# A Comparative Evaluation of Nature Inspired Algorithms for Telecommunication Network Design
## 5 Results and Discussion  
Computational results were obtained for seven optical networks that have different characteristics. The networks correspond to actual optical networks stemming from specified countries and were taken from [29]. Table 1 and Figures 4-10 provide the relevant parameters for both networks and their topologies. Figure 4: Schematic diagram of 10-node German national transmission optical backbone network. Figure 3: An example of a chromosome, based on Polish network. Figure 5: Schematic diagram of Polish national transmission optical backbone network. Figure 6: Schematic diagram of 15-node German national transmission optical backbone network. Figure 7: Schematic diagram of 20-node German national transmission optical backbone network. The demands that were used in the optimization of network costs are given by a demand matrix, which provides the values of traffic flow between selected nodes expressed in gigabits per second (Gbps). The calculations were carried out using a linear solver engine of CPLEX 12.8.0.0 on a 2.1 GHz Xeon E7-4830 v.3 processor with 256 GB RAM running under Linux Debian operating system. Table 2 describes in detail the sets and their settings and presents constant settings used during the computational process. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Network** & **\#Nodes** & **\#Links** & **\#Demands** \\ \hline Germany10 & 10 & 14 & 45 \\ Polish & 12 & 18 & 66 \\ Germany15 & 15 & 23 & 105 \\ Germany20 & 20 & 29 & 190 \\ USA & 26 & 42 & 325 \\ American & 39 & 61 & 741 \\ Germany & 50 & 88 & 1225 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of analyzed networks. Figure 8: Schematic diagram of a USA national transmission optical backbone network. Figure 9: Schematic diagram of an American national transmission optical backbone network. The following modeling parameters were used for heuristic algorithms: \(p_{a}=0.95\), \(p_{m}=0.05\) and \(memory\_size=30\) for HS; \(N=50\), \(m=12\), \(e=6\), \(n_{1}=8\), \(n_{2}=2\) and \(k=5\) for BA; and \(\mu=100\)\(\lambda/\mu=2\), \(p_{c}=0.9\) and \(p_{m}=0,05\) for EA. All these values were selected empirically after a series of tests. In the first numerical experiment a comparison of optimization methods was performed. For Polish, German10, German15 and German20 networks (Figure 4-7 and Figure 11), which are discussed first, all considered algorithms reached the optimal solution. Results of heuristic algorithms are characterized by a small standard deviation. This observation supports the claim that the simulations are quite repetitive and that they converge consistently to effectively the same value. Further, the results from Tables 3-6 show that average values are close to the minimum values. This is particularly the case for the BA algorithm. Thus, BA algorithm showed on average the best performance among all heuristic algorithms in terms of consistency. Figure 10: Schematic diagram of 50-node German national transmission optical backbone network. The results obtained by HS algorithm on the other hand, are characterized by the highest standard deviation and the highest average value of the cost function. Thus, HS algorithm performed worst among all heuristic algorithms. It is also important to note that CPLEX software took about 6 min to find the optimal solution of 1321. Therefore, on average, IP approach won the competition for the Polish network instance. Finally, it is noted that on average, the fastest heuristic algorithm turned out to be HC algorithm. A bit worse, in terms of time, was the HS algorithm. Both of these algorithms were close to the IP approach in terms of time. The swarm algorithms (BA and EA) finally reached the optimum, but needed about 20 times more time. The implemented algorithms were also applied to the large networks, i.e., the USA, American and German50 networks (Figures 8-10). That was the main purpose of this article. Analogously, the results were collected in Tables 7-9.