{\text{trend}}=X^ {*}-\beta\times\text{rand}(0,1)\times\mu\\ X_{i}(t+1)=X_{i}(t)+\text{rand}(0,1)\times\overrightarrow{\text{trend}}\\ \text{Passive motion}:X_{i}(t+1)=X_{i}(t)+\gamma\times\text{rand}(0,1)\times(U_{ \text{b}}-L_{\text{b}}),\text{rand}(0,1)>1-c(t)\\ \text{Active motion}\left\{\begin{array}{l}X_{i}(t+1)=X_{i}(t)+\text{rand}(0,1) \times\overrightarrow{\text{Direction}}\\ \overrightarrow{\text{Direction}}=\left\{\begin{array}{l}X_{i}(t)-X_{i}(t),f(X_{i})\geq f\big{(}X_{i}\big{)}\\ X_{i}(t)-X_{i}(t),f(X_{i})<f\big{(}X_{i}\big{)}\end{array}\right.\end{array} \right.,\text{rand}(0,1)\leq 1-c(t)\end{array}\right.\end{array} \right. \tag{4}\]  
where \(t\) is the current iteration, \(T\) is the maximum number of iterations, \(\overrightarrow{\text{trend}}\) is the ocean trend, \(X^{*}\) is the optimal jellyfish location in the current iteration, \(\beta\) is the distribution coefficient that is related to the length of \(\overrightarrow{\text{trend}}\), and its value is 3, \(\mu\) is the mean location of all jellyfishes, \(\gamma\) is the motion coefficient that is related to the length of motion around the locations of jellyfishes, and its value is 0.1, \(U_{\text{b}}\) and \(L_{\text{b}}\) are, respectively, the upper and lower bounds of the search space, \(X_{\text{i}}(t)\) and \(X_{\text{j}}(t)\) are, respectively, the i and j jellyfish locations in the current iteration, and \(f(X_{\text{i}})\) and \(f(X_{\text{j}})\) are, respectively, the food content of the location of the i and j jellyfish, that is, the fitness value. In order to overcome the shortcomings of the AJS algorithm, such as premature convergence and local optimization, this paper introduces Fuch chaotic mapping, lens-imaging reverse learning, and adaptive hybrid mutation strategy to improve the AJS algorithm. The AJS algorithm uses logistic chaotic mapping to generate the initial population, but the initial population generated by logistic chaotic mapping is concentrated in the edge of the space, which makes it difficult to search for the optimal solution quickly and reduces the optimization efficiency of the algorithm. Fuch chaotic mapping is an infinite folding chaotic mapping, which has a better ergodic, dynamic, and convergence than finite folding chaotic mapping such as logistic mapping and tent mapping [41]. The initial population generated by Fuch chaotic mapping is concentrated in several local areas, which enables a rapid population search.