# A Comparative Evaluation of Nature Inspired Algorithms for Telecommunication Network Design
## 5 Results and Discussion
Additionally, convergence curves over 50 independent runs are depicted in Figures 12-14 for the USA, American and German50 networks. In all three cases the IP approach found solutions which were much further away from the optimal value than the ones found by heuristic algorithms. In all cases studied, the highest minimum values were obtained by HC and HS algorithms. It is worth noticing that the ILP approach has one advantage over heuristic methods, i.e., ILP, in that it provides the lower bound for the minimum sought. The results obtained show that for the cases studied ILP is particularly effective when applied to German10, Polish, German15 and German20 networks, since in this case an ILP algorithm finds the optimum. For the USA, American and German networks, as mentioned, ILP finds the lower band and thus allows estimating the optimality gap. However, it is noted that for networks with exceedingly many nodes the optimality gap may be so large as to preclude any practical knowledge concerning the quality of the feasible solutions obtained. Considering the average results, the HC algorithm performed worst in all cases. On the other hand, the best results in all considered cases for USA, American and German networks were obtained consistently using BA and EA algorithms. BA and EA algorithms both reached the minimum, and most importantly, the lowest average value for the American network. This observation supports the claim that the swarm algorithms (BA and EA) are best suited for optimization of optical networks with a large number of nodes (i.e., USA, American and German). The BA and HC algorithms results have the highest values of the standard deviation. This suggests that BA and HC algorithms explore the solution space more robustly and thus give more diverse results. In the more complex cases, American, USA and German 50 node networks (Figures 8-10), algorithms based mainly on solution space exploitation (HC and HS) converged to a certain point, and then, due to small exploration, stopped at one of the extrema of local solution spaces. At this point, \begin{table}
\begin{tabular}{c c} \hline
**Set** & **Set Settings** \\ \hline \(\mathcal{N}\) & in Table 1 \\ \hline \(\mathcal{E}\) & in Table 1 \\ \hline \(\mathcal{S}\) & 768 slots \\ \hline \(\mathcal{B}\) & 2 bands \\ \hline \(\mathcal{T}\) & 4 transponders (\(t_{1}=40\) G, \(t_{2}=100\) G, \(t_{3}=200\) G and \(t_{4}=400\) G) \\ \hline \multirow{3}{*}{\(\mathcal{S}_{t}\)} & \(\mathcal{S}_{1}=\{1\ldots 380\}\cup\{385\ldots 764\}\) \\  & \(\mathcal{S}_{2}=\{1\ldots 380\}\cup\{385\ldots 762\}\) \\  & \(\mathcal{S}_{3}=\{1\ldots 378\}\cup\{385\ldots 762\}\) \\  & \(\mathcal{S}_{4}=\{1\ldots 376\}\cup\{385\ldots 760\}\) \\ \hline \multicolumn{2}{c}{**Constant**} & **Constant Settings** \\ \hline \(d(n,n^{\prime})\)[Gbps] & e.g., \(d(1,2)=70\) \\ \hline \(\xi(b)\) & \(\xi(1)=1\), \(\xi(2)=2\) \\ \hline \(\xi(t,b)\) & \(\xi(1,1)=2\), \(\xi(2,1)=5\), \(\xi(3,1)=7\), \(\xi(4,1)=9\) \\  & \(\xi(1,2)=24\), \(\xi(2,2)=6\), \(\xi(3,2)=8.4\), \(\xi(4,2)=11.8\) \\ \hline \end{tabular}
\end{table} 
Table 2: Set and constant settings. EA and BA algorithms show their superiority. This is because in EA and BA algorithms more emphasis is placed on exploration than in the previous two algorithms (HC and HS), which allows EA and BA algorithms to avoid the trap of local extremes and enables them to continue with further optimization. The Figures 11-14 also show the influence of initialization population by HS, EA and BA algorithms in contrast to HC algorithm. More than one solution at the start gives a potentially better base solution, so that these algorithms find a lower cost solution at the start (the chart starts with a much lower cost value). Figure 11: Comparison of the convergence for the Polish 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.