# Co-Operative Binary Bat Optimizer with Rough Set Reducts for Text Feature Selection
## 5 Results and Discussion
### Internal Evaluation
#### 5.1.3 Statistical Test
The population quality in certain generations (1, 20, 50, 80, 100) is calculated and recorded for 32 different runs in BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) for each dataset. Table 4 shows the results of the \(t\)-test which is conducted for average population quality that are obtained using BBA\({}_{\text{LHS}}\) and BBA\({}_{\text{CO}}\) on the Reuters and WebKB datasets. Table 4 shows that the average population quality in the early stages of the search process (i.e., generation 1 and 20) is significantly better with BBA\({}_{\text{LHS}}\) in both datasets. By the second half of the search process (i.e., generation 50) the average population quality with BBA\({}_{\text{CO}}\) improved and statistically outperformed the quality with BBA\({}_{\text{LHS}}\), in the Reuters dataset. In WebKB, the average population quality obtained by BBA\({}_{\text{CO}}\) statistically outperformed the quality obtained by BBA\({}_{\text{LHS}}\) by the last quarter of the search process (i.e., generation 80). In both datasets, the quality of the population in the end of search process is statistically better with BBA\({}_{\text{CO}}\) than BBA\({}_{\text{LHS}}\). From the results of the statistical test, it is clear that the population with BBA\({}_{\text{CO}}\) improves more slowly than that of BBA\({}_{\text{LHS}}\). However, the population with BBA\({}_{\text{CO}}\) converges with better quality than that of BBA\({}_{\text{LHS}}\). The reason behind the slow improvement of the population with BBA\({}_{\text{CO}}\) is the controlling of diversity by the cooperative coevolving strategy. In this way, the algorithm is allowed to continue exploring a wider range of the search space, which significantly improves the final solution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & \multicolumn{2}{c}{**Reuters**} & \multicolumn{2}{c}{**WebKB**} \\ \hline
**Method** & \(\text{BBA}_{\text{CO}}\) & \(\text{BBA}_{\text{LHS}}\) & \(\text{BBA}_{\text{CO}}\) & \(\text{BBA}_{\text{LHS}}\) \\ \hline \multicolumn{5}{c}{generation 1} \\ \hline Mean & 0.16 & 0.14 & 0.14 & 0.13 \\ \(p\)-Value & 0.13 & 0.36 & 0.74 & 0.29 \\ \(t\) State & 3.75 & & 4.38 \\ \(t\) Critical two-tail & 2.00 & & 2.01 \\ \hline \multicolumn{5}{c}{generation 20} \\ \hline Mean & 0.15 & 0.12 & 0.14 & 0.13 \\ \(p\)-Value & 0.58 & 0.16 & 0.36 & 0.12 \\ \(t\) State & 13.96 & & 1.94 \\ \(t\) Critical two-tail & 2.03 & & 2.01 \\ \hline \multicolumn{5}{c}{generation 50} \\ \hline Mean & 0.14 & 0.08 & 0.11 & 0.09 \\ \(p\)-Value & 0.12 & 0.18 & 0.53 & 0.13 \\ \(t\) State & 7.93 & & 3.61 \\ \(t\) Critical two-tail & 2.01 & & 2.00 \\ \hline \multicolumn{5}{c}{generation 80} \\ \hline Mean & 0.12 & 0.06 & 0.09 & 0.08 \\ \(p\)-Value & 0.20 & 0.29 & 0.18 & 0.08 \\ \(t\) State & 15.67 & & 2.98 \\ \(t\) Critical two-tail & 2.01 & & 2.00 \\ \hline \multicolumn{5}{c}{generation 100} \\ \hline Mean & 0.10 & 0.05 & 0.07 & 0.06 \\ \(p\)-Value & 0.17 & 0.13 & 0.09 & 0.07 \\ \(t\) State & 11.72 & & 2.24 \\ \(t\) Critical two-tail & 2.01 & & 2.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The \(t\)-test of standard deviation of population in different generations using BBA\({}_{\text{CO}}\) and BBA\({}_{\text{LHS}}\). The relative errors include Best Relative Error (BRE), Worst Relative Error (WRE) and Average Relative Error (ARE). BRE, WRE and ARE can be used to measure how far the distance between the best and worst solutions and the average quality of the population from the best-known quality that could be achieved by the solution. Whenever the error rate of a solution decreases, the solution becomes closer to the optimum solution. BRE, WRE and ARE have been used to compare BBA\({}_{\text{CO}}\) with BBA\({}_{\text{LHS}}\) in certain generations (i.e., 1, 20, 50, 80, 100).