## 5 Experimental Results
### Analysis of Results
#### 5.3.3 Compared with Conventional NSGA-III and NSGA-II  
(1) Comparison of the mean values of the three algorithms  
The mean values of the optimized NSGA-III, conventional NSGA-III, and NSGA-II outputs after 100 iterations are listed in Table 6, in which the mean values of \(f_{1}\), \(f_{2}\), and \(f_{3}\) for the optimized NSGA-III are clearly lower than those for the conventional NSGA-III and NSGA-II, indicating that all three objectives were simultaneously improved to some extent. When using the individuals in the solution set obtained by the optimized NSGA-III, the \(f_{1}\) berth deviation cost was CNY 95 and CNY 362 lower than that obtained by conventional NSGA-III and NSGA-II, respectively. The \(f_{2}\) total scheduling time was 274.3 min (approximately 4.57 h) and 1991.22 min (approximately 33.19 h) shorter than the total scheduling time of the conventional NSGA-III and NSGA-II, respectively. Finally, the \(f_{3}\) berth utilization rates obtained by the optimized NSGA-III, conventional NSGA-III, and NSGA-II were 33.33%, 33.31%, and 32.82%, respectively. This comparison indicates that the proposed algorithm achieved the lowest preference cost, lowest total scheduling time, and highest berth utilization. Figure 4: Optimized NSGA-III vs. original scheduling program objective values. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Ship Number**} & \multicolumn{2}{c}{**Actual Scheduling**} & \multirow{2}{*}{**Arrival Time at the Berth**} & \multirow{2}{*}{**Berthing Location**} & \multirow{2}{*}{**Departure Time**} \\  & **of Movement Control Time** & & & \\ \hline
1 & 24 Dec. 2023 at 11:10 & 24 Dec. 2023 at 11:28 & a1 & 24 Dec. 2023 at 16:28 \\
2 & 24 Dec. 2023 at 15:50 & 24 Dec. 2023 at 16:13 & b6 & 24 Dec. 2023 at 20:13 \\
3 & 25 Dec. 2023 at 08:42 &  
The comparison of the average objective values of the three algorithms is shown in Figure 5. Both the optimized NSGA-III algorithm and the conventional NSGA-III algorithm achieve significantly higher objective values than the NSGA-II algorithm. This improvement is due to the NSGA-III algorithm's enhancement of the optimization process, utilizing reference points to guide the population toward these points. The optimized NSGA-III shows slightly better average objective values compared to the conventional NSGA-III, thanks to several enhancements. First, the quality of initial solutions is improved through a mixed initial population. Additionally, the dynamic adjustment of crossover and mutation probabilities allows the algorithm to better explore the search space and find more precise solutions. In the first 30 generations, the crossover probability remains high, between 0.8899 and 0.9, to enhance population diversity, while the mutation probability stays low, between 0.01 and 0.0111, to guide the population toward better solutions. Around the 40 th generation, the crossover probability starts to decrease and the mutation probability begins to increase. By the 80 th generation, both probabilities change more gradually and, by the 100 th generation, they stabilize, with the crossover probability around 0.6 and the mutation probability around 0.3. This dynamic adjustment allows the algorithm to better adapt to different problems and search phases, thus improving its robustness and performance. Comparison of Gantt charts for the three algorithms  
The Gantt charts displaying the optimized NSGA-III, NSGA-III, and NSGA-II algorithms are shown in Figure 6, Figure 7, and Figure 8, respectively. The vertical axis represents berths (1 corresponds to a1,..., 8 corresponds to a8; 9 corresponds to b1,..., 16 corresponds to b8), and the horizontal axis represents dates, with the seven-day planning period ending on December 30, 2023, as indicated by the vertical line in the chart.