# CDDO-HS: Child Drawing Development Optimization-Harmony Search Algorithm
## 6 Testing, Results, and Discussion
### CDDO-HS vs. CDDO and HS
#### 6.4.2 CEC-C06 2019 Benchmark Test Functions  
CEC-C06 2019 Benchmark Test Functions are a set of 10 mathematical functions commonly used to evaluate the performance of optimization algorithms. These functions were specifically designed for the IEEE Congress on Evolutionary Computation (CEC) 2019 competition to provide a more challenging and diverse set of test functions compared to \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**CDDO–HS**} & \multicolumn{2}{c}{**CDDO**} & \multicolumn{2}{c}{**HS**} \\ \cline{2-7}
**Fun** & **Avg.** & **Std.** & **Avg.** & **Std.** & **Avg.** & **Std.** \\ \hline F1 & 5.087E\(-\)33 & 1.057E\(-\)32 & **1.328E\(-\)57** & **8.635E\(-\)73** & 2.850E+02 & 9.021E+01 \\ F2 & 4.921E\(-\)17 & 4.033E\(-\)17 & **2.453E\(-\)32** & **4.385E\(-\)32** & 3.005E+00 & 5.355E\(-\)01 \\ F3 & 1.249E\(-\)29 & 2.238E\(-\)29 & **2.736E\(-\)39** & **5.168E\(-\)40** & 1.754E+04 & 5.815E+03 \\ F4 & 1.966E\(-\)16 & 1.920E\(-\)16 & **7.815E\(-\)33** & **2.784E\(-\)48** & 2.214E+01 & 1.787E+00 \\ F5 & **2.298E+00** & **6.935E+00** & 2.419E+01 & 1.023E+01 & 2.040E+04 & 8.759E+03 \\ F6 & **5.589E\(-\)04** & **1.439E\(-\)04** & 7.074E\(-\)01 & 6.787E\(-\)01 & 2.834E+02 & 1.023E+02 \\ F7 & 2.901E\(-\)03 & 1.497E\(-\)03 & **1.361E\(-\)03** & **1.123E\(-\)03** & 2.042E\(-\)01 & 5.145E\(-\)02 \\ F8 & \(-\)1.178E+04 & 3.098E+03 & **\(-\)1.244E+04** & **5.537E+02** & \(-\)1.240E+04 & 7.638E+01 \\ F9 & **2.222E+00** & **6.070E+00** & 1.060E+01 & 1.724E+01 & 1.968E+01 & 3.683E+00 \\ F10 & **6.809E\(-\)15** & **1.703E\(-\)15** & 7.875E\(-\)15 & 4.118E\(-\)15 & 5.095E+00 & 5.702E\(-\)01 \\ F11 & **0.000E+00** & **0.000E+00** & 5.688E\(-\)01 & 1.532E+00 & 3.513E+00 & 8.925E\(-\)01 \\ F12 & **1.161E\(-\)06** & **3.112E\(-\)07** & 3.167E\(-\)01 & 9.0046E\(-\)01 & 7.060E+00 & 2.147E+00 \\ F13 & **1.555E\(-\)05** & **5.271E\(-\)06** & 4.128E\(-\)01 & 3.745E\(-\)01 & 1.622E+02 & 1.596E+02 \\ F14 & 5.372E+00 & 4.241E+00 & **9.981E\(-\)01** & **3.686E\(-\)04** & 9.980E\(-\)01 & 3.448E\(-\)11 \\ F15 & **6.249E\(-\)04** & **2.502E\(-\)04** & 1.181E\(-\)03 & 1.022E\(-\)03 & 6.699E\(-\)03 & 9.110E\(-\)03 \\ F16 & **-1.032E+00** & **3.777E\(-\)10** & -1.029E+00 & 3.247E\(-\)03 & -1.032E+00 & 1.889E\(-\)07 \\ F17 & **3.979E\(-\)01** & **2.675E\(-\)09** & 4.231E\(-\)01 & 4.814E\(-\)02 & 3.979E\(-\)01 & 6.467E\(-\)06 \\ F18 & 5.700E+00 & 8.238E+00 & **3.117E+00** & **1.579E\(-\)01** & 3.900E+00 & 4.930E+00 \\ F19 & **-3.863E+00** & **1.554E\(-\)10** & \(-\)3.728E+00 & 1.075E\(-\)01 & -3.863E+00 & 4.714E\(-\)08 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table comparing CDDO–HS with CDDO and standard HS. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**CDDO–HS**} & \multicolumn{2}{c}{**CDDO**} & \multicolumn{2}{c}{**HS**} \\ \cline{2-7}
**Fun** & **Avg. ** & **Std. ** & **Avg. ** & **Std. ** & **Avg. ** & **Std. ** \\ \hline F1 & **5.317E+04** & **8.142E+03** & 4.104E+05 & 3.377E+05 & 2.232E+10 & 2.295E+10 \\ F2 & **1.835E+01** & **6.390E\(-\)03** & 1.898E+01 & 3.663E\(-\)01 & 1.875E+01 & 2.090E\(-\)01 \\ F3 & **1.370E+01** & **5.785E\(-\)13** & 1.370E+01 & 1.633E\(-\)05 & 1.370E+01 & 4.987E\(-\)10 \\ F4 & 5.746E+01** & **3.066E+01** & 2.221E\(+\)03 & 8.515E+02 & 3.976E+01 & 2.003E+01 \\ F5 & **2.170E+00** & 2.109E\(-\)01 & 3.350E+00 & **1.421E\(-\)01** & 2.039E+00 & 2.623E\(-\)02 \\previous years. These functions cover a wide range of optimization problems, including unimodal, multimodal, separable, and non-separable functions. Some of the functions also incorporate features such as rotation, scaling, and shifting to further increase their complexity. Each function is defined over a set of input variables and has a known global minimum or maximum, which allows for optimization algorithms to be evaluated based on their ability to find the optimal solution. Thus, they are widely used in the field of optimization and evolutionary computation to compare the performance of different algorithms and to benchmark new algorithms.