## 6 Combined Algorithm of PSO and ACO
### Restart of the Search Process When It Gets Stuck
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{4}{c}{**Proposed BWAS Algo**} & \multicolumn{4}{c}{**MMAS**} \\ \hline
**Problem** & \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**ACO-PSO**} & \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**ACO-PSO**} \\ \hline  & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** \\ \hline Att48 & 3.2 & 920 & 2.9 & 890 & 3.9 & 999 & 3.3 & 992 \\ \hline Berlin52 & 15.4 & 410 & 14.9 & 388 & 16.2 & 455 & 15.5 & 403 \\ \hline Bier127 & 64.2 & 992 & 63.5 & 802 & 65.5 & 1005 & 64.1 & 920 \\ \hline kroE100 & 21.1 & 126 & 20.4 & 95 & 22.1 & 161 & 21 & 125 \\ \hline Lin105 & 30.5 & 1830 & 29.8 & 1695 & 31.2 & 2020 & 30.8 & 1725 \\ \hline Lin318 & 88.1 & 887 & 79.4 & 795 & 88.9 & 922 & 85.2 & 822 \\ \hline Pr124 & 66.9 & 1980 & 65.2 & 1910 & 67.8 & 2252 & 67.1 & 1920 \\ \hline Pr107 & 31.2 & 235 & 29.9 & 199 & 32.1 & 322 & 30.5 & 225 \\ \hline Ch130 & 75.1 & 159 & 73.8 & 102 & 76.2 & 205 & 74.5 & 155 \\ \hline Ch150 & 80.3 & 21.5 & 78.5 & 19.6 & 81.1 & 25.1 & 80.1 & 205 \\ \hline Ei151 & 80.5 & 9.4 & 78.4 & 9.1 & 81.4 & 10.4 & 79.9 & 94 \\ \hline Ei176 & 68.9 & 0.9 & 67.1 & 0.8 & 69.7 & 1.2 & 68.8 & 0.89 \\ \hline Ei1101 & 30.1 & 219 & 28.2 & 185 & 31.3 & 295 & 30 & 255 \\ \hline kroA100 & 21.3 & 212 & 20.4 & 175 & 22.1 & 289 & 21 & 220 \\ \hline kroC100 & 21.5 & 355 & 20.5 & 302 & 21.9 & 400 & 21 & 355 \\ \hline Pr144 & 78.6 & 958 & 77.9 & 898 & 79.4 & 992 & 78.4 & 958 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mean and standard deviation of Table 2 data. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{1}{c}{} & \multicolumn{4}{c}{**Proposed BWAS Algo**} & \multicolumn{4}{c}{**MMAS**} \\ \hline
**Problem** & \multicolumn{2}{c}{**ACO**} & \multicolumn{2}{c}{**ACO-PSO**} & \multicolumn{2}{c}{**ACO**} & \multicolumn{2}{c}{**ACO-PSO**} \\ \hline  & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** & **Mean** & **STD** \\ \hline Att48 & 3.9 & 1005.2 & 3.1 & 995 & 4.2 & 1009 & 3.9 & 999 \\ \hline Berlin52 & 16.9 & 502.4 & 15.9 & 410 & 17.5 & 520 & 16.5 & 499 \\ \hline Bier127 & 65.4 & 1115.5 & 64.2 & 995 & 67.2 & 1150 & 66 & 1005 \\ \hline kroE100 & 22.1 & 154 & 21.5 & 132 & 22.7 & 166 & 22.3 & 143 \\ \hline Lin105 & 31.9 & 2012 & 30.4 & 169 & 32.5 & 2040 & 31.8 & 201 \\ \hline Lin318 & 89.2 & 906.2 & 88.5 & 808 & 90.6 & 932 & 89.2 & 880 \\ \hline Pr124 & 68.5 & 2126 & 67.4 & 1884 & 69 & 2232 & 68 & 1934 \\ \hline Pr107 & 32.5 & 307 & 30.5 & 268 & 32.9 & 332 & 31.5 & 302 \\ \hline Ch130 & 76.2 & 209.2 & 74.9 & 200 & 76.8 & 235 & 75.5 & 210 \\ \hline Chi150 & 81 & 27.4 & 79.2 & 20.5 & 81.9 & 28.1 & 80.5 & 235 \\ \hline Ei151 & 81 & 10.2 & 79.5 & 8.4 & 82 & 11.2 & 81.2 & 99 \\ \hline Ei176 & 70.2 & 1.10 & 69.1 & 0.8 & 70.9 & 1.25 & 69.8 & 0.99 \\ \hline Ei1101 & 31.5 & 310 & 29.5 & 266 & 32 & 355 & 30.5 & 310 \\ \hline kroA100 & 22.2 & 309 & 21.5 & 275 & 22.8 & 350 & 21.9 & 299 \\ \hline kroC100 & 22.1 & 402 & 21.5 & 311 & 22.4 & 432 & 21.8 & 365 \\ \hline Pr144 & 80 & 1006.4 & 80 & 984 & 80.5 & 1025 & 80.4 & 1012 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean and standard deviation of Table 1 data. Figure 1: (**a**). Best tour Paths for PSO (BWAS); (**b**). Best cost for PSO (BWAS); (**c**). Average node branching for PSO (BWAS). Figure 2: (**a**). Best tour Paths for ACO (BWAS); (**b**). Best cost for ACO (BWAS); (**c**). Average node branching for ACO (BWAS). Figure 3: (**a**). Best tour Paths for ACO-PSO (BWAS); (**b**). Best cost for ACO-PSO (BWAS); (**c**). Average node branching for ACO-PSO (BWAS)

Figure 4: (**a**). Best tour Paths for PSO (MMAS); (**b**). Best cost for PSO (MMAS); (**c**). Average node branching for PSO (MMAS). Figure 5: (**a**). Best tour Paths for ACO (MMAS); (**b**). Best cost for ACO (MMAS); (**c**). Average node branching for ACO (MMAS). Figure 6: (**a**). Best tour Paths for ACO-PSO (MMAS); (**b**). Best cost for ACO-PSO (MMAS); (**c**). Average node branching for ACO-PSO (MMAS).