*4.2. Simulation Results*

The conventional ABC and the proposed IE-ABC are used to solve the proposed scheduling problem. The results are shown in Table 2. The cost function value obtained by IE-ABC is 10.31, while the cost function value obtained by ABC is 10.43. The cost function value obtained by IE-ABC is 0.67% lower than that of ABC. Additionally, the energy consumption and time required for the solution obtained by IE-ABC to complete the task are 8.93 <sup>×</sup> <sup>10</sup><sup>6</sup> J and 620.0 s, respectively. On the other hand, the energy consumption and time required for the solution obtained by ABC to complete the task are 9.18 <sup>×</sup> <sup>10</sup><sup>6</sup> <sup>J</sup> and 624.9 s, respectively. Consequently, the solution obtained by IE-ABC reduces the energy consumption and time required to complete the task by 0.23% and 0.93%, respectively, compared to ABC. The improved algorithm has achieved steady advantages in terms of both energy consumption and time. The scheduling Gantt chart of the solution obtained by IE-ABC is shown in Figure 4.

**Table 2.** Simulation result of different optimization algorithms.

**Figure 4.** Vehicle scheduling results presented in a Gantt chart.

It can be seen from Figure 4 that the effectiveness of the scheduling scheme is guaranteed. The obtained scheduling sequence can arrange the loading and unloading tasks of the unmanned dump truck in an orderly manner, and the charging tasks are interspersed among them to ensure the coordination and sustainability of the tasks. As shown in Figure 4, the Gantt chart of the scheduling scheme for 20 tasks is arranged for the four unmanned dump trucks, respectively. Different colors represent the unmanned dump trucks working at different task spots, among which No. 1 and No. 2 represent the loading spots, No. 3, No. 4, and No. 5 represent the unloading spots, No. 6 represent the charging spot, red represents the unmanned dump truck driving stage, and purple represents the unmanned dump truck waiting stage.

It can be seen from the figure that the unmanned dump truck #1 first travels to the No. 2 loading spot to complete the loading task, and then travels to the No. 4 unloading spot to perform the unloading task. The unmanned dump truck #2 reaches the No. 2 loading spot later than the unmanned dump truck #1, so the unmanned dump truck #2 waits for the unmanned dump truck #1 to complete the loading task at the No. 2 loading spot, and then performs the loading task at the No. 2 loading spot.

In order to explore the influence of different factors on ABC optimization, ablation experiments are carried out. The ablation experiment results are shown in Figure 5. Compared with the conventional ABC, IE-ABC mainly changes two factors. One is to add an adaptive multiplier to the global search equation to manipulate the search intensity, and the other is to implement the traditional re-initialization process through the overall degradation strategy. In Figure 5, AE-1 only changes the first factor compared with the conventional ABC, and AE-2 only changes the second factor. It can be seen from the results in the figure that changing these two items has promoted the optimization search, and changing the second factor has a greater impact on the early optimization.

In order to explore the impact of different cost function definition strategies on solving the scheduling problem, a cost function considering energy consumption, time, and output is established. This function is compared against a cost function that disregards time and only considers energy consumption and output. The experimental results are presented in Table 3. The cost function value of the optimal solution obtained using the cost function considering energy consumption, time, and output is 10.31. In comparison, the cost function value of the optimal solution obtained ignoring time and only considering energy consumption and output is 10.63. The former is 3.1% lower than the latter. With the timeincorporated cost function, the energy consumption and time for the optimal solution to complete the task are 8.93 <sup>×</sup> <sup>10</sup><sup>6</sup> J and 620.0 s, respectively. Using the cost function without time, the energy consumption and time required for the optimal solution to complete the task are 9.00 <sup>×</sup> 106 J and 652.9 s, respectively. Compared to the latter, the former reduces energy consumption and task time by 0.78% and 5.04%, respectively.

**Table 3.** Simulation result of different cost function definition strategies.


As shown in Figure 6, the Gantt chart illustrates the optimal scheduling scheme obtained using the cost function that disregarded time and only considered energy consumption and output. The meaning of different colors and numbers in Figure 6 is the same as that in Figure 4. Compared to the optimal scheduling scheme in Figure 4 found by comprehensively accounting for energy consumption, time, and output in the cost function, the time for each unmanned dump truck to complete its corresponding 20 tasks is increased. This indicates that incorporating time into the cost function along with energy consumption and output enabled optimization to find an improved solution.

To investigate the impact of different vector encoding strategies on the solution of the scheduling problem, we compared the solution vector encoding strategy proposed in Section 3.1 with the binary encoding strategy. In the binary encoding strategy, the allocation of tasks is represented by a binary string. For example, if there are two loading spots and three unloading spots, the scheduling sequence {01001} represents that the unmanned dump truck travels to No. 2 loading spot to load and then proceeds to No. 5 unloading spot to unload.

**Figure 6.** Scheduled Gantt chart with cost function that disregards time.

The comparative experimental results of the two encoding strategies are presented in Table 4. The cost function value of the optimal solution obtained using the proposed encoding strategy is 10.31, compared to 10.61 for the binary encoding strategy. The proposed encoding strategy's cost function value is 2.83% lower than that of the binary encoding strategy. The energy consumption and time for the proposed encoding strategy's optimal solution are 8.93 <sup>×</sup> <sup>10</sup><sup>6</sup> J and 620.0 s, respectively. In comparison, energy consumption and time for the binary encoding optimal solution are 9.07 <sup>×</sup> <sup>10</sup><sup>6</sup> J and 636.2 s, respectively. Compared to the binary encoding solution, the proposed encoding strategy's solution reduces energy consumption and task time by 1.54% and 2.55%, respectively.

**Table 4.** Simulation result of different encoding strategies.


Figure 7 shows the Gantt chart for the optimal scheduling scheme obtained through binary encoding. The meaning of different colors and numbers in Figure 7 is the same as that in Figure 4. Compared to the Gantt chart in Figure 4 using the proposed encoding strategy, a larger time gap existed between the earliest finishing unmanned dump truck #3 and the latest finishing unmanned dump truck #2 for their respective 20 assigned tasks. Additionally, the total time is longer with the binary encoding strategy. This indicates that the encoding strategy used in this study enabled obtaining an improved scheduling scheme.

**Figure 7.** The scheduling Gantt chart with binary encoding strategy.
