# Parallel Hierarchical Genetic Algorithm for Scattered Data Fitting through B-Splines
## 5 Simulation Results
### Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Test** & **Method** & **SNR = 1** & **SNR = 2** & **SNR = 3** \\ \hline
1 & CSSPL & 0.01877 \(\pm\) 0.00085 & 0.00490 \(\pm\) 0.00019 & 0.00247 \(\pm\) 0.00008 \\  & FCF & 0.02452 \(\pm\) 0.00116 & 0.00533 \(\pm\) 0.00027 & 0.00229 \(\pm\) 0.00009 \\  & LOWESS & 0.01786 \(\pm\) 0.00081 & 0.00867 \(\pm\) 0.00032 & 0.00647 \(\pm\) 0.00029 \\  & PHGA & **0.01376**\(\pm\) 0.00089 & **0.00423**\(\pm\) 0.00025 & **0.00221**\(\pm\) 0.00009 \\ \hline
2 & CSSPL & 0.03057 \(\pm\) 0.00108 & 0.00890 \(\pm\) 0.00030 & 0.00451 \(\pm\) 0.00016 \\  & FCF & 0.03407 \(\pm\) 0.00117 & 0.01518 \(\pm\) 0.00032 & 0.01126 \(\pm\) 0.00019 \\  & LOWESS & 0.03211 \(\pm\) 0.00105 & 0.02256 \(\pm\) 0.00069 & 0.01920 \(\pm\) 0.00056 \\  & PHGA & **0.02309**\(\pm\) 0.00089 & **0.00812**\(\pm\) 0.00033 & **0.00395**\(\pm\) 0.00071 \\ \hline
3 & CSSPL & 0.19089 \(\pm\) 0.00798 & **0.05298**\(\pm\) 0.00202 & 0.02970 \(\pm\) 0.00123 \\  & FCF & 0.23621 \(\pm\) 0.00941 & 0.07756 \(\pm\) 0.00265 & 0.04553 \(\pm\) 0.00139 \\  & LOWESS & **0.15365**\(\pm\) 0.00670 & 0.06323 \(\pm\) 0.00193 & 0.04921 \(\pm\) 0.00171 \\  & PHGA & 0.16749 \(\pm\) 0.00634 & 0.05770 \(\pm\) 0.00204 & **0.02885**\(\pm\) 0.00111 \\ \hline
4 & CSSPL & 0.29770 \(\pm\) 0.00717 & 0.21205 \(\pm\) 0.00352 & 0.02169 \(\pm\) 0.00101 \\  & FCF & 0.29902 \(\pm\) 0.00699 & 0.21747 \(\pm\) 0.00339 & 0.05238 \(\pm\) 0.00106 \\  & LOWESS & 0.24966 \(\pm\) 0.00628 & 0.20666 \(\pm\) 0.00314 & 0.05582 \(\pm\) 0.00217 \\  & PHGA & **0.21344**\(\pm\) 0.00626 & **0.18126**\(\pm\) 0.00403 & **0.01464**\(\pm\) 0.00092 \\ \hline
5 & CSSPL & 0.09322 \(\pm\) 0.00365 & **0.02750**\(\pm\) 0.00094 & **0.01376**\(\pm\) 0.00050 \\  & FCF & 0.10835 \(\pm\) 0.00430 & 0.04187 \(\pm\) 0.00104 & 0.02868 \(\pm\) 0.00068 \\  & LOWESS & 0.08719 \(\pm\) 0.00339 & 0.05131 \(\pm\) 0.00173 & 0.04007 \(\pm\) 0.00143 \\  & PHGA & **0.07993**\(\pm\) 0.00270 & 0.02758 \(\pm\) 0.00084 & 0.01436 \(\pm\) 0.00039 \\ \hline
6 & CSSPL & 0.01011 \(\pm\) 0.00029 & 0.00349 \(\pm\) 0.00015 & 0.00228 \(\pm\) 0.00023 \\  & FCF & 0.01301 \(\pm\) 0.00030 & 0.00889 \(\pm\) 0.00014 & 0.00827 \(\pm\) 0.00029 \\  & LOWESS & 0.01288 \(\pm\) 0.00032 & 0.01151 \(\pm\) 0.00028 & 0.01150 \(\pm\) 0.00033 \\  & PHGA & **0.00507**\(\pm\) 0.00024 & **0.00166**\(\pm\) 0.00008 & **0.00111**\(\pm\) 0.00007 \\ \hline \end{tabular}
\end{table} 
Table 4: Mean of the computed mean square errors (MSEs) with estimated standard errors based on 100 test sets with 100 samples. slightly less dispersed. For function 6, PHGA shows better performance due to the third quartile from PHGA was lower than first quartile from CSSPL, and the performance of FCF and LOWESS was too high compared to the other alternatives. For the results obtained with SNR = 2, showing in Figure 5, we can see that function 1 shows better performance than the other methods covered in this work, the third quartile of PHGA boxplot was similar to mean of CSSPL and FCF methods, and third quartile of PHGA was lower then first quartile than LOWESS. For function 2, PHGA and CSSPL had similar performance and better than FCF and LOWESS, due to results of third quartile from PHGA and CSSPL were below of first quartile of FCF and LOWESS. In function 3, the four methods had similar performance, being CSSPL who had the best performance which was slightly better than PHGA and LOWESS, and FCF had the worst result. For function 4, PHGA had better performance and the others methods had similar performance. In function 5, the best performance was obtained for CSSPL slightly better than PHGA, in this case it is important to emphasize that the difference between PHGA and CSSPL was very small and PHGA had a smaller dispersion of the error. Finally for function 6, PHGA was far superior to the other methods. Figure 4: Boxplots of the mean squared error (MSE) computed for each algorithm per function, using 100 test sets, 100 scattered points(x,y) and signal to noise ratio (SNR) = 3.