# Ferry Scheduling Optimization Considering Arrival Time Uncertainty and In-Place Time Differences
## 4 Numerical Example Analysis
### Research on Algorithm Parameters
In Figure 9, the relationship between the number of iterations and the convergence of the algorithm is shown. The horizontal axis represents the number of iterations, while the vertical axis represents the maximum number of iterations to obtain the optimal solution. When the number of iterations is set to 50, it can ensure that the problem reaches a convergence state. Therefore, the recommended range for the number of iterations is 50 or more. To avoid taking too long to solve the problem, the number of iterations should be minimized as much as possible. As shown in Table 3, a probability model was constructed to approximate the original problem, with an important parameter involved being the number of samples \(|W|\). According to the Monte Carlo sampling method, the larger the number of randomly generated samples, the closer the statistical law of the sample set to the law of the original problem. When the number of samples is too small, the pattern of the scheme exhibits significant randomness; when the number of samples is too large, it takes too much time to calculate. Therefore, it is ideal to use the minimum sample size while meeting the stability of the scheme. Five sets of experiments were conducted for each sample value, and the results with a sample size of 10 and 1000 are presented in Table 4. From the results in the table, it can be seen that there is a significant difference in experimental results when the sample size is 10. Notably, when the value of resource quantity is 10, the cumulative percentage range is 0.500. However, when the sample size is 1000, the corresponding range is only 0.025. In Figure 10, the stability of the scheme results with different sample sizes ranging from 10 to 10,000 is shown. The horizontal axis represents the number of samples, while the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{_iMax_} & **The Maximum** & & & **Proportion of** \\  & **Number of Iterations** & **Single Experiment** & **Repetitive** & **Experiments** \\  & **to Obtain the** & **Run Time/s** & **Experiments** & **Achieving** \\  & **Optimal Solution** & & & **Optimal Solutions** \\ \hline
10 & 10 & 0.57 & 500 & 51.0 \\
20 & 20 & 1.05 & 500 & 85.8 \\
30 & 30 & 1.48 & 500 & 96.2 \\
40 & 40 & 1.94 & 500 & 99.2 \\
50 & 40 & 2.15 & 500 & 100.0 \\
60 & 46 & 2.42 & 500 & 100.0 \\
70 & 41 & 2.79 & 500 & 100.0 \\
80 & 37 & 3.18 & 500 & 100.0 \\
90 & 41 & 3.42 & 500 & 100.0 \\
100 & 44 & 3.95 & 500 & 100.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The experimental results of different iterations. Figure 9: The influence of iteration time on convergence. vertical axis represents a percentage. There are three sets of data under each sample value. The black, white, and gray bars show the results of experiments for resource numbers 9, 10, and 11, respectively. When the sample size is small, the stability of the experimental results is poor. When the sample size is greater than 700, the results tend to be stable. The number of different resources ultimately tends to reach a certain value. For example, when the number of resources is 9, it tends to be 0.025; when the number of resources is 10, it tends to be 0.460. Therefore, to avoid accidental results caused by a small sample size, it is recommended to keep the sample size at 700 or above. After the above research on algorithm parameters, a reference is provided for determining the range of different parameter values. The algorithm population size is set at 100 or above, the number of iterations is set at 50 or above, and the sample size is set at 700 or above.