# Efficient Feature Selection Using Weighted Superposition Attraction Optimization Algorithm
## 3 Results and Discussion
### Performance of the Metaheuristic on the Real-World Datasets  
The best fitness value obtained among the 20 independent runs for each algorithm for all the nine datasets is reported in Table 3. The average rank of each algorithm based on its relative performance on all the nine datasets was calculated and is also provided in Table 3. It is worthwhile to mention here that the bold letters symbolize the best solutions achieved. Thus, it can be observed from this table that WSA achieved the best optimal solution in six out of nine datasets. Thus, based on the best fitness value, the algorithms can be ranked as WSA > MPA > GA (T) > MRFO > GA (R) > FPA > PSO > DE > SOS. The mean best fitness and standard deviation values of 20 independent runs for each algorithm are reported in Table 4. A mean best fitness close to the best fitness reported in Table 3 would indicate that an algorithm is constantly able to achieve 'good' results in repeated trials. Moreover, a low standard deviation would mean low variability in the repeated trials. Thus, for a 'high'-performing algorithm, it is desired that the mean best fitness would be close to its best fitness, accompanied by low standard deviation. Such an algorithm can be deemed to be more robust in terms of reproducibility. In terms of the mean best fitness and standard deviation, the algorithms can be ranked as WSA > MPA > MRFO > FPA > GA (R) > GA (T) > DE > PSO > SOS. \begin{table}
\begin{tabular}{l l l} \hline
**Algorithm** & **Parameter** & **Value** \\ \hline \multirow{4}{*}{Common parameters} & \(K\) & 5 \\  & Iteration limit & 200 \\  & Search agents & 30 \\  & Independent runs & 20 \\  & Validation data & 20\% \\ \hline \multirow{2}{*}{DE} & Crossover rate & 0.9 \\  & Constant factor & 0.5 \\ \hline GA (R) & Crossover rate & 0.8 \\  & Mutation rate & 0.01 \\ \hline \multirow{2}{*}{GA (T)} & Crossover rate & 0.8 \\  & Mutation rate & 0.01 \\  & Tournament size & 3 \\ \hline \multirow{2}{*}{PSO} & \(c_{1}\) & 2 \\  & \(c_{2}\) & 2 \\  & \(w\) & 0.9 \\ \hline \multirow{2}{*}{FPA} & Levy component & 1.5 \\  & Switch probability & 0.8 \\ \hline \multirow{4}{*}{MPA} & Levy component & 1.5 \\  & Constant & 0.5 \\  & Fish aggregating devices effect & 0.2 \\ \hline MRFO & Somersault factor & 2 \\ \hline \multirow{4}{*}{WSA} & \(\tau\) & 0.8 \\  & \(\varphi\) & 0.001 \\ \cline{1-1}  & \(\lambda\) & 0.75 \\ \cline{1-1}  & Step length & 0.035 \\ \hline \end{tabular}
\end{table} 
Table 2: Description of tuning parameters used in each algorithm. The convergence curves for all the algorithms for all the datasets under consideration are exhibited in Figure 2. The convergences of WSA and MPA are noticed to be quite rapid, whereas the FPA and PSO algorithms are slightly sluggish. In addition, the trend followed by FPA and PSO is very similar. On the other hand, notable similarity in convergence trends between WSA and MPA is observed. Table 5 presents the best classification accuracy for each dataset as obtained by each of the algorithms. An ideal classification accuracy of 1 would indicate that the algorithm can correctly classify 100% of the instances. With respect to the best classification accuracy, the considered algorithms can be ranked as WSA \(>\) GA (T) \(>\) GA (R) \(>\) DE \(>\) MPA \(\approx\) MRFO \(>\) PSO \(>\) FPA \(>\) SOS. In the case of datasets large numbers of features, such as the Ovarian Cancer dataset (with 4000 features), it is interesting to notice that all the algorithms are able to achieve a 100% classification rate. The mean best classification accuracy and standard deviation of 20 independent runs are provided in Table 6. Based on this table, the algorithms can be graded as WSA \(>\) MPA \(>\) MRFO \(>\) GA (T) \(>\) GA (R) \(>\) FPA \(>\) DE \(>\) PSO \(>\) SOS.