## 4 Experiments and Discussion
In addition, comparisons between TSCS-BD and TSCS-NL in Table 6 show that bottleneck-degree guidance for neighborhood structure can help the algorithm yield better solutions than node-load guidance. In order to further analyze the relationship and difference between bottleneck degree and node load, L1 is taken as an example to analyze complex network features associated with bottleneck degree (Figure 4). Machines are sorted in descending order according to complex network features, as shown in Table 7.  
The top five node machines in Table 7 sorted by bottleneck degree are \(M_{12}\), \(M_{1}\), \(M_{3}\), \(M_{8}\), and \(M_{28}\), and the top five node machines sorted by node load are \(M_{12}\), \(M_{4}\), \(M_{30}\), \(M_{8}\), and \(M_{26}\). Among them, both the bottleneck degree and the node load of \(M_{12}\) and \(M_{8}\) are large. This shows that bottleneck degree has a correlation with node load. Both of them could reflect the importance of the machines to a certain extent. However, the bottleneck degrees of \(M_{4}\), \(M_{30}\), and \(M_{26}\) are not large compared with the other nodes. According to Equation (9), this is because the network efficiency and betweenness centrality of \(M_{4}\), \(M_{30}\), and \(M_{26}\) are small. Taking the complex network model for L1 in Figure 4 as an example, \(M_{30}\) has no outgoing edges, indicating that the machine mainly processes the last process of the parts. This type of machine has less impact on other machines and is less important than the others. Therefore, the node load itself cannot adequately reflect the roles of machines in the manufacturing system. In addition, the bottleneck degrees of \(M_{1}\), \(M_{3}\), and \(M_{28}\) are large but they have small node loads, which is because the network efficiency and betweenness centrality of \(M_{1}\), \(M_{3}\), and \(M_{28}\) are large. \(M_{3}\) in Figure 4 connects with nine directed edges and 14 nodes (including second-order neighbor nodes), which is higher than the average of the machines connected with four directed edges and 8 nodes. Although there are few operations processed on \(M_{3}\), it associates with many machines and has great impact on the processes of other machines. This type of machine remains important in the manufacturing system. Therefore, bottleneck degree considers not only node load but also interaction between machines in processing tasks, which is a better indicator than node load to measure the importance of machines in manufacturing systems. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Rank** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline \multirow{2}{*}{Bottleneck Degree} & \(\mathbf{M_{12}}\) & \(\mathbf{M_{1}}\) & \(\mathbf{M_{3}}\) & \(\mathbf{M_{8}}\) & \(\mathbf{M_{28}}\) & \(M_{20}\) & \(M_{15}\) & \(M_{14}\) & \(M_{25}\) & \(M_{2}\) \\  & 1.00 & 0.98 & 0.67 & 0.43 & 0.28 & 0.27 & 0.23 & 0.18 & 0.13 & 0.13 \\ \hline \multirow{2}{*}{Node Load} & \(\mathbf{M_{12}}\) & \(\mathbf{M_{4}}\) & \(\mathbf{M_{30}}\) & \(\mathbf{M_{8}}\) & \(\mathbf{M_{26}}\) & \(M_{13}\) & \(M_{20}\) & \(M_{14}\) & \(M_{16}\) & \(\mathbf{M_{1}}\) \\  & 1.00 & 0.94 & 0.92 & 0.90 & 0.86 & 0.86 & 0.84 & 0.84 & 0.80 & 0.80 \\ \hline \multirow{2}{*}{Network Efficiency} & \(\mathbf{M_{1}}\) & \(M_{27}\) & \(\mathbf{M_{3}}\) & \(\mathbf{M_{12}}\) & \(M_{14}\) & \(\mathbf{M_{8}}\) & \(M_{10}\) & \(M_{6}\) & \(\mathbf{M_{28}}\) & \(M_{11}\) \\  & 1.00 & 0.85 & 0.85 & 0.81 & 0.79 & 0.78 & 0.75 & 0.73 & 0.72 & 0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Complex network features analysis for L1.