# Kernel Clustering with a Differential Harmony Search Algorithm for Scheme Classification
## 4 Experiments
### Numerical Experiments of DHS
#### 4.1.2 Sensitivity Analysis of Parameters  
In this section, the effect of each parameter in the search process of the DHS algorithm will be discussed. Similar with the basic HS, the DHS algorithm has parameters that include _hms_, _hmcr_, _par_, and _fw_. The default parameters of DHS are _hms_ = 50, _hmcr_ = 0.9, _par_ = 0.3, _fw_ = 0.005, _sc_ = 20. The maximum number of evaluations is set to 100,000. Then we change each parameter and test via the benchmark functions. Each scene runs 50 times. Tables 5-9 show the results of the optimization of the benchmark functions. The results in Table 5 show that the performance of the DHS algorithm will be better if _sc_ is smaller. The value of _sc_ determines the replacement frequency of the memories in the HM. Results show that _sc_ values between 10 and 40 are suggested. In Tables 6 and 7, we found that although values of _hms_ and _hmcr_ have impacts on the optimization results, but there is no obvious rule for the selection of _hms_ and _hmcr_. _Hms_ values between 30 and 70 are applicable for most cases, while _hmcr_ values between 0.8 and 0.99 are suggested. In Table 8, DHS performs better when _par_ values are less than 0.3. In Table 9, we found that the algorithm is not sensitive to the parameter _fw_. A value of 0.005 is applicable for most cases. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Function** & & _hms_ = 10 & _hms_ = 30 & _hms_ = 50 & _hms_ = 70 & _hms_ = 90 \\ \hline \multirow{2}{*}{Ackley} & Mean & \(1.71\times 10^{-11}\) & \(3.11\times 10^{-15}\) & \(3.76\times 10^{-13}\) & \(1.58\times 10^{-9}\) & \(1.68\times 10^{-7}\) \\  & Stdv & \(3.45\times 10^{-13}\) & \(3.11\times 10^{-15}\) & \(1.66\times 10^{-13}\) & \(6.43\times 10^{-10}\) & \(8.20\times 10^{-8}\) \\ \hline \multirow{2}{*}{[PERSON]} & Mean & \(6.58\times 10^{-2}\) & \(2.47\times 10^{-4}\) & \(9.37\times 10^{-6}\) & \(4.32\times 10^{-7}\) & \(2.64\times 10^{-5}\) \\  & Stdv & \(7.93\times 10^{-2}\) & \(1.74\times 10^{-3}\) & \(6.62\times 10^{-5}\) & \(7.10\times 10^{-7}\) & \(1.92\times 10^{-5}\) \\ \hline \multirow{2}{*}{Rastrigin} & Mean & \(0\) & \(0\) & \(0\) & \(2.72\times 10^{-6}\) & \(2.46\times 10^{-6}\) \\  & Stdv & \(0\) & \(0\) & \(0\) & \(1.92\times 10^{-5}\) & \(1.74\times 10^{-5}\) \\ \hline \multirow{2}{*}{Rosenbrock} & Mean & \(1.94\) & \(1.38\) & \(8.70\times 10^{-1}\) & \(7.11\times 10^{-1}\) & \(1.09\) \\  & Stdv & \(1.51\) & \(1.35\) & \(1.14\) & \(6.14\times 10^{-1}\) & \(6.05\times 10^{-1}\) \\ \hline \multirow{2}{*}{Sphere} & Mean & \(1.16\times 10^{-89}\) & \(6.20\times 10^{-43}\) & \(1.97\times 10^{-28}\) & \(1.96\times 10^{-21}\) & \(2.62\times 10^{-17}\) \\  & Stdv & \(2.96\times 10^{-89}\) & \(8.53\times 10^{-43}\) & \(1.93\times 10^{-28}\) & \(1.36\times 10^{-21}\) & \(1.20\times 10^{-17}\) \\ \hline \multirow{2}{*}{Schwefel} & Mean & \(1.57\times 10^{-41}\) & \(9.47\times 10^{-19}\) & \(2.92\times 10^{-12}\) & \(3.76\times 10^{-9}\) & \(2.27\times 10^{-7}\) \\  & Stdv & \(4.08\times 10^{-41}\) & \(6.63\times 10^{-19}\) & \(1.37\times 10^{-12}\) & \(1.78\times 10^{-9}\) & \(8.24\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The effect of _hms_ on means and standard deviations.