## 5 Entanglement and Numerical Test of DE-MPFSC Algorithm Stability
### Test and Analysis of DE-MPFSC Algorithm about Several Classic DE Algorithms
#### 5.4.2 Numerical Test of DE-MPFSC Algorithm about Several Classic DE Algorithms  
We analyze the test results of the above data Table 6. We already know that when the number of individuals is 200, 400, 600, 800, 1000, the entanglement error range of DE-MPFSC is \(\varepsilon\in(\pm 0.133\%,\pm 0.578\%)\), The entanglement range of DE-MPFSC is \(\frac{1}{\xi}\in(0.15,0.35)\), and the entanglement error range of DE-MPFSC is \(\zeta\in(0.015,0.1)\). When the number of individuals is 200, the entanglement error rate ranges of JDE, OBDE, DEGL and SADE are \(\varepsilon\in(\pm 0.4\%,\pm 0.45\%)\), \(\varepsilon=\pm 1\%\), \(\varepsilon=\pm 1\%\), \(\varepsilon\in(\pm 0.3\%,\pm 0.4\%)\), compared with DE-MPFSC, the former has a higher entanglement error rate, which shows that the entanglement degree of DE-MPFSC (since we have done a detailed analysis of the entanglement effect of the DE-MPFSC algorithm in the case of the same number of individuals, we will not repeat it here. For all comparative data, see Section 5.3) is significantly higher than that of JDE, OBDE, DEGL and SADE, and the algorithm has good stability and effectiveness. We also found a special case, when the number of individuals is 200, the entanglement degree and entanglement degree error of JDE, OBDE, DEGL are infinite or non-existent. The reason for the case is that the entangled branches are too discrete or the edges of the entangled branches are too severely differentiated. Obviously, their entanglement efficiency is significantly lower than DE-MPFSC. The entanglement range and entanglement error of SADE are \(\frac{1}{\xi}\in(2.43\times 10^{-2},1.06\times 10^{-1})\) and \(\zeta\in(2.43\times 10^{-2},\)\(1.06\times 10^{-1})\), which is also lower than the entanglement effect of DE-MPFSC, which shows that the degree of entanglement of DE-MPFSC is significantly higher than that of JDE, OBDE, DEGL and SADE. The algorithm has small fluctuations and good convergence. When the number of individuals is 400, the entanglement error rate ranges of JDE, OBDE, DEGL and SADE are \(\varepsilon\in(\pm 0.4\%,\pm 0.45\%)\), \(\varepsilon=\pm 1\%\), \(\varepsilon=\pm 0.25\%\), \(\varepsilon=\pm 0.15\%\), compared with DE-MPFSC, the entanglement error rate is higher, which shows that the degree of entanglement of DE-MPFSC is significantly higher than that of JDE, OBDE, DEGL and SADE, and the algorithm is better stability and effectiveness. The entanglement ranges of JDE, OBDE, DEGL and SADE are \(\frac{1}{\xi}\in(5.44\times 10^{-2},2.33\times 10^{-1})\), \(\frac{1}{\xi}\in(0.53\times 10^{0},4.22\times 10^{-2})\), \(\frac{1}{\xi}\in(1.73\times 10^{-1},2.04\times 10^{-1})\), \(\frac{1}{\xi}\in(6.23\times 10^{-2},2.43\times 10^{-1})\), which shows that the degree of entanglement of the DE-MPFSC is significantly higher than that of JDE, OBDE, DEGL, SADE, and the DE-MPFSC algorithm has less volatility. The entanglement degree error ranges of JDE, OBDE, DEGL and SADE are \(\zeta\in(1.13\times 10^{-3},1.49\times 10^{-1})\), \(\zeta\in(0.59\times 10^{0},0.69\times 10^{-1})\), \(\zeta\in(1.34\times 10^{-1},3.70\times 10^{-2})\), \(\eta\in(2.95\times 10^{-2},1.08\times 10^{-1})\), which shows that the degree of entanglement of DE-MPFSC is significantly higher than that of JDE, OBDE, DEGL and SADE, and the algorithm has strong convergence. When the number of individuals is 600, 800, 1000, the comparison between DE-MPFSC and JDE, OBDE, DEGL and SADE is similar, and the data has been marked in the Table 6. On the whole, the effectiveness, stability, and convergence of DE-MPFSC are higher than JDE, OBDE, DEGL and SADE on average.