# Parameter Combination Framework for the Differential Evolution Algorithm
## 6 Experiments and Discussion
 \\ \hline \multirow{3}{*}{1} & 1.50e+03 & 3.68e-09 & \multirow{3}{*}{\(-\)} & 6.42e+04 & 1.31e+04 & \multirow{3}{*}{\(-\)} & 4.03e+05 & 3.25e+05 & \multirow{3}{*}{\(-\)} \\  & (2.35e+03) & (2.63e-08) & (3.19e+04) & (1.03e+04) & & & & \\ \hline \multirow{3}{*}{2} & 0.00e+00 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 0.00e+00 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 8.00e-09 & 0.00e+00 & \multirow{3}{*}{\(-\)} \\  & (0.00e+00) & (0.00e+00) & & (0.00e+00) & & & & \\ \hline \multirow{3}{*}{3} & 0.00e+00 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 0.00e+00 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 2.54e-03 & 2.57e-04 & \multirow{3}{*}{\(-\)} \\  & (0.00e+00) & (0.00e+00) & & (0.00e+00) & & & & (3.77e-03) & (1.83e-03) & \\ \hline \multirow{3}{*}{4} & 0.00e+00 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 2.52e+01 & 4.49e+01 & \multirow{3}{*}{\(\approx\)} & 1.26e+02 & 1.71e+02 & \multirow{3}{*}{\(+\)} \\  & (0.00e+00) & (0.00e+00) & & (3.72e+01) & (4.82e+01) & & & (4.50e+01) & (3.06e+01) & \\ \hline \multirow{3}{*}{5} & 2.01e+01 & 2.00e+01 & \multirow{3}{*}{\(-\)} & 2.03e+01 & 2.03e+01 & \multirow{3}{*}{\(-\)} & 2.08e+01 & 2.07e+01 & \multirow{3}{*}{\(-\)} \\  & (5.54e-02) & (7.46e-03) & & (1.18e-01) & (4.59e-02) & & & 2.08e+01 & 2.07e+01 & \multirow{3}{*}{\(-\)} \\ \hline \multirow{3}{*}{6} & 2.11e+00 & 3.08e-01 & \multirow{3}{*}{\(-\)} & 8.11e+00 & 2.67e-01 & \multirow{3}{*}{\(-\)} & 3.86e+01 & 4.15e+00 & \multirow{3}{*}{\(-\)} \\  & (1.10e+00) & (1.42e+00) & & (2.11e+00) & (5.60e-01) & & & (2.82e+00) & (2.19e+00) & \\ \hline \multirow{3}{*}{7} & 7.04e-03 & 0.00e+00 & \multirow{3}{*}{\(-\)} & 6.56e-03 & 0.00e+00 & \multirow{3}{*}{\(-\)} & 3.52e-03 & 0.00e+00 & \multirow{3}{*}{\(-\)} \\  & (1.07e-02) & (0.00e+00) & & (8.83e-03) & (0.00e+00) & & & (6.99e-03) & (0.00e+00) & \\ \hline \multirow{3}{*}{8} & 0.00e+00 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 1.15e-09 & 0.00e+00 & \multirow{3}{*}{\(\approx\)} & 5.99e+01 & 3.59e+01 & \multirow{3}{*}{\(-\)} \\  & (0.00e+00) & (0.00e+00) & & (8.19e-09) & (0.00e+00) & & & (5.03e+00) & (2.53e+00) & \\ \hline \multirow{3}{*}{9} & 1.28e+01 & 1.82e+01 & \multirow{3}{*}{\(+\)} & 3.30e+01 & 3.93e+01 & \multirow{3}{*}{\(+\)} & 1.49e+02 & 1.41e+02 & \multirow{3}{*}{\(-\)} \\  & (2.31e+00) & (2.83e+00) & & (4.13e+00) & (3.53e+00) & & & (1.20e+01) & (1.02e+01) & \\ \hline \multirow{3}{*}{10} & 4.08e-04 & 3.82e-02 & \multirow{3}{*}{\(+\)} & 1.49e-01 & 4.28e+01 & \multirow{3}{*}{\(+\)} & 3.86e+02 & 1.82e+03 & \multirow{3}{*}{\(+\)} \\  & (2.92e-03) & (5.36e-02) & & (1.67e-01) & (6.66e+00) & & & (1.38e+02) & (1.75e+02) & \\ \hline \multirow{3}{*}{11} & 1.50e+03 & 1.55e+03 & \multirow{3}{*}{\(\approx\)} & 4.37e+03 & 4.22e+03 & \multirow{3}{*}{\(-\)} & 1.55e+04 & 1.43e+04 & \multirow{3}{*}{\(-\)} \\  & (1.76e+02) & (2.08e+02) & & (3.77e+02) & (2.92e+02) & & & (5.75e+02) & (5.50e+02) & \\ \hline \multirow{3}{*}{12} & 1.86e-01 & 1.29e-01 & \multirow{3}{*}  
As seen in Table 4, for the test of 30\(D\) problems, PVCDE has significant advantages on 15 functions according to the rank-sum statistics, and has five significantly worse results in comparison to SHADE. As the dimensions increase, the number of superior results also increases. The number of cases in which PVCDE performs better than SHADE is higher than the number of cases in which PVCDE performs more poorly than SHADE. Therefore, we believe that parameter combination technology can improve algorithm performance. Analyzing the results of specific functions, we found that some problems are suitable for SHADE and some problems are suitable for PVCDE. For functions f9, f10, f15, f16, and f30, PVCDE performs more poorly than SHADE on most high-dimensional issues. f10 is a multi-mode separable problem; after the initial stage, its most suitable parameter values become 1 for \(F\) and 0 for \(CR\). SHADE has a strategy that locks \(CR\) to 0, which is more suitable for f10. In PVCDE, since the \(CR\) locked to 0 cannot be recovered, this technique is only used in so\({}_{1}\) and so\({}_{2}\).