## 5 Case Study
### Comparison Results and Analysis  
To validate the advantages of the proposed NSGA-II-MOEA/D-CIS hybrid algorithm in model solving, this case study first combines the upper and lower layers with NSGA-II and MOEA/D algorithms in pairs, resulting in three additional hybrid models: MOEA/D in both the upper and lower layers, NSGA-II in both the upper and lower layers, and MOEA/D in the upper layer with NSGA-II in the lower layer. Additionally, two other multi-objective optimization algorithms are introduced for comparison: Multi-Objective Particle Swarm Optimization (MOPSO) and Strength Pareto Evolutionary Algorithm 2 (SPEA2). MOPSO extends Particle Swarm Optimization (PSO) for multi-objective optimization problems and is widely used in supply chain optimization due to its strong global search capability and rapid convergence. Meanwhile, SPEA2, with its elite archiving mechanism and diversity maintenance, is highly regarded in decision optimization research. Then, to comprehensively compare the advantages and disadvantages of the hybrid algorithms, this section evaluates them from three dimensions: algorithm performance, model-solving results, and algorithm execution efficiency. To ensure fairness, the parameters of each hybrid algorithm are set according to the parameter configuration method  
Figure 8: Main effects plot of each parameter. \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Level Number**} & \multicolumn{3}{c}{**Parameters**} \\ \cline{2-4}  & \(N_{upper}\) & \(P_{\mathbf{c}}\) & \(P_{m}\) \\ \hline
1 & **0.572** & 4.962 & **6.506** \\
2 & 2.876 & **4.308** & 5.966 \\
3 & **9.804** & 6.024 & 5.250 \\
4 & 7.074 & **6.750** & 5.318 \\
5 & 7.556 & 5.838 & **4.842** \\ Range & 9.232 & 2.442 & 1.664 \\ \hline \end{tabular}
\end{table} 
Table 5: Average performance values of each parameter at different levels. outlined in Section 5.2, ensuring that all algorithm combinations operate at their optimal performance. Additionally, to address probabilistic variations, each algorithm combination is executed 50 times, and the results are averaged. Furthermore, the collaborative iterative strategy proposed in this paper is applied to all hybrid models. 1. Multi-objective performance comparison. The convergence and distribution of the Pareto solution set are evaluated using indicators such as Hypervolume (HV), Inverted Generational Distance (IGD), Spacing Metric (SP), and Maximum Spread (MS). To facilitate data processing and visualization, all indicator values are normalized to the [0,1] range using min-max normalization. The final comparison results are shown in Table 6, where \(\uparrow\) indicates that a larger value within the normal range corresponds to better algorithm performance, while \(\downarrow\) indicates that a smaller value within the normal range corresponds to better algorithm performance (all subsequent comparison tables follow this notation). Furthermore, each of the four indicators is assigned an equal weight of 25%, resulting in a comprehensive ranking of algorithm performance. The results indicate that the proposed combination of NSGA-II in the upper layer and MOEA/D in the lower layer achieves the best performance in terms of HV, IGD, and MS metrics, with only a slight disadvantage in the SP metric compared to the NSGA-II-based dual-layer combination. According to the evaluation criteria, the proposed NSGA-II-MOEA/D-CIS algorithm ranks first in overall performance, demonstrating its superiority in solving the optimization problem. 1. Comparison of model solution results. The performance of each algorithm is evaluated based on the obtained Pareto front (only the results of the lower-layer order reorganization are presented). The comparison considers dominance relationships and the number of non-dominated solutions to assess algorithmic effectiveness. Figure 9 illustrates the Pareto fronts obtained by different algorithmic combinations.