## 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
Compared with the DE-MPFSC algorithm, the entanglement phenomenon of the convergence speed and convergence precision of the JDE algorithm is less obvious. When the number of individuals is 200, 600 and 1000, the entangled image is highly dispersed, which causes a severe edge differentiation on the entangled branches. Although, when the number of individuals is 400 and 600, the state of entanglement is better than that of 200, 600 and 800, the continuity of individual evolution is not reached as a whole, it does not converge to the center of entanglement along the convergence curve. JDE's entangled image shows irregular fluctuations. The OBDE algorithm is slightly better than the JDE algorithm in fluctuation, when the number of individuals is 200 and 1000, the entangled branches are severely differentiated and the dispersed degree is higher than that of JDE, which shows that the OBDE algorithm is not suitable. When the number of individuals is 400, 600 and 800, the dispersed degree of the entangled branches of the OBDE algorithm is lower but the edge dispersion of the entangled branches is more obvious than the DE-MPFSC algorithm. OBDE and JDE algorithms also do not show evolutionary continuity. The performance of the DEGL algorithm on evolutionary fluctuation is weaker than JDE and OBDE. When the number of individuals is 200 and 1000, the entangled branches are highly dispersed and do not converge to the entangled center. The DEGL is similar to the JDE algorithm and the OBDE algorithm. The individual convergence speed and convergence accuracy completely deviate from the entanglement center. The number of entangled branches integrated with 400 and 800 individuals is much higher than that with 200 and 1000 individuals. Although DEGL converges to the center of entanglement along the convergence curve, the edge differentiation of entangled branches is still not resolved. The continuity, volatility and convergence of the SADE algorithm are the closest to the DE-MPFSC algorithm but, unfortunately, a discrete state occurs when the number of individuals is 200, which makes the entanglement center distributed on the fitted line rather than an entanglement center. When the number of individuals is 400, 600, 800 and 1000, the edge dispersion of the entangled branches is weakened but it is not used for large-scale evolution. Then we analyze from the correct test rate of entangled branches. The entanglement degree of the DE-MPFSC algorithm is divided into two branches about convergence precision and convergence speed. From the image, the convergence speed and convergence precision are lower discrete and they converge to the entanglement center point along the convergence curve. The detection efficiency are 3, 19, 19, 19, 19, which shows that when the population individuals are 200, 400, 600, 800, 1000, the stability of the DE-MPFSC algorithm is higher. Due to the fluctuation of the JDE algorithm, its correct test rate is 0, and its error test rates are 0.4, 0.4, 0.95, 0.6 and 0.95, respectively. JDE's higher error test rate is easy to eliminate optimal individuals. The OBDE algorithm is weaker than the JDE algorithm in fluctuation. Its correct test rate is 0 but its error test rates are 1, 1, 0.4, 0.4, 1, which are higher than that of the JDE algorithm. When the number is 1000, the error test rate suddenly rebounds. The DEGL algorithm has a non-zero in correct test rate, which at least shows that there is a certain ability to adapt to individual mutations. But when the number of individuals is 200 and 1000, the error test rate of entangled branches is 1 and 0.95, which is still too high. When the number of individuals is 400 and 800, the correct test rate of entangled branches declines. The instability of this entanglement behavior is still not conducive to the evolution of mutation individuals. The correct test rate of the SADE algorithm are 0, 0, 0.35, 0.38, 0.35, and the error test rates are 0.4, 0.15, 0.15, 0.2, 0.15, which are much better than the JDE, OBDE and DEGL algorithms.