# Parallel Hierarchical Genetic Algorithm for Scattered Data Fitting through B-Splines
## 5 Simulation Results
### Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Islands**} & \multirow{3}{*}{**Size Island**} & \multirow{3}{*}{**Knots**} & \multirow{3}{*}{**Sequential**} & \multicolumn{6}{c}{**Parallel Version**} \\ \cline{5-10}  & & & & \multicolumn{2}{c}{**8 CPUs**} & \multicolumn{2}{c}{**16 CPUs**} & \multicolumn{2}{c}{**32 CPUs**} \\ \cline{5-10}  & & & & **Time** & **Speed-Up** & **Time** & **Speed-Up** & **Time** & **Speed-Up** \\ \hline
10 & 60 & 50 & 31.14 s & 1.55 s & 20.04 & 1.22 s & 25.59 & 1.10 s & 28.19 \\
10 & 60 & 100 & 106.15 s & 3.20 s & 33.19 & 2.67 s & 39.72 & 2.01 s & 52.82 \\
10 & 200 & 50 & 109.21 s & 4.40 s & 24.83 & 3.36 s & 32.50 & 2.82 s & 38.79 \\
20 & 200 & 50 & 216.14 s & 7.67 s & 28.18 & 5.67 s & 38.15 & 4.47 s & 48.33 \\
10 & 200 & 100 & 374.60 s & 9.33 s & 40.14 & 6.97 s & 53.75 & 5.14 s & 72.94 \\
10 & 60 & 200 & 421.54 s & 8.71 s & 48.37 & 7.00 s & 60.24 & 4.84 s & 87.07 \\
20 & 200 & 100 & 753.52 s & 152.27 s & 49.47 & 10.76 s & 70.21 & 8.33 s & 90.62 \\
10 & 200 & 200 & 1562.72 s & 25.78 s & 59.21 & 16.57 s & 92.16 & 12.01 s & 127.17 \\
20 & 200 & 200 & 3046.42 s & 50.27 s & 60.60 & 27.92 s & 109.10 & 20.97 s & 145.30 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Average time execution in seconds and speed-up. Figure 9: Data and best fitting with SNR = 1 for PHGA, CSSPL, FCF and LOWESS methods (solid line: estimated function; dashed line: real function). implemented, under an OpenCL framework, with the aim of reduce the time of processing, exploiting the characteristics of separability and modularity of hierarchical problems and island models. In our experiments we obtained a speed-up from 20 to 145, depending on the amount of data and the number of processors, which represents a significant reduction of execution time with respect to a sequential implementation  
To test our approach, we performed several simulations on six benchmark functions with three leaves of SNRs, which were compared to solutions obtained using CSSPL, FCF and LOWESS methods. Simulation results show that the proposed approach presents better results than CSSPL, FCF and LOWESS method. Although in some cases numerically the results obtained for some function were not favorable, an important aspect to note is that, the difference is very small and the curves fitted using our approach look smoother than those obtained using the CSSPL, FNF and LOWESS method, which in some cases produce over fitted curves. Finally, this paper has focused on smooth curve functions, but we are interested in extending our approach to un-smooth functions and surface fitting, as well as, experiment with other basis functions. Conceptualization, J.E.L.-R., C.H.G.-C. and H.R.-G.; funding acquisition, C.H.G.-C. and H.R.-G.; methodology, J.E.L.-R., J.G.A.-C. and C.H.G.-C.; project administration, M.d.J.E.-A., C.H.G.-C. and H.R.-G.; software, R.E.S.-Y., and J.E.L.-R.; supervision, C.H.G.-C. and H.R.-G.; validation, M.d.J.E.-A., J.E.L.-R. and C.H.G.-C.; writing--review and editing, J.E.L.-R., C.H.G.-C. and H.R.-G.; writing--original draft, and visualization, R.E.S.-Y., J.G.A. [PERSON] and [PERSON]. This research was funded by the CONACYT project FC2016-1961 \"Neurociencia Computacional: de la teoria al desarrollo de sistemas neuromorificos\" and the PRODEP project \"Desarrollo de Tecnicas para Mejorar el Desempeno Computacional de Algoritmos Bio-inspiredos y su Aplicacion en la Solucion de Problemas de Optimizacion\". The authors declare no conflict of interest.