## 4 Experiments and Discussion
For TSCS-BD, TSCS-NL, TSCS, SWGA, and CS, crossover rate \(p_{\text{c}}=0.8\), mutation rate \(p_{\text{m}}=0.1\). The number of iterations was set as 1500 generations. The termination condition was to reach the set maximum number of iterations or for solutions to remain unchanged within 120 generations. To eliminate interference of random factors, the same experiments were conducted 10 times. Average makespan and average convergence iteration times are used for comparison. In order to show the effects of the proposed algorithm, completion time yielded by the TSCS-BD is used as a benchmark and compared with completion time yielded by other algorithms, as shown in Equation (13). \(P\) represents the percentage of average completion time better than the other algorithms. Comparison results are shown in Table 6, and iteration times for algorithms are shown in Figure 9.  
\[P(X,IS)=\frac{C_{time}(X,IS)-C_{time}(TSCS-BD,IS)}{C_{time}(X,IS)}\times 100\% \tag{13}\]  
\[X\in(SWGA,RPSO-VM,CS,TSCS,\ TSCS-NL)\] \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Example**} & \multirow{2}{*}{**TSCS-BD**} & \multirow{2}{*}{**SWGA**} & \multicolumn{2}{c}{**RPSO-VM**} & \multicolumn{2}{c}{**CS**} & \multicolumn{2}{c}{**TSCS**} & \multicolumn{2}{c}{**TSCS-NL**} \\ \cline{2-11}  & & **C\({}_{\text{time}}\)** & **C\({}_{\text{time}}\)** & **P (\%)** & **C\({}_{\text{time}}\)** & **P (\%)** & **C\({}_{\text{time}}\)** & **P (\%)** & **C\({}_{\text{time}}\)** & **P (\%)** & **C\({}_{\text{time}}\)** & **P (\%)** & **C\({}_{\text{time}}\)** & **P (\%)** \\ \hline L1 & 402.2 & 441.7 & 8.94 & 448.3 & 10.32 & 475.3 & 15.38 & 418.1 & 3.80 & 429 & 6.25 \\ L2 & 527.7 & 584.5 & 9.72 & 580.2 & 9.05 & 635.5 & 16.98 & 550.4 & 4.12 & 557.4 & 5.33 \\ L3 & 654.1 & 728.3 & 10.19 & 721.4 & 9.33 & 795.3 & 17.74 & 685.7 & 4.61 & 673.7 & 2.91 \\ \hline L4 & 365.3 & 403.4 & 9.44 & 407.8 & 10.40 & 427.2 & 14.49 & 372.8 & 2.01 & 368.8 & 0.95 \\ L5 & 469.5 & 521.3 & 9.94 & 528.5 & 11.16 & 564.4 & 16.81 & 482.3 & 2.65 & 500.3 & 6.16 \\ L6 & 578.7 & 641.6 & 9.82 & 632.5 & 8.49 & 708.5 & 18.32 & 602.4 & 3.93 & 615.4 & 5.96 \\ \hline L7 & 348.3 & 379.1 & 8.20 & 389.1 & 10.46 & 411.7 & 15.38 & 356.2 & 2.22 & 359.2 & 3.03 \\ L8 & 424.3 & 469.4 & 9.61 & 478.6 & 11.35 & 513.9 & 17.42 & 437.7 & 3.06 & 428.7 & 1.03 \\ L9 & 507.7 & 562.7 & 9.79 & 572.3 & 11.29 & 618.7 & 17.94 & 526.3 & 3.53 & 529.3 & 4.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results and comparisons. Figure 8: Distance matrix (numbers are time needed for transportation between two cells in the same vehicles at the same speed). Figure 9: Comparisons of iteration times. Table 6 clearly indicates that TSCS-BD yielded the best solutions among the algorithms for all of the nine examples. Among them, both TSCS-BD and TSCS are better than CS in terms of solution quality, indicating that the TS in TSCS-BD and TSCS could help CS to improve local searching ability compared with the original local search strategy. Moreover, bottleneck-degree guidance for the neighborhood structure in TSCS-BD could help the TS yield better quality solutions than the general neighborhood structure in TSCS. With increasing of part numbers in experiments with the same machine numbers, for example part numbers increased to 50, 70, and 90 in L1, L2, and L3, the solution quality of TSCS-BD is further improved compared with that of TSCS. This shows that the proposed bottleneck-degree guidance for the neighborhood structure in TSCS-BD is more suitable for large-scale problems than the general neighborhood structure in TSCS. Figure 9 shows that the iteration times of TSCS-BD are the least among all the algorithms. It can be concluded that bottleneck-degree guidance for a TS in TSCS-BD can construct a neighborhood structure on machines with large bottleneck degree, which reduces the search scope of low-quality solution space and efficiently finds the descent direction of the algorithm within less iteration time. Therefore, TSCS-BD is effective for large-scale inter-cell scheduling problems.