# A Reward Population-Based Differential Genetic Harmony Search Algorithm
## 4 Experiments
### Comparative Study on RDEGA-HS and HS Variants
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Dimensions** & **Theoretical Optimum** & **Average Optimum** & **Standard Deviation** \\ \hline  & 30 & 0 & \(8.72\times 10^{-38}\) & \(3.26\times 10^{-28}\) \\  & 40 & 0 & \(9.21\times 10^{-36}\) & \(1.25\times 10^{-28}\) \\ HS & 50 & 0 & \(4.11\times 10^{-36}\) & \(3.67\times 10^{-28}\) \\  & 60 & 0 & \(8.42\times 10^{-34}\) & \(1.63\times 10^{-27}\) \\  & 70 & 0 & \(8.16\times 10^{-34}\) & \(1.09\times 10^{-26}\) \\  & 80 & 0 & \(2.91\times 10^{-33}\) & \(1.28\times 10^{-26}\) \\  & 30 & 0 & \(2.45\times 10^{-38}\) & \(2.56\times 10^{-28}\) \\  & 40 & 0 & \(6.49\times 10^{-37}\) & \(2.06\times 10^{-28}\) \\ RHS & 50 & 0 & \(1.14\times 10^{-35}\) & \(1.63\times 10^{-28}\) \\  & 60 & 0 & \(4.80\times 10^{-36}\) & \(3.32\times 10^{-27}\) \\  & 70 & 0 & \(7.41\times 10^{-35}\) & \(2.46\times 10^{-27}\) \\  & 80 & 0 & \(3.56\times 10^{-34}\) & \(2.33\times 10^{-27}\) \\  & 30 & 0 & \(9.17\times 10^{-38}\) & \(3.63\times 10^{-29}\) \\  & 40 & 0 & \(3.90\times 10^{-38}\) & \(1.40\times 10^{-28}\) \\ DEGA-HS & 50 & 0 & \(6.56\times 10^{-37}\) & \(3.06\times 10^{-28}\) \\  & 60 & 0 & \(8.62\times 10^{-35}\) & \(3.05\times 10^{-28}\) \\  & 70 & 0 & \(1.07\times 10^{-33}\) & \(1.73\times 10^{-27}\) \\  & 80 & 0 & \(1.14\times 10^{-32}\) & \(2.39\times 10^{-27}\) \\  & 30 & 0 & \(7.00\times 10^{-40}\) & \(6.58\times 10^{-31}\) \\  & 40 & 0 & \(2.66\times 10^{-39}\) & \(5.84\times 10^{-30}\) \\  & 50 & 0 & \(2.77\times 10^{-38}\) & \(2.27\times 10^{-29}\) \\  & 60 & 0 & \(3.92\times 10^{-36}\) & \(3.14\times 10^{-28}\) \\  & 70 & 0 & \(1.01\times 10^{-34}\) & \(3.69\times 10^{-28}\) \\  & 80 & 0 & \(3.89\times 10^{-34}\) & \(8.51\times 10^{-29}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of the Sphere function under different optimization algorithms. As to a comparison of the algorithms' stability, the experiments were repeated 100 times. In addition to the optimization ability, which has received a lot of attention, the algorithms' stability is also an index worth paying attention to when evaluating the performance of the algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Dimensions** & **Theoretical Optimum** & **Average Optimum** & **Standard Deviation** \\ \hline \multirow{6}{*}{HS} & 30 & 0 & \(3.93\times 10^{-35}\) & \(7.20\times 10^{-27}\) \\  & 40 & 0 & \(3.36\times 10^{-34}\) & \(3.55\times 10^{-25}\) \\  & 50 & 0 & \(7.14\times 10^{-35}\) & \(3.82\times 10^{-26}\) \\  & 60 & 0 & \(2.59\times 10^{-33}\) & \(2.93\times 10^{-24}\) \\  & 70 & 0 & \(1.58\times 10^{-32}\) & \(3.07\times 10^{-23}\) \\  & 80 & 0 & \(5.24\times 10^{-31}\) & \(3.24\times 10^{-23}\) \\  & 30 & 0 & \(2.44\times 10^{-36}\) & \(6.47\times 10^{-28}\) \\  & 40 & 0 & \(3.70\times 10^{-35}\) & \(1.69\times 10^{-26}\) \\  & 50 & 0 & \(1.60\times 10^{-34}\) & \(1.23\times 10^{-25}\) \\  & 60 & 0 & \(4.13\times 10^{-33}\) & \(3.01\times 10^{-25}\) \\  & 70 & 0 & \(2.17\times 10^{-32}\) & \(1.79\times 10^{-23}\) \\  & 80 & 0 & \(4.43\times 10^{-32}\) & \(3.38\times 10^{-23}\) \\  & 30 & 0 & \(4.63\times 10^{-38}\) & \(9.70\times 10^{-29}\) \\  & 40 & 0 & \(9.97\times 10^{-36}\) & \(1.24\times 10^{-27}\) \\  & 50 & 0 & \(3.25\times 10^{-35}\) & \(8.49\times 10^{-27}\) \\  & 60 & 0 & \(1.13\times 10^{-33}\) & \(8.16\times 10^{-26}\) \\  & 70 & 0 & \(1.97\times 10^{-32}\) & \(3.24\times 10^{-24}\) \\  & 80 & 0 & \(5.93\times 10^{-32}\) & \(2.29\times 10^{-22}\) \\  & 30 & 0 & \(1.52\times 10^{-39}\) & \(2.19\times 10^{-29}\) \\  & 40 & 0 & \(5.42\times 10^{-36}\) & \(8.45\times 10^{-29}\) \\ \multirow{2}{*}{RDEGA-HS} & 50 & 0 & \(3.76\times 10^{-35}\) & \(3.19\times 10^{-26}\) \\  & 60 & 0 & \(6.41\times 10^{-35}\) & \(2.42\times 10^{-25}\) \\  & 70 & 0 & \(1.09\times 10^{-34}\) & \(1.53\times 10^{-25}\) \\  & 80 & 0 & \(3.20\times 10^{-33}\) & \(2.06\times 10^{-24}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of the Schwefel function under different optimization algorithms.