# 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** & **Mean Optimum** & **Standard Deviation** \\ \hline \multirow{8}{*}{HS} & 30 & 0 & \(3.66\times 10^{-2}\) & 2.35 \\  & 40 & 0 & \(3.55\times 10^{-1}\) & 3.51 \\  & 50 & 0 & \(1.25\) & 4.21 \\  & 60 & 0 & \(3.35\) & \(3.23\times 10^{1}\) \\  & 70 & 0 & \(8.70\times 10^{1}\) & \(5.64\times 10^{2}\) \\  & 80 & 0 & \(9.49\times 10^{2}\) & \(6.43\times 10^{2}\) \\  & 30 & 0 & \(2.41\times 10^{-2}\) & \(5.33\times 10^{-2}\) \\  & 40 & 0 & \(1.02\times 10^{-1}\) & \(6.25\times 10^{-1}\) \\ \multirow{2}{*}{RHS} & 50 & 0 & \(1.01\) & 4.22 \\  & 60 & 0 & \(8.25\) & \(1.10\times 10^{1}\) \\  & 70 & 0 & \(6.59\times 10^{1}\) & \(4.56\times 10^{2}\) \\  & 80 & 0 & \(1.88\times 10^{2}\) & \(3.12\times 10^{3}\) \\  & 30 & 0 & \(8.20\times 10^{-5}\) & \(2.03\times 10^{-2}\) \\ \multirow{2}{*}{DEGA-HS} & 40 & 0 & \(1.22\times 10^{-2}\) & \(6.01\times 10^{-2}\) \\  & 50 & 0 & \(1.25\times 10^{-1}\) & \(8.85\times 10^{-1}\) \\ \multirow{2}{*}{DEGA-HS} & 60 & 0 & \(7.22\) & 6.43 \\  & 70 & 0 & \(6.96\times 10^{1}\) & \(7.80\times 10^{1}\) \\ \multirow{2}{*}{RDEGA-HS} & 80 & 0 & \(1.69\times 10^{2}\) & \(9.72\times 10^{3}\) \\  & 30 & 0 & \(2.67\times 10^{-5}\) & \(1.22\times 10^{-3}\) \\ \multirow{2}{*}{RDEGA-HS} & 40 & 0 & \(5.44\times 10^{-3}\) & \(3.25\times 10^{-3}\) \\  & 50 & 0 & \(9.56\times 10^{-2}\) & \(5.26\times 10^{-1}\) \\ \multirow{2}{*}{RDEGA-HS} & 60 & 0 & \(2.29\times 10^{-1}\) & \(4.14\) \\  & 70 & 0 & \(9.61\times 10^{-1}\) & \(2.34\times 10^{1}\) \\ \multirow{2}{*}{RDEGA-HS} & 80 & 0 & \(5.77\) & \(1.22\times 10^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Result of the Ackley function under different optimization algorithms. Figure 4: Change in average optimal fitness value of Ackley function with number of iterations. Figure 5: Change in average optimal fitness value of Griewank 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  & 30 & 0 & \(4.00\times 10^{-11}\) & 1.00 \\  & 40 & 0 & \(6.02\times 10^{-9}\) & 1.50 \\ HS & 50 & 0 & \(1.38\times 10^{-8}\) & 2.64 \\  & 60 & 0 & \(4.86\times 10^{-7}\) & 7.16 \\  & 70 & 0 & \(5.99\times 10^{-7}\) & \(5.99\times 10^{1}\) \\  & 80 & 0 & \(6.98\times 10^{-6}\) & \(7.94\times 10^{1}\) \\  & 30 & 0 & \(3.13\times 10^{-10}\) & \(5.19\times 10^{-1}\) \\  & 40 & 0 & \(1.66\times 10^{-9}\) & \(7.73\times 10^{-1}\) \\ RHS & 50 & 0 & \(7.84\times 10^{-9}\) & 1.15 \\  & 60 & 0 & \(2.06\times 10^{-8}\) & 7.52 \\  & 70 & 0 & \(6.34\times 10^{-8}\) & 7.93 \\  & 80 & 0 & \(4.54\times 10^{-7}\) & \(1.87\times 10^{1}\) \\  & 30 & 0 & \(8.82\times 10^{-11}\) & \(2.15\times 10^{-1}\) \\  & 40 & 0 & \(2.08\times 10^{-10}\) & \(5.25\times 10^{-1}\) \\ DEGA-HS & 50 & 0 & \(1.08\times 10^{-9}\) & \(7.96\times 10^{-1}\) \\  & 60 & 0 & \(8.90\times 10^{-8}\) & \(8.11\times 10^{-1}\) \\  & 70 & 0 & \(8.22\times 10^{-7}\) & 4.48 \\  & 80 & 0 & \(7.91\times 10^{-6}\) & 5.21 \\  & 30 & 0 & \(1.13\times 10^{-12}\) & \(1.24\times 10^{-2}\) \\  & 40 & 0 & \(1.35\times 10^{-11}\) & \(1.68\times 10^{-1}\) \\ RDEGA-HS & 50 & 0 & \(1.35\times 10^{-10}\) & \(2.29\times 10^{-1}\) \\  & 60 & 0 & \(7.44\times 10^{-9}\) & \(7.67\times 10^{-1}\) \\  & 70 & 0 & \(4.93\times 10^{-8}\) & \(9.45\times 10^{-1}\) \\  & 80 & 0 & \(8.01\times 10^{-7}\) & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the Griewank function under different optimization algorithms.