# A Multi-Objective Evolutionary Algorithm Model for Product Form Design Based on Improved SPEA2
## 4 Discussion
### Performance of ISPEA2
From Table 17 and Figure 11, we can see that the \(C\) metric value of ISPEA2 is obviously smaller than that of SPEA2 and the \(S\) metric value of ISPEA2 is also lower than that of SPEA2, which manifests that the convergence of ISPEA2 has been obviously improved, and the diversity of ISPEA2 has also been enhanced. In addition, \(C(A^{2},A^{1})=0\) means that there is no solution in SPEA2 that can dominate the solution in ISPEA2. The high value of the \(C(A^{1},A^{2})\) metric demonstrates that the outcomes of ISPEA2 remarkably dominate the outcomes of SPEA2, and the solutions of ISPEA2 are closer to the true Pareto front and more widely distributed. Consequently, the comparative results prove that ISPEA2 has better convergence and diversity. It should be pointed out that the standard deviations of two metrics are very close, which demonstrates that the stability of two algorithms is relatively consistent. \begin{table}
\begin{tabular}{c c c c} \hline
**Method** & \(C\) & \(S\) & \(C(A^{1},A^{2})\) \\ \hline ISPEA2 & 0.0505 (0.0424) & 0.0431 (0.0236) & 0.7931 \\ SPEA2 & 0.1802 (0.0430) & 0.0942 (0.0184) & 0.0000 \\ \hline \end{tabular}
\end{table} 
Table 17: Means and standard deviations of \(C\), \(S\), and \(C(A^{1},A^{2})\) values for ISPEA2 and SPEA2. Figure 11: Trend graph of \(C\) and \(S\) metrics of 30 independent runs of the two algorithms. The ISPEA2 algorithm is the main source of the proposed PFDMOEAM's comprehensive performance superiority and value, helping the model to generate high quality Pareto design solutions. The overall forms of these solutions are rich and free, and the form details are fine and smooth, even the morphological information of local structures such as car lights can be observed. Rich and fine forms match the multi-image objective better, which significantly improves the innovation and application value of the proposed PFDMOEAM. Superiorities and Values of EFA for Product Form Design Multi-Objective Evolutionary Algorithm Model (PFDMOEAM)  
In the authors' previous work, it has been proved that EFA as an effective PFIA method has shown significant superiorities in the DA module. Compared with other traditional PFIA methods, it improves the precision and degree of freedom of PF, and enhances the accuracy and comprehensiveness of KIR. This paper further proves that EFA can provide a new idea and way for optimizing the performance of MOEA in the MOO module. This is reflected in the fact that the MO operator is proposed by using the consistency correlation between PC scores and IEMSs both obtained by EFA. Because PC scores can reflect overall form features, and the perception mode of product image also adheres to the principle of overall form priority of product image recognition [49], the relationships of PC scores and IEMSs relative to product form are both more based on the whole rather than the local. By using these relations, the MO operator adjusts the evolutionary direction, which reduces the amount of computation and improves the efficiency and performance of ISPEA2 algorithm in approximating the true Pareto solution set. It can be seen that EFA not only promotes the achievement of the goals of DA and MOO modules better, but also creates an organic connection between different methods in these two modules, which helps to integrate the model as a whole more effectively. Therefore, EFA is a significant basis for gaining the superiorities of the proposed PFDMOEAM.