## 5 Computational Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Input**} & \multicolumn{6}{c}{**Fitness value**} & \multicolumn{6}{c}{**Execution Time**} & \multirow{2}{*}{**Success**} \\ \cline{2-2} \cline{4-9}
**instance** & **Best** & **Worst** & **Average** & **STD** & **CV (\%)** & **Best** & **Worst** & **Average** & **STD** & **Rate** \\ \hline Valouxis-1 & 20 & 120 & 73.33 & 30.55 & 41.7 & 17.64 s & 222.88 s & 90.19 s & 75.6 & 20\% \\ BCV3-46.2 & 894 & 894 & 894 & 0 & 0 & 16 min & 31 min & 25 min & 4.37 & 100\% \\ MUSA & 175 & 175 & 175 & 0 & 0 & 0.12 s & 0.52 s & 0.22 s & 0.13 & 100\% \\ LLR & 301 & 305 & 301.48 & 0.93 & 0.3 & 0.3 s & 5.5 s & 1.85 s & 1.4 & 67\% \\ BCV4-13.1 & 10 & 10 & 10 & 0 & 0 & 3 s & 14.2 s & 7.1 s & 0.7 & 100\% \\ WHPP & 5 & 5 & 5 & 0 & 0 & 9.1 s & 27.2 s & 16.2 s & 5.9 & 100\% \\ HED01 & 129 & 156 & 143.28 & 7.88 & 5.5 & 29.1 s & 5 min, 40 s & 2 min, 47 s & 2.13 & 6\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Computational experiments demonstrating the efficiency, stability and homogeneity of the proposed algorithm. STD, standard deviation; CV, coefficient of variation. Figure 8: Convergence behavior of the proposed algorithm for four input instances: (**a**) Input instance, MUSA; (**b**) Input instance, LLR; (**c**) Input instance, BCV4-13.1; (**d**) Input instance HED01. Figure 8: _Cont._  
As shown in Table 7, setting the value of swapping probability equal to 0.99995 assists the algorithm in achieving both the lowest best fitness value and the highest success rate. In Tables 8-10, experimental results that investigate the effect of parameter setting to algorithms' performance and behavior regarding input instance BCV3-46.2 are presented. As shown in Table 8, setting the first phase's number of cycles equal to 1 assists the algorithm in achieving the lowest best and average fitness values in the lowest best and average execution times, respectively. Except for that, if we do not use the first phase at all (first phase cycles = 0), execution times are rather worse. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Input instance** & \multicolumn{5}{c}{**Fitness value**} & \multicolumn{5}{c}{**Execution time (s)**} & \multicolumn{2}{c}{**Success**} \\
**Valouxis-1** & **Best** & **Worst** & **Average** & **STD** & **CV (\%)** & **Best** & **Worst** & **Average** & **STD** & **rate** \\ \hline POPSIZE = 1 & 60 & 140 & 88 & 30.11 & 34.21 & 61 & 180 & 130 & 36 & 30\% \\ POPSIZE = 2 & 20 & 120 & 73.33 & 30.55 & 41.7 & 17.64 & 222.88 & 90.19 & 75.6 & 20\% \\ POPSIZE = 3 & 60 & 160 & 83 & 34.01 & 40.97 & 62 & 246 & 135 & 57.3 & 30\% \\ POPSIZE = 4 & 60 & 140 & 100 & 28.28 & 28.28 & 72 & 222.9 & 140 & 55 & 10\% \\ POPSIZE = 5 & 60 & 100 & 84 & 20.66 & 24.59 & 80 & 200 & 150 & 62 & 30\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Investigating the effect of population size for input instance, Valouxis-1. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Input instance** & \multicolumn{5}{c}{**Fitness value**} & \multicolumn{5}{c}{**Execution time (s)**} & \multicolumn{2}{c}{**Success**} \\
**Valouxis-1** & **Best** & **Worst** & **Average** & **STD** & **CV (\%)** & **Best** & **Worst** & **Average** & **STD** & **rate** \\ \hline Swapping probability & 40 & 120 & 82 & 25.73 & 31.37 & 100 & 190 & 150 & 33 & 10\% \\ \(=0.85\) & & & & & & & & & & \\ Swapping probability & 20 & 160 & 76 & 40.88 & 53.78 & 80 & 200 & 112 & 38.4 & 10\% \\ Swapping probability & 40 & 100 & 68 & 19.32 & 28.41 & 66 & 253 & 129 & 60.9 & 20\% \\ Swapping probability & 20 & 100 & 60 & 24.94 & 41.56 & 18 & 93.6 & 71 & 39.24 & 10\% \\ Swapping probability & 20 & 120 & 73.33 & 30.55 & 41.7 & 17.64 & 222.88 & 90.19 & 75.6 & 20\% \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Investigating the effect of swapping probability for input instance, Valouxis-1.