# DMFO-CD: A Discrete Meth-Flame Optimization Algorithm for Community Detection
## 5 Experimental Evaluation
### Performance Evaluation  
In this subsection, the performance of the proposed DMFO-CD algorithm was experimentally evaluated, and the experimental results were compared with comparative algorithms. As shown in Table 1, the parameter settings of all comparative algorithms were considered the same as suggested values in their original works. All algorithms were evaluated to detect the communities of network dataset using 30 independent runs, except email-Eu and dblp network that were evaluated by using 10 runs; in each run, the maximum number of iterations (MaxIter) was set by 100. Similar to previous works [61] the population number (N) for karate, email-Eu, dblp, dolphins, all webkbs, adjnoun, football, and polbooks datasets were set by 100, 100, 100, 200, 200, 200, 400, and 400, respectively. The average modularity (\(Q_{avg}\)), the standard deviation of modularity (\(Q_{std}\)), the optimal modularity (\(Q_{max}\)), the average NMI (\(NMI_{avg}\)), and the number of detected communities (\(C_{number}\)) are used to report. The reported results are shown in Tables 2 and 3, in which the best-obtained values are remarked in boldface. \begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{2}{c}{**Algorithms**} & \multicolumn{2}{c}{**Parameter Settings**} \\ \hline DPSO-PDM & r = [0,1], c1, c2 = 2, \(\omega_{\text{max}}\) = 0.8, \(\omega_{\text{min}}\) = 0.6, pm = 0.2 \\ GA-Net & pm = 0.2, pc = 0.8, r = 1.5 \\ GACD & pm = 0.2, pc = 0.8 \\ EGACD & pm = 0.2, pc = 0.8 \\ DECS & pm = 0.2, pmi = 0.5, pmu-mi = 0.5, iter\({}_{\text{m}}\) = 5 \\ DMFO-1.5 \(\omega_{\text{min}}\) = 0.2 \(\omega_{\text{min}}\) = 0. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Network** & **Index** & **DPSO-PDM** & **GA-Net** & **GACD** & **EGACD** & **DECS** & **DMFO-CD** \\ \hline \multirow{3}{*}{Polbooks} & Q\({}_{\text{avg}}\) & \(5.26\times 10^{-1}\) & \(4.63\times 10^{-1}\) & \(5.15\times 10^{-1}\) & \(5.22\times 10^{-1}\) & \(5.20\times 10^{-1}\) & \(\mathbf{5.27\times 10^{-1}}\) \\ \cline{2-7}  & Q\({}_{\text{std}}\) & \(1.22\times 10^{-4}\) & \(2.05\times 10^{-2}\) & \(9.94\times 10^{-3}\) & \(5.08\times 10^{-3}\) & \(4.52\times 10^{-3}\) & \(1.08\times 10^{-4}\) \\ \cline{2-7}  & Q\({}_{\text{max}}\) & \(5.27\times 10^{-1}\) & \(4.93\times 10^{-1}\) & \(5.26\times 10^{-1}\) & \(5.26\times 10^{-1}\) & \(5.27\times 10^{-1}\) \\ \hline \multirow{3}{*}{WebKB-Cornell} & Q\({}_{\text{avg}}\) & \(6.24\times 10^{-1}\) & \(5.32\times 10^{-1}\) & \(6.45\times 10^{-1}\) & \(6.41\times 10^{-1}\) & \(5.97\times 10^{-1}\) & \(\mathbf{6.46\times 10^{-1}}\) \\ \cline{2-7}  & Q\({}_{\text{std}}\) & \(7.10\times 10^{-3}\) & \(8.16\times 10^{-3}\) & \(2.20\times 10^{-3}\) & \(3.12\times 10^{-3}\) & \(7.88\times 10^{-3}\) & \(1.03\times 10^{-3}\) \\ \cline{2-7}  & Q\({}_{\text{max}}\) & \(6.37\times 10^{-1}\) & \(5.47\times 10^{-1}\) & \(6.48\times 10^{-1}\) & \(6.44\times 10^{-1}\) & \(6.11\times 10^{-1}\) & \(6.48\times 10^{-1}\) \\ \hline \multirow{3}{*}{WebKB-Texas} & Q\({}_{\text{avg}}\) & \(3.57\times 10^{-1}\) & \(4.54\times 10^{-1}\) & \(\mathbf{5.57\times 10^{-1}}\) & \(5.52\times 10^{-1}\) & \(4.25\times 10^{-1}\) & \(5.47\times 10^{-1}\) \\ \cline{2-7}  & Q\({}_{\text{std}}\) & \(1.38\times 10^{-2}\) & \(8.88\times 10^{-3}\) & \(2.29\times 10^{-3}\) & \(2.96\times 10^{-3}\) & \(2.29\times 10^{-2}\) & \(7.82\times 10^{-3}\) \\ \cline{2-7}  & Q\({}_{\text{max}}\) & \(3.92\times 10^{-1}\) & \(4.73\times 10^{-1}\) & \(5.60\times 10^{-1}\) & \(5.57\times 10^{-1}\) & \(4.53\times 10^{-1}\) & \(5.60\times 10^{-1}\) \\ \hline \multirow{3}{*}{WebKB-Washington} & Q\({}_{\text{avg}}\) & \(3.63\times 10^{-1}\) & \(4.42\times 10^{-1}\) & \(\mathbf{5.69\times 10^{-1}}\) & \(5.59\times 10^{-1}\) & \(4.11\times 10^{-1}\) & \(\mathbf{5.69\times 10^{-1}}\) \\ \cline{2-7}  & Q\({}_{\text{std}}\) & \(1.88\times 10^{-2}\) & \(8.39\times 10^{-3}\) & \(3.73  
Table 2 and Figure 10 show the obtained modularity by DMFO-CD and comparative algorithms on eleven datasets.