# Cargo Terminal Intelligent-Scheduling Strategies Based on Improved Bee Colony Algorithms
## 4 Implementation and Experimental Results
### Verification with Benchmark Functions  
CEC benchmark functions as shown in Table 1 are introduced, and ABC, fdABC, PfdABC, as well as RmdABC are applied to solve them with MATLAB. The algorithms are  
The results show that the average runtime and shortest runtime on all benchmark functions corresponding to PfdABC, fdABC, and RmdABC increase, but the quality of the optimal solution as well as the local-searching ability have been improved significantly compared to ABC, meanwhile the optimal variances on different dimensions show that the stabilities have been greatly improved with the three proposed strategies. Figure 1 graphically shows the fitness values for solving Expanded Schaffer's Function with different dimensions. Obviously, fdABC, PfdABC, and RmdABC algorithms possess faster convergence speeds and better accuracies compared with ABC. Based on the results above, the introduction of the random multidimensional strategy and parallel full-dimensional strategy greatly improves the performance of traditional ABC. fdABC possesses the best optimization result, but it spends too much time on optimizing. The optimization solutions corresponding to PfdABC and RmdABC are not as good as fdABC, but they can reduce the optimization time effectively. The time cost of RmdABC is lower than fdABC and PfdABC, as RmdABC randomly selects part of dimensions in each iteration. Obviously, the proposed PfdABC and RmdABC algorithms could balance the abilities of exploration and exploitation compared to ABC and fdABC, and the corresponding algorithms must be selected during application on the basis of the practical problems. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Function Name**} & \multirow{2}{*}{**Algorithm**} & **Average** & **Average Optimal** & **Best Optimal** & **Shortest** & **Var Optimal** \\  & & **Runtime/s** & **Result/s** & **Result/s** & **Runtime/s** & **Result/s** \\ \hline \multirow{4}{*}{1. Bent Cigar Function} & ABC & 223.196 & 3.787 \(\times\) 10\({}^{8}\) & \(3.416\times 10^{8}\) & 222.774 & \(1.099\times 10^{15}\) \\  & fdABC & 425.692 & 2.044 \(\times\) 10\({}^{-251}\) & \(1.091\times 10^{-251}\) & 420.020 & 0 \\  & RmdABC & 303.243 & 12.037 & 0.405 & 300.169 & 199.478 \\  & PfdABC & 399.895 & \(4.392\times 10^{-8}\) & \(3.463\times 10^{-8}\) & 387.853 & \(6.669\times 10^{-17}\) \\  & ABC & 199.808 & \(2.279\times 10^{120}\) & \(7.215\times 10^{111}\) & 197.343 & \(2.222\times 10^{241}\) \\  & fdABC & 1664.371 & \(1.671\times 10^{-245}\) & \(6.863\times 10^{-248}\) & 1619.398 & 0 \\  & RmdABC & 920.823 & \(3.470\times 10^{-6}\) & \(4.151\times 10^{-9}\) & 911.149 & \(1.069\times 10^{-10}\) \\  & PfdABC & 1120.629 & \(8.680\times 10^{-57}\) & \(3.9115\times 10^{-58}\) & 1115.067 & \(5.118\times 10^{-113}\) \\  & ABC & 189.997 & \(5.919\times 10^{3}\) & \(4.346\times 10^{5}\) & 186.093 & \(9.399\times 10^{9}\) \\
3. Rosenbrock’s & fdABC & 538.976 & 0.00884 & 0.001 & 504.637 & \(1.04\times 10^{-4}\) \\ Function & RmdABC & 351.792 & 6.042937 & 1.430 & 337.071 & 18.386 \\  & PfdABC & 456.292 & 1.021 & 0.201 & 449.671 & 1.568 \\  & ABC & 193.990 & 152.642 & 193.287 & 193.2873 & 65.193 \\
4. Rastrigin’s & fdABC & 458.470157 & 0 & 0 & 452.714 & 0 \\ Function & RmdABC & 574.398 & \(7.97\times 10^{-4}\) & \(8.599\times 10^{-5}\) & 573.802 & \(7.859\times 10^{-7}\) \\  & PfdABC & 454.618 & \(1.136\times 10^{-10}\) & \(8.356\times 10^{-11}\) & 450.936 & \(2.190\times 10^{-22}\) \\  & ABC & 189.754 & 78.395 & 63.6545 & 187.726 & 97.986519 \\
5. Step’s Function & fdABC & 637.867 & 0 & 0 & 622.008 & 0 \\  & RmdABC & 289.625 & \(1.379\times 10^{-7}\) & \(1.838\times 10^{-8}\) & 287.601 & \(1.8710\times 10^{-14}\) \\  & PfdABC & 398.953 & \(5.632\times 10^{-14}\) & \(2.467\times 10^{-14}\) & 391.252 & \(3.979\times 10^{-28}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The performance of PfdABC, RmdABC, fdABC and ABC on 100 dimensions.