# A Comparative Evaluation of Nature Inspired Algorithms for Telecommunication Network Design
## 5 Results and Discussion
Figure 12: Comparison of the convergence for the USA network of all considered methods: artificial bee colony (BA), evolutionary algorithm (EA), harmony search algorithm (HS) and stochastic hill climbing algorithm (HC). Each curve is an average of 50 independent runs. Further, it is noted that it took more than 6 days for the IP approach to find a solution, which is still further away from the optimum value than the solutions obtained by heuristic algorithms. On average,  
Figure 14: Comparison of the convergence for 50-node the German network of all considered methods: artificial bee colony (BA), evolutionary algorithm (EA), harmony search algorithm (HS) and stochastic hill climbing algorithm (HC). Each curve is an average of 50 independent runs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{5}{c}{**German10**} \\ \cline{2-9}  & \multicolumn{3}{c}{**Solution**} & \multicolumn{3}{c}{**\#Evaluation**} & \multicolumn{3}{c}{**Time [sec.]**} \\ \cline{2-9}  & **Best** & **Mean** & **std. dev.** & **Mean** & **Mean** & **std. dev.** & **Gap [\%]** \\ \hline
**BA** & 152 & 152.63 & 0.48 & 69,992 & 6990.8 & 170.7 & – \\
**EA** & 152 & 152.59 & 0.49 & 21,220 & 2170.0 & 51.0 & – \\
**HS** & 152 & 152.96 & 0.19 & 5293 & 529.18 & 25.86 & – \\
**HC** & 153 & 153.96 & 0.19 & 5226 & 522.18 & 25.86 & – \\
**IP** & **152** & – & – & – & 461.12 & – & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of all considered algorithms for the 10-node German network. Figure 13: Comparison of the convergence for the American network of all considered methods: artificial bee colony (BA), evolutionary algorithm (EA), harmony search algorithm (HS) and stochastic hill climbing algorithm (HC). Each curve is an average of 50 independent runs. it took almost three times less time for the BA algorithm than for IP approach, and almost six times less time was needed by the EA algorithm. This is due to the fact that the iterations of the climbing algorithm are computationally very efficient when compared with other algorithms, e.g., the EA algorithm. Finally, the same amount of time was needed for completing calculations using HS and HC algorithms. In fact, HS and HC algorithms proved to be the fastest among all algorithms tested. However, these algorithms did not find the best solutions, which were provided by BA and EA algorithms. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Method**} & \multicolumn{6}{c}{**German20**} \\ \cline{2-9}  & \multicolumn{3}{c}{**Solution**} & \multicolumn{3}{c}{**\#Evaluation**} & \multicolumn{3}{c}{**Time [sec.]**} \\ \cline{2-9}  & **Best** & **Mean** & **std. dev.** & **Mean** & **Mean** & **std. dev.** & **Gap [\%]** \\ \hline
**BA** & **500** & 502.1 & 0.21 & 55,612 & 5561.0 & 417.7 & – \\
**EA** & 500 & 506.0 & 0.70 & 29,770 & 2870.0 & 20.7 & – \\
**HS** & 501 & 503.7 & 0.4 & 5245 & 524.5 & 47.1 & – \\
**HC** & 501 & 504.0 & 0.3 & 6255 & 625.3 & 562.0 & – \\
**IP** & 500 & – & – & – & 17304.75 & – & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of all considered algorithms for the 20-node German network. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{3}{*}{**Method**} & \multicolumn{6}{c}{**USA**} \\ \cline{2-9}  & \multicolumn{3}{c}{**Solution**} & \multicolumn{3}{c}{**\#Evaluation**} & \multicolumn{3}{c}{**Time [sec.]**} \\ \cline{2-9}  & **Best** & **Mean** & **std. dev.** & **Mean** & **Mean** & **std. dev.** & **Gap [\%]** \\ \hline
**BA** & **1846** & **1851.6** & **8.6** & 108000 & 18113.2 & 187.4 & – \\
**EA** & 1846 & 1872.6 & 10.2 & 40,000 & 19,006.0 & 514.4 & – \\
**HS** & 1866 & 1884.8 & 10.3 & 9057 & 1696.3 & 230.5 & – \\
**HC** & 1862 & 1886.4 & 11.9 & 4868 & 1661.5 & 279.7 & – \\
**HY** & 1846 & 1864.4 & 8.8 & 21248 & 9717.8 & 455.0 & – \\
**IP** & 2366 & – & – & – & \(3\cdot 10^{5}\) & – & 25.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of all considered algorithms for the USA network.