# Dual-Neighborhood Tabu Search for Computing Stable Extensions in Abstract Argumentation Frameworks
## 6 Discussion and Analysis
### The Importance of Perturbation Techniques
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & \multicolumn{3}{c}{**DINTS**} & \multicolumn{3}{c}{**DINTS-NP**} \\ \hline
**Group** & **Instance** & **Best** & **Worst** & **Average** & **Best** & **Worst** & **Average** \\ \hline \multirow{9}{*}{vertex\_500} & v500\_1 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 \\  & v500\_2 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 \\  & v500\_3 & 0.07 & 0.12 & 0.09 & 0.07 & 0.12 & 0.1 \\  & v500\_4 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 & 0.07 \\  & v500\_5 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 \\  & v500\_6 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 & 0.12 \\  & v500\_7 & 0.07 & 0.12 & 0.11 & 0.12 & 0.12 & 0.12 \\  & v500\_8 & 0.07 & 0.07 & 0.08 & 0.07 & 0.07 & 0.07 \\  & v500\_9 & 0.07 & 0.12 & 0.08 & 0.07 & 0.12 & 0.08 \\  & v500\_10 & 0.07 & 0.12 & 0.09 & 0.07 & 0.12 & 0.09 \\ \hline \multirow{9}{*}{vertex\_1000} & v1000\_1 & 0.42 & 1.04 & 0.55 & 0.37 & 0.43 & 0.4 \\  & v1000\_2 & 0.42 & 2.66 & 0.88 & 0.37 & 0.53 & 0.45 \\  & v1000\_3 & 0.42 & 0.53 & 0.46 & 0.42 & 0.60 & 120.36 \\  & v1000\_4 & 0.32 & 0.53 & 0.4 & 0.37 & 0.38 & 0.37 \\  & v1000\_5 & 0.53 & 6.12 & 1.98 & 0.47 & 0.99 & 0.68 \\  & v1000\_6 & 0.37 & 0.43 & 0.4 & 0.37 & 0.43 & 0.41 \\  & v1000\_7 & 0.42 & 0.58 & 0.49 & 0.42 & 600 & 120.37 \\  & v1000\_8 & 0.83 & 6.06 & 2.24 & 0.58 & 2.26 & 1.22 \\  & v1000\_9 & 0.32 & 1.14 & 0.53 & 0.32 & 98.03 & 19.88 \\  & v1000\_10 & 0.37 & 1.65 & 0.66 & 0.32 & 527.63 & 105.81 \\ \hline \multirow{9}{*}{vertex\_2000} & v2000\_1 & 9.17 & 37.30 & 19.15 & 21.43 & 600.00 & 153.29 \\  & v2000\_2 & 20.83 & 39.49 & 28.35 & 36.29 & 600.00 & 366.56 \\  & v2000\_3 & 3.83 & 5.61 & 5.04 & 3.32 & 5.01 & 4.18 \\  & v2000\_4 & 2.97 & 4.14 & 3.80 & 3.43 & 6.38 & 5.10 \\  & v2000\_5 & 3.12 & 5.16 & 3.91 & 3.02 & 5.61 & 4.60 \\  & v2000\_6 & 2.21 & 2.41 & 2.30 & 2.10 & 2.61 & 2.39 \\  & v2000\_7 & 2.51 & 2.71 & 2.61 & 2.26 & 3.22 & 2.70 \\  & v2000\_8 & 21.33 & 66.75 & 45.77 & 20.47 & 600.00 & 152.72 \\  & v2000\_9 & 4.90 & 6.53 & 5.82 & 3.37 & 4.49 & 3.87 \\  & v2000\_10 & 2.31 & 2.46 & 2.41 & 2.10 & 2.82 & 2.46 \\ \hline \multirow{9}{*}{vertex\_3000} & v3000\_1 & 4.95 & 6.78 & 5.98 & 5.51 & 6.37 & 5.97 \\  & v3000\_2 & 6.43 & 8.82 & 7.12 & 6.53 & 9.22 & 7.97 \\  & v3000\_3 & 8.21 & 24.28 & 13.56 & 11.06 & 14.16 & 12.09 \\  & v3000\_4 & 9.43 & 14.52 & 11.09 & 9.63 & 16.75 & 13.03 \\  & v3000\_5 & 13.75 & 78.64 & 42.33 & 19.76 & 600.00 & 156.63 \\  & v3000\_6 & 6.28 & 11.36 & 8.36 & 7.49 & 12.83 & 10.34 \\  & v3000\_7 & 8.36 & 9.84 & 8.88 & 9.53 & 15.53 & 12.31 \\  & v3000\_8 & 6.53 & 10.65 & 8.85 & 7.34 & 11.51 & 9.78 \\  & v3000\_9 & 12.12 & 16.55 & 14.16 & 13.70 & 20.78 & 16.61 \\  & v3000\_10 & 11.11 & 114.46 & 44.33 & 25.19 & 42.69 & 33.60 \\ \hline \multirow{9}{*}{vertex\_5000} & v4000\_1 & 19.70 & 27.79 & 23.40 & 24.89 & 30.99 & 27.36 \\  & v4000\_2 & 23.87 & 76.72 & 42.90 & 35.78 & 153.08 & 66.36 \\ \cline{1-1}  & v4000\_3 & 35.22 & 169.90 & 77.79 & 68.02 & 215.63 & 135.98 \\ \cline{1-1}  & v4000\_4 & 16.95 & 24.94 & 19.55 & 20.11 & 32.12 & 24.14 \\ \cline{1-1}  & v4000\_5 & 19.96 & 30.18 & 24.49 & 24.28 & 32.42 & 29.03 \\ \cline{1-1}  & v4000\_6 & 35.67 & 73.36 & 49.53 & 42.18 & 600.00 & 277.31 \\ \cline{1-1}  & v4000\_7 & 27.84 & 58.36 & 39.37 & 44.08 & 62.87 & 48.87 \\ \cline{1-1}  & v4000\_8 & 24.13 & 34.50 & 30.25 & 31.80 & 38.52 & 34.20 \\ \cline{1-1}  & v4000\_9 & 25.40 & 35.93 & 29.72 & 28.91 & 37.10 & 32.72 \\ \cline{1-1}  & v4000\_10 & 27.08 & 62.94 & 43.40 & 34.86 & 52.15 & 42.5 Comprehensive analyses show that DNTS and DNTS-NP perform close to each other in most cases. However, the DNTS-NP algorithm is prone to produce extremely poor results in some instances. This result emphasizes the importance of perturbation techniques in improving the stability of the DNTS algorithm and its ability to escape from locally optimal solutions.