# Dual-Neighborhood Tabu Search for Computing Stable Extensions in Abstract Argumentation Frameworks
## 6 Discussion and Analysis
### The Importance of Initializing Solutions
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**DNTS**} & \multicolumn{3}{c}{**DNTS-OUT**} \\ \hline
**Group** & **Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline  & v500\_1 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 \\  & v500\_2 & 0.12 & 0.12 & 0.12 & 0.17 & 0.17 & 0.17 \\  & v500\_3 & 0.07 & 0.12 & 0.09 & 0.12 & 0.12 & 0.12 \\  & v500\_4 & 0.07 & 0.07 & 0.07 & 0.12 & 0.12 & 0.12 \\ vertex\_500 & v500\_5 & 0.12 & 0.12 & 0.12 & 0.17 & 0.17 & 0.17 \\  & v500\_6 & 0.12 & 0.12 & 0.12 & 0.12 & 0.17 & 0.16 \\  & v500\_7 & 0.07 & 0.12 & 0.11 & 0.12 & 0.17 & 0.14 \\  & v500\_8 & 0.07 & 0.12 & 0.08 & 0.12 & 0.12 & 0.12 \\  & v500\_9 & 0.07 & 0.12 & 0.08 & 0.12 & 0.12 & 0.12 \\  & v500\_10 & 0.07 & 0.12 & 0.09 & 0.12 & 0.12 & 0.12 \\ \hline  & v1000\_1 & 0.42 & 1.04 & 0.55 & 0.68 & 0.73 & 0.7 \\  & v1000\_2 & 0.42 & 2.66 & 0.88 & 0.68 & 0.83 & 0.75 \\  & v1000\_3 & 0.42 & 0.53 & 0.46 & 0.98 & 1.19 & 1.04 \\  & v1000\_4 & 0.32 & 0.53 & 0.40 & 0.48 & 0.58 & 0.53 \\ vertex\_1000 & v1000\_5 & 0.53 & 6.12 & 1.98 & 0.98 & 2.1 & 1.47 \\ v1000\_6 & 0.37 & 0.43 & 0.40 & 0.63 & 1.75 & 0.88 \\  & v1000\_7 & 0.42 & 0.58 & 0.49 & 0.68 & 0.73 & 0.71 \\  & v1000\_8 & 0.83 & 6.06 & 2.24 & 1.09 & 1.85 & 1.48 \\  & v1000\_9 & 0.32 & 1.14 & 0.53 & 0.37 & 3.88 & 2.46 \\  & v1000\_10 & 0.37 & 1.65 & 0.66 & 0.48 & 0.53 & 0.51 \\ \hline  & v2000\_1 & 9.17 & 37.30 & 19.15 & 55.00 & 151.85 & 103.30 \\  & v2000\_2 & 20.83 & 39.49 & 28.35 & 34.10 & 188.72 & 88.81 \\  & v2000\_3 & 3.83 & 5.61 & 5.04 & 17.26 & 22.55 & 19.65 \\  & v2000\_4 & 2.97 & 4.14 & 3.80 & 4.85 & 9.73 & 7.39 \\ vertex\_2000 & v2000\_5 & 3.12 & 5.16 & 3.91 & 19.55 & 23.82 & 20.76 \\  & v2000\_6 & 2.21 & 2.41 & 2.30 & 2.51 & 3.07 & 2.79 \\  & v2000\_7 & 2.51 & 2.71 & 2.61 & 5.21 & 7.65 & 6.23 \\  & v2000\_8 & 21.33 & 66.75 & 45.77 & 176.36 & 374.11 & 291.23 \\  & v2000\_9 & 4.90 & 6.53 & 5.82 & 17.72 & 24.18 & 20.88 \\  & v2000\_10 & 2.31 & 2.46 & 2.41 & 4.95 & 6.73 & 5.79 \\ \hline  & v3000\_1 & 4.95 & 6.78 & 5.98 & 7.49 & 9.02 & 8.56 \\  & v3000\_2 & 6.43 & 8.82 & 7.12 & 26.67 & 30.13 & 28.32 \\  & v3000\_3 & 8.21 & 24.28 & 13.56 & 54.70 & 69.09 & 59.55 \\  & v3000\_4 & 9.43 & 14.52 & 11.09 & 83.03 & 87.70 & 84.60 \\  & v3000\_5 & 13.75 & 78.64 & 42.33 & 139.24 & 150.02 & 143.93 \\  & v3000\_6 & 6.28 & 11.36 & 8.36 & 26.83 & 29.82 & 28.31 \\  & v3000\_7 & 8.36 & 9.84 & 8.88 & 24.23 & 31.05 & 28.40 \\  & v3000\_8 & 6.53 & 10.65 & 8.85 & 27.69 & 37.25 & 29.77 \\  & v3000\_9 & 12.12 & 16.55 & 14.16 & 108.18 & 120.71 & 117.22 \\  & v3000\_10 & 11.11 & 114.46 & 44.33 & 100.17 & 119.29 & 106.65 \\ \hline  & v4000\_1 & 19.70 & 27.79 & 23.40 & 155.34 & 173.01 & 162.97 \\  & v4000\_2 & 23.87 & 76.72 & 42.90 & 184.01 & 262.12 & 206.70 \\  & v4000\_3 & 35.22 & 169.90 & 77.79 & 309.48 & 600.00 & 405.81 \\  & v4000\_4 & 16.95 & 24.94 & 19.55 & 85.26 & 95.58 & 88.29 \\ vertex\_4000 & v4000\_5 & 19.96 & 30.18 & 24.49 & 150.98 & 182.36 & 162.84 \\  & v4000\_6 & 35.67 & 73.36 & 49.53 & 321.31 & 380.52 & 347.62 \\  & v4000\_7 & 27.84 & 58.36 & 39.37 & 246.75 & 269.32 & 257.73 \\  & v4000\_8 & 24.13 & 35.47 & 30.25 & 223.92 & 232.01 & 226.24 \\  & v4000\_9 & 25.40 & 35.93 & 29.72 & 237.76 & 246.97 & 241.41 \\  & v4000\_10 & 27.08 & 62.94 & 43.40 & 310.87 & 386.32 & 346.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of different initialization solutions. We use the same 200 instances as Section 5.2.2. The experimental results in Table 9 show that, for smaller-sized instances, both algorithms can successfully solve 50 instances. However, when facing the larger size instances of 3000 and 4000 arguments, both algorithms fail or time out, but the DNTS algorithm is still able to successfully solve more instances than DNTS-OUT. Combining the above experimental results, the use of the random label initialization strategy shows significant advantages over the initialization approach of marking all labels as out.