## 5 Case Study
### Comparison Results and Analysis
The results indicate that NSGA-II-MOEA/D-CIS achieves a superior Pareto front in optimizing both production costs and delayed delivery time compared to other algorithms. Additionally, the number of Pareto solutions obtained by NSGA-II-MOEA/D-CIS is tied for first place (equivalent to the NSGA-II-NSGA-II combination). Furthermore, the findings reveal that NSGA-II exhibits a stronger global search capability than MOEA/D (as evidenced by NSGA-II-NSGA-II ranking second and MOEA/D-MOEA/D ranking sixth). Therefore, incorporating NSGA-II within the hybrid framework significantly enhances the model's solution quality. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Upper**} & \multirow{2}{*}{**Lower**} & \multicolumn{5}{c}{**Indictors**} & \multirow{2}{*}{**Rank**} \\ \cline{3-3} \cline{5-6}  & & \(\mathbf{HV}\uparrow\) & & \(\mathbf{IGD}\downarrow\) & \(\mathbf{SP}\downarrow\) & \(\mathbf{MS}\uparrow\) \\ \hline MOEA/D & MOEA/D & 0.72 & 0.25 & 0.32 & 0.47 & 6 \\ NSGA-II & NSGA-II & 0.88 & 0.12 & **0.18** & 0.58 & 2 \\ MOEA/D & NSGA-II & 0.78 & 0.21 & 0.28 & 0.50 & 5 \\ MOPSO & MOEA/D & 0.85 & 0.15 & 0.22 & 0.55 & 3 \\ SPEA2 & MOEA/D & 0.82 & 0.18 & 0.25 & 0.53 & 4 \\
**NSGA-II** & **MOEA/D** & **0.95** & **0.06** & 0.19 & **0.62** & **1** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison results of different algorithm combinations (\(\uparrow\) 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). 3. Comparison of algorithmic efficiency. The efficiency of each algorithmic combination is evaluated based on convergence generations, execution time, and memory consumption. These factors directly impact the feasibility of solving large-scale problems and the practical applicability of the algorithms. The comparative results are presented in Table 7. The analysis reveals a dichotomy in the efficiency of homogeneous algorithmic combinations. The MOEA/D-MOEA/D configuration demonstrates superior efficiency due to the natural compatibility of its decomposition strategy, significantly reducing computational redundancy and achieving optimal convergence generations and execution time. This highlights the advantage of algorithmic consistency in strongly coupled multi-objective optimization scenarios. In contrast, the NSGA-II-NSGA-II configuration suffers from the cumulative computational burden of dual-layer non-dominated sorting and crowding distance calculations, leading to high memory consumption and prolonged convergence time. This exposes the limitations of algorithmic consistency in high-complexity problem settings. Furthermore, a deeper analysis of combination patterns reveals that the upper-layer algorithm's global search capability and the lower-layer algorithm's constraint-handling efficiency collectively determine the performance ceiling. For instance, MOPSO-MOEA/D leverages the upper-layer MOPSO's swarm intelligence for rapid exploration of the solution space, while the lower-layer MOEA/D efficiently decomposes subproblems, striking a balance between computational speed and solution stability. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**Indictors**} \\ \cline{3-6}
**Upper** & **Lower** & **Convergence** & **Running** & **Memory** & **Rank** \\  & & **Generation**\(\downarrow\) & **Time/s**\(\downarrow\) & **Usage/MB**\(\downarrow\) & \\ \hline MOEA/D & MOEA/D & **60** & 857 & **98** & **1** \\ NSGA-II & NSGA-II & 100 & 1554 & 239 & 6 \\ MOEA/D & NSGA-II & 96 & 1288 & 241 & 5 \\ MOPSO & MOEA/D & 75 & **786** & 125 & 2 \\ SPEA2 & MOEA/D & 88 & 1233 & 227 & 4 \\
**NSGA-2** & **MOEA/D** & 84 & 1178 & 202 & 3 \\ \hline \hline \end{tabular}
\end{table}