## 2 Related Concepts
### ACDE Algorithm  
Differential evolution (DE) is a stochastic parallel optimization algorithm [25; 26] based on population differences proposed by [PERSON] and [PERSON] in 1997 [27] on the basis of evolutionary ideas such as the genetic algorithm. DE solves optimization problems by imitating the heuristic swarm intelligence generated by competition and cooperation among organisms [28]; the algorithm has strong usability, global optimization capability and stability [29] and is widely used in clustering optimization calculations, neural network optimizations, constrained optimization calculations and filter designs. However, the DE algorithm also has two defects: (1) the fixed scaling factor hinders the full search performance of the algorithm when performing mutation operations [30]; (2) in the later stage of optimization, the population diversity is reduced and the algorithm falls easily into local optima [31; 32]. Among them, the first defect has been basically solved by [PERSON] et al. 13 years ago. [PERSON] et al. [33]. They assign a separate scaling factor to each individual, so that it can be automatically adjusted according to two thresholds during the running of the algorithm but this will inevitably have some randomness and blindness [34]. To solve these problems, this study uses an improved DE algorithm, ACDE, which improves upon DE in two aspects. First, in the mutation operation stage, the adaptive scaling factor can be changed with the number of iterations, thus addressing the insufficient searching ability caused by the fixed scaling factor. In the standard differential evolution algorithm, increasing the scaling factor can expand the search range and speed up the individual update in the population. The reduction of the scaling factor can enhance the ability of local search and improve the convergence of the algorithm. Based on this, in the early stage of algorithm evolution, the search range can be expanded by increasing the scaling factor. In the later stage of algorithm evolution, the scaling factor is reduced to speed up the convergence of the algorithm. At the same time, in order to avoid the destruction of the genetic structure of the dominant individual, the scaling factor of the individual with higher fitness should be reduced; in order to promote the improvement of the structure of the disadvantaged individual, the scaling factor of the individual with lower fitness should be increased. Second, chaotic motion has the characteristics of sensitivity, randomness, regularity and ergodicity and it can traverse the entire space state without repeating within the specified range. Based on chaos theory, a chaotic fine search strategy is proposed to improve the local search efficiency of the algorithm in order to avoid premature population. For any optimization problem,  
\[ \begin{array}{l}\min f(x_{1},x_{2},...,x_{N})\\ \text{s.t.}\ x_{j}\in\left[L_{j},U_{j}\right]1\leq j\leq N\end{array}  \tag{13}\]  
where \(N\) is the dimension of the solution space and \(L_{j}\) and \(U_{j}\) represent the upper and lower bounds of the range of \(x_{j}\) values, respectively. The specific process of the ACDE algorithm is as follows:  
Step 1: Population initialization. \(D\) individuals randomly satisfying the constraint condition are generated in the \(N\)-dimensional solution space as the \(i\)-th individual of the 0-th generation population: \(\left\{x_{i}(0)\left|x_{j,i}(0)\in\left[L_{j,i},U_{j,i}\right],i=1,2,3,...,D;j=1,2,3,...,N\right\}\right\). At the same time, the maximum number of iterations is assumed to be \(M\). The value of the \(j\)-th dimension of the \(i\)-th individual is calculated according to the following formula:  
\[x_{j,i}(0)=L_{j,i}+rand(0,1)\cdot\left(L_{j,i}-U_{j,i}\right), \tag{14}\]  
where \(rand(0,1)\) represents a random number between [0,1] and obeys a uniform distribution. Step 2: Chaos initialization [13]. Chaotic motion has the characteristics of randomness, regularity and ergodicity and can traverse the entire space state without repetition within a specified range.