# Efficient Feature Selection Using Weighted Superposition Attraction Optimization Algorithm
## 3 Results and Discussion
### Performance of the Metaheuristic on the Real-World Datasets
For all the datasets combined, the algorithms are ranked in terms of the best feature reduction as MPA > WSA > SOS > GA (T) > GA (R) > PSO > FPA > MRFO > DE. In terms of repeated trials of 20 independent evaluations (Table 10), the algorithms are ranked as SOS > MPA > GA (T) > GA (R) > WSA > PSO > FPA > DE > MRFO. \begin{table}
\begin{tabular}{l l l l l l l l l l} \hline
**Dataset** & **DE** & **GA (R)** & **GA (T)** & **PSO** & **FPA** & **SOS** & **MPA** & **MRFO** & **WSA** \\ \hline Heart & 37.67 & 60.41 & 62.8 & 37.34 & 41.35 & 130.76 & 74.69 & 68.33 & 38.59 \\  & (0.62) & (2.35) & (5.57) & (0.23) & (5.03) & (4.1) & (2.17) & (1.93) & (2.44) \\ Ionosphere & 4.97 & 15.37 & 15.85 & 9.4 & 5.05 & 19.48 & 10.29 & 8.71 & 5.62 \\  & (0.11) & (0.9) & (0.63) & (0.2) & (0.1) & (0.81) & (0.36) & (0.32) & (0.1) \\ German & 63.37 & 138.45 & 154.66 & 96.22 & 46.88 & 183.47 & 89.79 & 78.52 & 46.01 \\  & (29.87) & (10.19) & (5.76) & (1.04) & (0.71) & (11.72) & (2.52) & (2.36) & (0.92) \\ Breast & 43.33 & 69.46 & 67.98 & 43.26 & 38.24 & 142.41 & 76.91 & 64.25 & 48 \\  & (0.96) & (6.36) & (3.03) & (0.93) & (0.27) & (4.31) & (1.78) & (2.11) & (2.63) \\ Sonar & 32.96 & 58.05 & 55.76 & 33.3 & 32.63 & 132.15 & 66.85 & 56.81 & 34.78 \\  & (0.1) & (1.22) & (1.05) & (1.2) & (0.11) & (1.64) & (0.87) & (0.58) & (0.25) \\ Ovarian & 131.01 & 142.65 & 138.86 & 123.76 & 103.8 & 168.66 & 90.99 & 91.38 & 217.57 \\  & (3.26) & (3.87) & (1.46) & (1.4) & (0.42) & (9.57) & (7.2) & (7.58) & (82.28) \\ Australian & 39.88 & 62.9 & 62.87 & 39.64 & 40.54 & 147.99 & 78.32 & 68.75 & 39.71 \\  & (1.03) & (1.76) & (0.6) & (1.79) & (2.29) & (7.3) & (0.81) & (9.5) & (2.51) \\ Colon & 39.07 & 57.78 & 57.14 & 48.27 & 37.8 & 121.52 & 67.78 & 55.4 & 42.31 \\  & (0.59) & (1.11) & (0.43) & (0.18) & (0.09) & (8.99) & (0.21) & (1.89) & (0.22) \\ Diabetes & 88.07 & 139.5 & 138.37 & 86.84 & 83.91 & 334.15 & 75.12 & 64.34 & 40.15 \\  & (2.02) & (4.17) & (7.08) & (3.4) & (3.36) & (7.5) & (1.27) & (1.14) & (0.34) \\ \hline Av. Rank (mean) & 3.00 & 6.78 & 6.33 & 3.44 & 2.44 & 8.89 & 6.11 & 4.67 & 3.33 \\ \hline Av. Rank (SD) & 3.89 & 6.78 & 5.78 & 3.56 & 3.00 & 8.22 & 4.22 & 5.22 & 4.33 \\ \hline Combined av. rank & 3.44 & 6.78 & 6.06 & 3.50 & 2.72 & 8.56 & 5.17 & 4.94 & 3.83 \\ \hline \end{tabular}
\end{table} 
Table 8: Mean (and standard deviation) of computational time achieved by each algorithm for each dataset in repeated trials. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline
**Dataset** & **DE** & **GA (R)** & **GA (T)** & **PSO** & **FPA** & **SOS** & **MPA** & **MRFO** & **WSA** \\ \hline Heart & 4 & 3 & 3 & 3 & 3 & 3 & 3 & **2** & 3 \\ Ionosphere & 12 & 6 & 7 & 10 & 11 & **2** & 3 & 10 & 3 \\ German & 12 & 9 & 8 & 11 & 9 & 7 & **6** & 10 & 7 \\ Breast & **2** & 3 & 3 & 3 & 3 & 3 & **2** & 3 & **2** \\ Sonar & 26 & 10 & 10 & 12 & 19 & **6** & **6** & 23 & 9 \\ Ovarian & 2014 & 1326 & 1294 & 1805 & 1888 & **2** & 5 & 1944 & 44 \\ Australian & 3 & **1** & **1** & 3 & 3 & 4 & 2 & 7 & **1** \\ Colon & 951 & 526 & 484 & 791 & 912 & **1** & **1** & 942 & 2 \\ Diabetes & 4 & 3 & 3 & **2** & 3 & 4 & 3 & 4 & **2** \\ \hline Average rank & 7.78 & 4.67 & 4.39 & 5.72 & 6.28 & 3.89 & 2.67 & 6.89 & 2.72 \\ \hline \end{tabular}
\end{table} 
Table 9: Least features selected by each algorithm for each dataset.