# Dual-Neighborhood Tabu Search for Computing Stable Extensions in Abstract Argumentation Frameworks
## 5 Experiment
### Algorithm Comparison
#### 5.2.1 Comparison on Algorithm Efficiency
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**DNTS**} & \multicolumn{4}{c}{**HAYWOOD**} & \multicolumn{4}{c}{**u-toksia**} \\ \hline
**Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline V500\_1 & 0.07 & 0.12 & 0.1 & 0.07 & 0.12 & 0.08 & 0.02 & 0.02 & 0.02 \\ V500\_2 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.02 & 0.02 & 0.02 \\ V500\_3 & 0.07 & 0.12 & 0.1 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_4 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_5 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.02 & 0.02 & 0.02 \\ V500\_6 & 0.07 & 0.12 & 0.11 & 0.12 & 0.12 & 0.12 & 0.02 & 0.02 & 0.02 \\ V500\_7 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.02 & 0.02 & 0.02 \\ V500\_8 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_9 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_10 & 0.07 & 0.12 & 0.1 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_11 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.01 & 0.02 & 0.02 \\ V500\_12 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_13 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.02 & 0.02 & 0.02 \\ V500\_14 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.02 & 0.03 & 0.02 \\ V500\_15 & 0.07 & 0.12 & 0.11 & 0.12 & 0.12 & 0.12 & 0.02 & 0.04 & 0.02 \\ V500\_16 & 0.07 & 0.12 & 0.11 & 0.12 & 0.12 & 0.12 & 0.02 & 0.04 & 0.02 \\ V500\_17 & 0.07 & 0.12 & 0.1 & 0.07 & 0.07 & 0.07 & 0.02 & 0.03 & 0.02 \\ V500\_18 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.02 & 0.02 & 0.02 \\ V500\_19 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.01 & 0.02 & 0.02 \\ V500\_20 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.01 & 0.02 & 0.01 \\
**Att** & 0.08 & 0.1 & 0.09 & 0.09 & 0.09 & 0.09 & 0.02 & 0.02 & 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results for instances of 500 vertices. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**DNTS**} & \multicolumn{4}{c}{**HAYWOOD**} & \multicolumn{4}{c}{**u-toksia**} \\ \hline
**Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline V1000\_1 & 0.37 & 0.43 & 0.41 & 0.37 & 0.43 & 0.38 & 0.93 & 1.04 & 0.94 \\ V1000\_2 & 0.37 & 0.48 & 0.42 & 0.37 & 0.38 & 0.37 & 5.92 & 6.07 & 6.02 \\ V1000\_3 & 0.42 & 0.48 & 0.44 & 0.42 & 0.48 & 0.45 & 0.07 & 0.07 & 0.07 \\ V1000\_4 & 0  
Based on the results presented in Table 4, the performance evaluation for random instances generated with 2000 arguments shows that the DNTS algorithm has significantly lower best values than the HAYWOOD and u-toksa algorithms for most instances. It shows that the DNTS algorithm is the fastest for these instances. However, the DNTS algorithm performs poorly in terms of worst values. The DNTS algorithm is better than HAYWOOD and u-toksa in terms of att values of average, indicating that worst values do not occur as frequently. The overall performance of DNTS is similar to that of HAYWOOD in most of the cases, and significantly better than HAYWOOD in V2000_2, V2000_8, V2000_20, and V2000_20. Both of them outperform the u-toksa algorithms in most of the cases in terms of the best and average values, but the performance of worst is not as stable as the u-toksa algorithms. Based on the results presented in Tables 5 and 6, in the performance evaluation for randomly generated instances with 3000 and 4000 arguments, the DNTS algorithm shows a clear advantage in the best values over HAYWOOD and u-toksa in most instances. DNTS exhibits significant fluctuations in its worst values. In terms of average values, DNTS performs similarly to HAYWOOD in most instances but significantly outperforms HAYWOOD in some complex instances with longer solution times (such as V3000_10, V3000_17, V3000_18, V4000_3, V4000_6, V4000_7). The superior performance of DNTS in complex instances results in a better average total time (att), compared with HAYWOOD and u-toksa.