# Multi-User Detection Based on Improved Cheetah Optimization Algorithm
## 2 Methods
### Improved Cheetah Optimization Algorithm
#### 2.4.1 Control Parameter Update Strategy  
The key concept behind improving the cheetah optimization algorithm is to update the typical linear change mechanism strategy, which can better adapt to the algorithm's nonlinear optimization process. This nonlinear change provides a guarantee for the global convergence of the algorithm. The improved cheetah optimization algorithm parameter update strategy is  
\[a_{i,j}^{t}=\left\{\begin{array}{ll}0.001\frac{t}{t}(UB-LB)&k=1\\ 0.001\frac{t}{t}\Big{|}X_{s}+\frac{a_{1}}{a_{1}+a_{2}}\times[X_{b}{}^{t}(i,j)- \overline{X}_{i}^{k}]+\frac{a_{2}}{a_{1}+a_{2}}\times[X^{t}(i,j)-\overline{X} _{i}^{k}]-X^{t}(i,j)\Big{|}+rand&k\
eq 1\end{array}\right. \tag{18}\]  
\[\beta_{i,j}^{t}=X_{s}+\frac{a_{3}}{a_{3}+a_{2}}\times[X_{1}{}^{t}(i,j)- \overline{X}_{i}^{k}]+\frac{a_{2}}{a_{3}+a_{2}}\times[X^{t}(i,j)-\overline{X} _{i}^{k}] \tag{19}\]  
where \(X_{s}\) represents a random number selected from the range of values denoted by \([UB,LB]\), \([UB,LB]\) represents the limiting boundary value of the algorithm individual, and \(\overline{X}_{i}^{k}\) represents the initial population of individuals. \(a_{1}\), \(a_{2}\), \(a_{3}\) represent the fitness values of the leader, Cheetah-i, and neighboring Cheetah at the \(t\)-th iteration, respectively. \(X_{b}^{t}\), \(X_{1}^{t}\), are the leader position, Cheetah-i position, and neighbor Cheetah position at the \(t\)-th iteration.  
Compared to traditional algorithms, in Equation (18), the new evolutionary position is obtained by using the information of the evolutionary vectors of the leader and Cheetah-i as well as the ratio of the fitness values, and the search strategy of adjusting the step size by the difference of the distance between the leader and the Cheetah-i is improved to dynamically adjusting the search step size by using the difference of the distance between the new evolutionary position and the Cheetah-i [16]. The improvement scheme is shown in Figure 3. The solid arrows represent the algorithm's optimization direction, and the dashed lines represent the information on each cheetah's evolution vector. The two solid line ranges represent the algorithm search space and the cheetah sitting area, respectively, and the two dotted dashed line ranges represent search asymptotic surfaces of the Cheetah gradually converging to the prey with the iteration before and after the change in the step size updating strategy. As can be seen from the figure, the improved step size adjustment strategy not only enhances the precision of the search but also significantly accelerates the convergence ability of the algorithm's pre-search range.  
In Equation (19), the updating of the optimal evolutionary position depends on the proportion of fitness values, using the information of the evolutionary vectors of neighboring cheetah and Cheetah-i. The Interaction Factor, which is indicated by the disparity between the positions of the neighboring cheetah and Cheetah-i in the attacking strategy, is improved to the difference between the optimal evolutionary location and Cheetah-i's location. The original Interaction Factor mainly controls the degree of movement toward the neighbor position through the difference between current and neighboring locations and guiding the search agent to move toward the neighbor position. The improved method not only considers the difference between the current position and the neighbor position but also adjusts it according to the proportion of its fitness value to better guide the degree of the search agent's movement towards the neighbor position. Such a setup can better reflect the interaction between search agents, scientifically plan the prey escape route based on the fitness ratio data within the capture range, and improve the cheetah's ability to accurately capture prey on escape routes.