# Adaptive Dynamic Disturbance Strategy for Differential Evolution Algorithm
## 4 Simulation Experiment and Algorithm Performance Analysis
### Analysis of Results  
This experiment was programmed using Matlab. It was run 20 times independently on a HP PC with Intel(R) Core(TM) i5-2450M CPU, 2.50 GHz RAM 4.00 GB. The algorithm parameters were set as follows: The adaptive dynamic disturbance strategy for differential evolution (ADDSDE) algorithm, population number \(N=50\), \(F_{\max}=0.9\), \(F_{\min}=0.2\), \(CR_{\max}=0.9\), \(CR_{\min}=0.2\), \(Q=15\), \(\delta=1\times 10^{-6}\), the parameter settings of the comparison algorithm DE, SADE and CAPSO are the same as the original. Consider the cases when variable dimension D = 30 and D = 50. The number of iterations is appropriately changed according to the complexity of each test function. The optimal value, average optimal value and standard deviation of each algorithm are shown in Tables 2 and 3, and the convergence curve of each algorithm is shown in Figure 1.  
As can be seen from Tables 2 and 3, the optimization result of the ADDSDE algorithm is significantly higher than that of the other three algorithms. For the five standard test functions selected, the ADDSDE algorithm can obtain the optimal value 0, except f5 = Ackley function. The convergence accuracy is optimal. The standard deviation shows that the ADDSDE algorithm is very stable. For ill-conditioned high-dimensional complex functions, other algorithms cannot get the theoretical optimal value, some algorithms are far from the theoretical optimal value, and the stability of the algorithm is not satisfactory. From Tables 2 and 3, it can be seen that with the increase of the dimension of the solution, the evolutionary abilities of other algorithms also decrease accordingly with different degrees. Analyzing the convergence curve of each algorithm in Figure 1, we know that the convergence curve of ADDSDE converges to the optimal solution almost at the speed of vertical descent. Additionally, its optimization ability is strong, and the convergence accuracy is high. Even for high-dimensional solutions, it can be quickly fixed to the optimal position. Due to the complexity of the function and the high dimension of the problem, the other comparison algorithms are easily trapped in the local optimumand the convergence speed is also slow. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Type**} & **Function** & **Range of** & **Optimal** \\  & **Name** & **Formula** & **Optimization** & **Value** \\ \hline \multirow{2}{*}{Unimodal} & Sphere & \(f_{1}(x)=\sum\limits_{i=1}^{n}x_{i}^{2}\) & [–100,100] & 0 \\  & Rosenbrock & \(f_{2}(x)=\sum\limits_{i=1}^{n}\left[100(x_{i+1}-x_{i})^{2}+(x_{i}-1)^{2}\right]\) & [–10,10] & 0 \\ \hline \multirow{3}{*}{Multi-peak} & Rastrigin & \(f_{3}(x)=\sum\limits_{i=1}^{n}\left[x_{i}^{2}-10\cos(2\pi x_{i})+10\right]\) & [–5.12,5.12] & 0 \\  & [PERSON] & \(f_{4}(x)=\frac{1}{400}\sum\limits_{i=1}^{n}x_{i}^{2}-\prod\limits_{i=1}^{n} \cos(\frac{x_{i}}{\sqrt{t}})+1\) & [–600,600] & 0 \\  & [PERSON] & \(f_{5}(x)=-20\exp(-0.2\sqrt{\sum\limits_{i=1}^{n}x_{i}^{2}})-\exp(\frac{1}{n} \sum\limits_{i=1}^{n}\cos(2\pi x_{i}))+20+e\) & [–32,32] & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Test Functions.