## 6 Results and Discussion
### Comparative Experiments  
Comparative experiments were carried out according to the experimental scheme and the results were recorded in Table 5.  
Figure 14: Task Gantt chart of the picking stations. Figure 15: (**a**) Evolution curve of the \(F_{1}\) number. (**b**) Evolution curve of the reference solution cost. (**c**) Pareto front distribution. It is not difficult to find from the experimental data in the above table that, although MADPSO has significantly better optimization effects in general situations, its computational speed is significantly inferior to other optimization methods. From the perspective of algorithm code running logic, the decoding of each individual in the MADPSO method requires a relatively complex queuing service simulation calculation. This computational burden will overlap with the increase in task size, the number of iterations, and the expansion of population size, leading to weaknesses in the computational speed of the MADPSO method. However, considering that in the actual production environment of shipyards, the demand for pallet-picking tasks usually comes several days in advance, the weakness of the MADPSO method in terms of calculation speed will not have a significant impact on the actual use of shipyards in the environment. Therefore, this article will not further pursue the computational speed of the MADPSO method. To further discuss the influence of each experimental factor on the experimental index, the range \(R_{j}\) of each factor is calculated according to the range analysis method of the orthogonal experiment and filled in the last row of Table 5. For the interaction columns, the average range of the two columns is taken as the range of the interaction factor. According to the size of the range, the order of factors' influence is A \(>\) C \(>\) A\(\times\)C  
According to the experimental results and the statistical data in the above table, the following two obvious conclusions can be drawn:  
* **Conclusion 1**: _In the experiments, MADPSO showed a better optimization effect than TPPM and RMFSOM under all task scale conditions. In particular, it showed a more than 50% optimization improvement of MADPSO to widely used TPPM._
* **Conclusion 2**: _With the expansion of the task scale, the optimization effect of MADPSO shows a slight downward trend._  
Conclusion 1 shows the effectiveness of MADPSO under different task scale conditions, while Conclusion 2 points out that the task scale has some limitations on the performance of MADPSO. Considering the capacity limit of the picking station and the additional penalty cost caused by the fact that orders exceeding the capacity limit need to be sent to the buffer for waiting, an Inference can be speculated as follows:  
**Inference 2**: _Whether the task scale exceeds the upper limit of the total capacity of all picking stations (we call this different state a pseudo factor PF, which is \(T\) when exceeding and \(F\) when not exceeding) will affect the experimental index AROS._  
To verify Inference 2, the data in Table 5 are sorted according to the level of pseudo-factor PF, as shown in Table 7. The data in the table show that when the task scale exceeds the upper limit of the total capacity of the picking stations, the AROS value will rise, weakening the effect of the algorithm. On the other hand, within the timeslot when a pallet-picking task remains open, the number of pallets circulating in the whole system is limited. We call this situation the limited vision of single pallet optimization. This means that the relationship between single pallet-picking tasks in large-scale SACOP is not close. Therefore, the direct solution of large-scale SACOP is not only a lack of algorithm performance support, but also a lack of necessity. At the same time, it also increases the interference risk of uncontrollable factors, such as machine failure, personnel fatigue, and so on.