## 5 Entanglement and Numerical Test of DE-MPFSC Algorithm Stability
### Test and Analysis of DE-MPFSC Algorithm about Several Classic DE Algorithms  
#### 5.4.1 Entanglement Degree Test of DE-MPFSC Algorithm about Several Classic DE Algorithms  
We choose four classic DE improved algorithms JDE, OBDE, DEGL and SADE for related tests. Through entanglement degree test and data analysis, we can verify the related performance of the DE-MPFSC algorithm and its superiority in data integration. From the previous experiments, we can know that the DE-MPFSC is better than the DE in stability, effectiveness and convergence. At the same time, the optimal dynamic mutation factor \(F=0.2\) and the optimal crossover probability \(CR=0.3\) of the DE-MPFSC algorithm were obtained through data experiments. In the following test experiments, we use them as the initial mutation factor and the initial cross probability to better compare with other classic DE algorithms. Because the function of data integration is closely related to the data size and dimension, the algorithm in this paper sets the number of individuals to 1000 and are divided into 5 experiments. The number of individuals gradually increases in each test and the test runs an average of 4 times. We record relevant experimental indicators: dynamic mutation probability \(F\), dynamic cross probability \(CR\), entanglement degree \(\frac{1}{\xi}\), entanglement error \(\zeta\), error rate \(\varepsilon\%\), average individual loss efficiency. Figures 11-15 below shows a numerical results of the experiment. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11} NP & \(F\) & \(CR\) & \(\xi\) & \(\zeta\) & \(\epsilon\%\) & \(F^{*}\) & \(CR^{*}\) & \(\xi\) & \(\zeta\) & \(\epsilon\%\) \\ \hline
1000 & 0.1 & 0.9 & 0.69 & 0.40 & \(\pm 0.579\) & 0.1 & 0.9 & 0.15 & 0.015 & \(\pm 0.1\) \\
1000 & / & / & 0.82 & 0.66 & \(\pm 0.805\) & 0.3 & 0.4 & 0.30 & 0.04 & \(\pm 0.133\) \\
1000 & / & / & 0.67 & 0.49 & \(\pm 0.731\) & 0.3 & 0.3 & 0.29 & 0.02 & \(\pm 0.068\) \\
1000 & / & / & 0.77 & 0.58 & \(\pm 0.753\) & 0.2 & 0.3 & 0.27 & 0.019 & \(\pm 0.070\) \\
1000 & / & / & 0.79 & 0.44 & \(\pm 0.557\) & 0.2 & 0.3 & 0.32 & 0.018 & \(\pm 0.056\) \\ \hline \multirow{2}{*}{Average} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11}  & 0.1 & 0.9 & 0.748 & 0.514 & \(\pm 0.685\) & 0.22 & 0.44 & 0.266 & 0.0224 & \(\pm 0.0854\) \\ \hline \multirow{2}{*}{Variance} & \multicolumn{4}{c}{\(DE\)} & \multicolumn{4}{c}{\(DE-MPFSC\)} \\ \cline{2-11}  & 0 & 0 & 0.00422 & 0.01118 & \(\pm 0.01219\) & 0.007 & 0.068 & 0.00453 & 0.0001 & \(\pm 0.00097\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Numerical Analysis of Entanglement Degree \(\frac{1}{\xi}\) and Entanglement Degree Error \(\zeta\) of the DE algorithm and the DE-MPFSC algorithm 1000 times. Figure 11: The Entanglement Degree, Correction Rate and Loss Curve of DE-MPFSC algorithm. Figure 12: The Entanglement Degree, Correction Rate and Loss Curve of the (Self-Adapting Parameter Setting in Differential Evolution) JDE algorithm. Figure 13: The Entanglement Degree, Correction Rate and Loss Curve of the Opposition Based Differential Evolution (OBDE) algorithm. Figure 14: The Entanglement Degree, Correction Rate and Loss Curve of the (Differential Evolution with Global and Local neighborhoods) DEGL algorithm. Figure 15: The Entanglement Degree, Correction Rate and Loss Curve of the (Self-Adaptive Differential Evolution) SADE algorithm. We analyze the above Figures 11-15. First we analyze from the entanglement degree. In the process of the DE-MPFSC algorithm, the convergence speed and convergence precision of population individuals gradually stabilized as the population increased. The density and integration of the two entangled images gradually increase and, at the same time, the edge differentiation phenomenon is further weakened on each branch, which make the entangled branch converge to the center of the entanglement along the convergence curve.