## 6 Simulations and Result Analysis
### Simulation Results and Analysis
#### 6.2.1 Algorithm Convergence  
Shown in Figures 11 and 12 are the PFs obtained by the baseline algorithm BOGA/TD and the proposed MOEA/D-AMSF with the increase of evolution generation, respectively. It can be seen from Figure 11 that BOGA/TD algorithm evolves drastically from 1000 to 5000 generations, but it evolves slowly from 5000 to 50,000 generations and hardly evolves from 50,000 to 100,000 generations, which implies that the algorithm has converged around 50,000 generations. As shown in Figure 12, the proposed MOEA/D-AMSF continues to evolve from 5000 to 100,000 generations, which shows its convergence is gradual. The difference in convergence speed between the two algorithms is mainly due to their different search spaces. The core coding on the links along the selected path is considered in this paper, and the core search space for each connection request changes from \(|C|\) to \(|C|^{\mathcal{I}_{n}^{p}}\) (\(1\leq L_{n}^{p}\leq L_{\text{max}}\)). Therefore, the search space of the proposed algorithm becomes larger than that of the baseline algorithm, resulting in its gradual evolution and a larger number of generations required for convergence. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline Population size (\(N\)) & 100 & neighborhood size (\(\delta\)) & 15 \\ maximum generation (\(G_{max}\)) & 100,000 & gene length (\(geneLen\)) & \(1+L_{max}\) \\ \(P_{c}^{min}\) & 0.4 & \(P_{c}^{max}\) & 0.9 \\ \(P_{m}^{min}\) & 0.3 & \(P_{m}^{max}\) & 0.9 \\ \(G_{LO}\) & 10,000 & multi-point mutation & three-point \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The List of Physical Parameters and Their Values used in MOEAD/AMSF Algorithm. Figure 10: NSFNET topology. Figure 13 compares PFs obtained by the two algorithms with two evolution generations of 5000 and 50,000. Note that legends \(A\) and \(B\) in Figures 13-19 denote the abbreviations of MOEA/D-AMSF and BOGA/TD, respectively. It can be seen from Figure 13 that the proposed algorithm has a lower search speed in the early evolution stage (e.g., 5000 generations), and about 2/3 of the resulting solutions are not as good as those by the baseline algorithm. However, we can see that MOEA/D-AMSF has a better diversity compared to BOGA/TD; about 1/3 of the MOEA/D-AMSF solutions dominate those of BOGA/TD. In the later evolution stage, MOEA/D-AMSF can search for more dominated and diverse solutions. This result stems from the initial population generation method and the adaptive crossover and bi-layer mutation strategies designed in this paper. Some individuals in the initial population are solutions generated by the heuristic algorithm without core switching. In the early stage, single-point crossover and mutation with small crossover and mutation probabilities are adopted. Such mechanisms are designed to reduce the probability that the cores on different links change simultaneously in the early evolution stage so that the algorithm has a good evolutionary basis and guides itself to search for solutions in the global solution space, lowering the evolution speed of the algorithm. While the probabilities of crossover and mutation in the later evolution stage are increased and multi-point mutation is adopted, which makes the algorithm jump out of the local search and find fo more solutions, accelerating algorithm convergence and enhancing solution diversity. Figure 11: PFs evolution of baseline BOGA/TD (\(\left|R\right|=300\), \(\left|C\right|=5\)). Figure 12: PFs evolution of MOEA/D-AMSF (\(\left|R\right|=300\), \(\left|C\right|=5\)). Figure 14: Comparison of PFs under different cores (\(\left\lvert\,R\,\right\rvert=300\)). Figure 13: PFs evolution comparison of two algorithms (\(\left\lvert\,R\,\right\rvert=300\), \(\left\lvert\,C\,\right\rvert=5\)). Figure 15: Comparison of PFs under different cores (\(\left\lvert\,R\,\right\rvert=400\)). Figure 16: Comparison of PFs under different cores (\(1\,R\,|=500\)). Figure 17: Comparison of PFs under different traffic volumes (\(1\,C\,|=3\)).