# Distributed Global Function Model Finding for Wireless Sensor Network Data
## 6 Comparative Analysis
In Figure 6, it is shown that for _LOPEX93, EUNITE, GSADD and DLS_ datasets, compared with ACO, SA, GP, GA and GEP, average number of convergence generation for FF-GEP drops by 11.44%, 14.31%, 21.53% and 19.82%. This is mainly because, in FF-GEP, adaptive population generation strategy based on collaborative evolution of sub-population is applied to dynamically increase population size and diversity of individual so as to improve the probability of the global optimal solution and convergence speed. In Table 2, it is shown that for _LOPEX93, EUNITE, GSADD and DLS_ datasets, compared with ACO, SA, GP, GA and GEP, value of \(R^{2}\) based on FF-GEP increases by 11.62%, 7.04%, 19.45% and 15.04%, respectively; and by Definition 5, value of \(R^{2}\) based on FF-GEP is 0.9381, 0.9575, 0.8686 and 0.9097, respectively. It means that function model for all test datasets based on FF-GEP is best and can fit sample data well. From Figure 7, using FF-GEP, we can see that for _LOPEX93, EUNITE, GSADD and DLS_ dataset, the maximum error between real value and model value is 1.1804, 0.9135, 0.9639 and 0.9515, respectively, and the minimum error is 0.0007, 0.0071, 0.0114 and 0.0251, respectively. It can be seen that the model has high prediction accuracy. **Example 2:** In order to better evaluate performance of algorithm, Example 2 focuses on comparison of average time-consumption and fitting degree between real value and model value. Figure 8 shows average time-consumption of ACO, SA, GP, GA, GEP and FF-GEP. Average time-consumption of DGFMF-WSND with the increase of number of computing nodes is shown in Figure 9. Comparison of value of \(R^{2}\) for LOPEX 93, EUNITE, GSADD and DLS datasets with the increase of number of computing nodes is shown in Figure 10. Figure 11 shows fitting degree between model value and real value of four test datasets in Table 1 based on DGFMF-WSND on six computing nodes. From Figure 8, we know that for _LOPEX93, EUNITE, GSADD_ and _DLS_ datasets, compared with ACO, average time-consumption of FF-GEP drops by 51.57%, 44.3%, 70.05% and 65.03%, respectively, compared with SA, average time-consumption of FF-GEP drops by 51.84%, 44.5%, 70.29% and 63.89%, respectively, and compared with GEP, average time-consumption of FF-GEP drops by 26.01%, 4.34%, 58.03% and 42.7%, respectively, in contrast to GP, decreases by 52.03%, 43.58%, 70.57% and 65.38%, respectively. While for _LOPEX93, EUNITE, GSADD_ and _DLS_, average time-consumption of FF-GEP drops by 50.54%, 37.48%, 66.36% and 63.2% respectively in contrast to GA. This means that for _LOPEX93, EUNITE, GSADD_ and _DLS_, FF-GEP outperforms all other algorithms on average time-consumption, followed by GEP. Especially, for _GSADD_ dataset, average time-consumption of FF-GEP declines most quickly, and while, for _EUNITE_ dataset, average time-consumption of FF-GEP declines most slowly. This is mainly because that compared with the other datasets, number of attributes of _GSADD_ dataset is maximum, and number of attributes and instances of _EUNITE_ dataset is minimum. Meanwhile, FF-GEP adopts adaptive population generation strategy based on  
Figure 8: Comparison of average time-consumption of ACO (Ant Colony Optimization), SA(Simulated Annealing), genetic programming (GP), genetic algorithm (GA), gene expression programming (GEP) and function finding algorithm using gene expression programming (FF-GEP) for four datasets. Figure 9: Comparison of average time-consumption of DGFMF-WSND for four datasets with the increase of number of computing nodes. collaborative evolution of sub-population to increase convergence speed. Figure 9 shows that with the increasing of number of computing nodes, average time-consumption of DGFMF-WSND drops gradually for _LOPEX93_, _EUNITE_, _GSADD_ and _DLS_ datasets. However, when number of computing nodes is increased from 7 to 10, average time-consumption of DGFMF-WSND will increase for all test datasets.