# 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 \multirow{6}{*}{HS} & 30 & 0 & \(1.39\times 10^{-7}\) & \(3.32\times 10^{-2}\) \\  & 40 & 0 & \(8.52\times 10^{-7}\) & 4.98 \\  & 50 & 0 & \(2.86\times 10^{-5}\) & 8.75 \\  & 60 & 0 & \(5.20\times 10^{-5}\) & \(6.11\times 10^{1}\) \\  & 70 & 0 & \(5.38\times 10^{-4}\) & \(4.85\times 10^{2}\) \\  & 80 & 0 & \(3.59\times 10^{-3}\) & \(8.09\times 10^{2}\) \\  & 30 & 0 & \(4.02\times 10^{-7}\) & \(1.72\times 10^{-1}\) \\  & 40 & 0 & \(8.30\times 10^{-7}\) & 2.56 \\  & 50 & 0 & \(3.12\times 10^{-5}\) & 3.80 \\  & 60 & 0 & \(4.32\times 10^{-5}\) & 8.60 \\  & 70 & 0 & \(2.73\times 10^{-4}\) & \(4.56\times 10^{1}\) \\  & 80 & 0 & \(5.91\times 10^{-3}\) & \(5.87\times 10^{2}\) \\  & 30 & 0 & \(9.46\times 10^{-8}\) & \(7.12\times 10^{-2}\) \\  & 40 & 0 & \(2.09\times 10^{-7}\) & \(1.74\times 10^{-1}\) \\ \multirow{2}{*}{DEGA-HS} & 50 & 0 & \(1.03\times 10^{-5}\) & 2.64 \\  & 60 & 0 & \(4.81\times 10^{-4}\) & 7.34 \\  & 70 & 0 & \(9.85\times 10^{-3}\) & \(1.67\times 10^{1}\) \\  & 80 & 0 & \(6.95\times 10^{-2}\) & \(5.74\times 10^{1}\) \\  & 30 & 0 & \(1.46\times 10^{-8}\) & \(4.12\times 10^{-3}\) \\ \multirow{2}{*}{RDEGA-HS} & 40 & 0 & \(1.91\times 10^{-8}\) & \(5.57\times 10^{-3}\) \\  & 50 & 0 & \(1.06\times 10^{-7}\) & \(7.60\times 10^{-1}\) \\ \multirow{2}{*}{RDEGA-HS} & 60 & 0 & \(8.34\times 10^{-7}\) & 4.21 \\  & 70 & 0 & \(4.63\times 10^{-6}\) & 7.84 \\ \multirow{2}{*}{RDEGA-HS} & 80 & 0 & \(9.85\times 10^{-6}\) & 8.73 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the Rastrigin function under different optimization algorithms. Figure 6: Change in average optimal fitness value of Rastrigin function with number of iterations. \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 & \(8.43\times 10^{-2}\) & \(6.36\times 10^{-2}\) \\  & 40 & 0 & \(4.82\times 10^{-1}\) & \(4.65\times 10^{-1}\) \\  & 50 & 0 & \(2.86\) & \(6.80\) \\  & 60 & 0 & \(7.14\times 10^{2}\) & \(9.45\times 10^{2}\) \\  & 70 & 0 & \(7.14\times 10^{2}\) & \(9.45\times 10^{2}\) \\  & 80 & 0 & \(5.23\times 10^{3}\) & \(7.35\times 10^{3}\) \\  & 30 & 0 & \(4.08\times 10^{-2}\) & \(2.77\times 10^{-2}\) \\  & 40 & 0 & \(4.68\times 10^{-1}\) & \(8.47\times 10^{-1}\) \\ \multirow{2}{*}{RHS} & 50 & 0 & \(6.93\) & \(3.72\) \\  & 60 & 0 & \(9.63\) & \(5.71\times 10^{1}\) \\  & 70 & 0 & \(3.72\times 10^{1}\) & \(6.62\times 10^{2}\) \\  & 80 & 0 & \(7.52\times 10^{2}\) & \(5.04\times 10^{3}\) \\  & 30 & 0 & \(7.77\times 10^{-3}\) & \(7.98\times 10^{-1}\) \\ \multirow{2}{*}{DEGA-HS} & 40 & 0 & \(2.67\times 10^{-1}\) & \(2.91\) \\  & 50 & 0 & \(6.12\times 10^{-1}\) & \(6.84\) \\  & 60 & 0 & \(1.55\) & \(8.15\times 10^{1}\) \\  & 70 & 0 & \(7.15\times 10^{1}\) & \(3.43\times 10^{2}\) \\  & 80 & 0 & \(7.02\times 10^{2}\) & \(1.48\times 10^{3}\) \\  & 30 & 0 & \(2.21\times 10^{-3}\) & \(9.98\times 10^{-2}\) \\ \multirow{2}{*}{RDEGA-HS} & 40 & 0 & \(9.04\times 10^{-2}\) & \(4.56\times 10^{-2}\) \\  & 50 & 0 & \(2.53\times 10^{-1}\) & \(9.10\times 10^{-1}\) \\ \multirow{2}{*}{RDEGA-HS} & 60 & 0 & \(5.90\) & \(5.78\) \\  & 70 & 0 & \(1.31\times 10^{1}\) & \(1.74\times 10^{1}\) \\ \multirow{2}{*}{RDEGA-HS} & 80 & 0 & \(8.33\times 10^{1}\) & \(4.77\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results of the Rosenbrock function under different optimization algorithms. Figure 7: Change in average optimal fitness value of Rosenbrock function with number of iterations. Figure 8: Change in average optimal fitness value of Sphere function with number of iterations.