# Cargo Terminal Intelligent-Scheduling Strategies Based on Improved Bee Colony Algorithms
## 4 Implementation and Experimental Results
### Scheduling Problem
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{(**a**)} \\ \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
**Iteration** & 488 & 230 & 223 & 501 & 179 & 346 & 267 & 464 & 202 & 595 \\ \hline
**Result/s** & 6621.11 & 6623.11 & 6613.61 & 6609.98 & 6617.36 & 6617.24 & 6617.36 & 6611.73 & 6617.12 & 6615.49 \\ \hline
**Iteration** & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\ \hline
**Iteration** & 213 & 464 & 228 & 82 & 82 & 536 & 153 & 524 & 422 & 388 \\ \hline
**Result/s** & 6606.35 & 6617.48 & 6630.49 & 6615.37 & 6611.86 & 6617.36 & 6617.48 & 6619.24 & 6615.37 & 6611.74 \\ \hline \end{tabular}
\end{table} 
Table 8: **(a)** The scheduling results with PfdABC. (**b**) Entrances and exits allocation scheme with PfdABC. Optimal scheduling route: 15 39 59 21 52 14 11 30 27 34 38 41 40 7 26 31 46 44 12 42 9 47 19 29 8 58 1 36 54 49 48 13 22 37 20 3 57 50 6 18 28 32 23 10 24 25 17 60 2 33 45 5 53 16 4 51 55 35 43 56. The statistical information of the above results are described in the box plot as Figure 2. The numbers 1, 2, 3, and 4 in horizontal coordinate represent PSO, ABC, PfdABC, and RmdABC, respectively. The plot shows that PfdABC and RmdABC are better as the upper limits are lower than the lower limits of PSO and ABC, PfdABC possesses higher optimization accuracy because of its lower low limit, and RmdABC is more stable as the distance between the lower and upper limits is shorter. In addition, several important indices, including the average time required to execute the resulting sequence (Avg), the shortest executed time (Min), the longest inbound and outbound time (Max), and the average convergence generations (Ite) are calculated based on the results of 20 independent runs and shown in Table 10. It can be easily found that the \begin{table}
\begin{tabular}{c c c} \hline  & (b) \\ \hline \multicolumn{3}{c}{**Inbound tasks**} & \multicolumn{3}{c}{**Outbound tasks**} \\ \hline
1 & 15, 16, 24, 25, 17, 7, 11, 26, 4, 30, 2 & 1 & 46, 31, 41, 45, 44, 59, 38, 33, 60, 51, 34, 39, 40 \\ \hline
2 & 14, 12, 5, 1, 10, 21 & 2 & 55, 42, 35, 58, 52, 36, 53 \\ \hline
3 & 9 & 3 & 54, 56, 47, 43, 49 \\ \hline
4 & 29, 27 & 4 & 32, 48 \\ \hline
5 & 19 & 5 & 37 \\ \hline
6 & 23 & 6 & \\ \hline
7 & 13, 28 & 7 & 57, 50 \\ \hline
8 & 18, 6, 3, 20, 8, 3 \\ \hline \end{tabular}
\end{table} 
Table 8: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline Iteration & 209 & 209 & 213 & 209 & 223 & 546 & 580 & 209 & 331 & 423 \\ \hline Result/s & 6617.12 & 6617.12 & 6611.86 & 6617.12 & 6611.86 & 6611.86 & 6615.61 & 6617.12 & 6617.24 & 6617.36 \\ \hline  & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\ \hline Iteration & 539 & 191 & 209 & 223 & 529 & 580 & 546 & 223 & 209 & 223 \\ \hline Result/s & 6621.11 & 6611.86 & 6617.12 & 6611.86 & 6615.61 & 6615.61 & 6615.61 & 6611.86 & 6617.12 & 6611.86 \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\  & & & & & & & & & \\ \end{tabular}
\end{table} 
Table 9: (a) The scheduling results with RmdABC. (b) Entrances and exits allocation scheme with RmdABC. minimum, maximum, and average inbound and outbound time corresponding to PfdABC and RmdABC decreased by 4% at most compared to conventional ABC and PSO, and there are relatively small gaps among the values of Avgs. On the other hand, by examining the values of Ite, it can be seen that PfdABC and RmdABC require less generations to locate the optimal solutions and that it improves by almost 60% compared to ABC and PSO, that is, the advantage of fast convergence speed could be proved. Therefore, PfdABC and RmdABC can obtain faster convergence speed and smaller mean values than those of ABC and PSO in the scheduling problem, and they are demonstrated to be useful tools for solving the air cargo terminal scheduling problem.