# A Multi-Objective Evolutionary Algorithm Model for Product Form Design Based on Improved SPEA2
## 3 Empirical Study
### Design Analysis
#### 3.1.2 Image Analysis  
Firstly, 128 affective adjectives describing car profiles were collected from literature, car catalogs and professionals. Next, an informal survey was conducted on 16 industrial design students (8 males and 8 females) to select 36 relevant adjectives preliminarily (see Table 5), which were suitable for these subjects to express their perceptions on the representative sample profiles. Then, the focus group finalized 11 most representative adjectives, with application of the Delphi method. After that, questionnaires were designed by combining 45 representative samples with the 11 representative adjectives, using a 7-point semantic differential method (-3-3), in which -3 and 3 are the lowest and the highest score of adjectives, respectively. Subsequently, the IEMSs was calculated after the focus group completed the questionnaire (Table 6, whole set of data see Table S3), and the correlation analysis matrix for all samples was obtained by concatenating the IEMSs and PC scores matrixes. Finally, the FIOCS and rankings of 11 representative adjectives were obtained via using the IOCSM (Table 7). The top three adjectives in the rankings were set as the target adjectives in the case study of this paper, namely \"luxurious\", \"steady\", and \"modern\". \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Sample**} & \multicolumn{6}{c}{**PC Scores**} \\ \cline{2-7}  & **PC 1** & **PC 2** & **PC 3** & **PC 4** & **PC 5** & **PC 6** & **PC 7** \\ \hline
1 & \(-\)0.6524 & \(-\)0.4649 & \(-\)0.0129 & 0.1124 & \(-\)0.1042 & \(-\)0.0128 & \(-\)0.0966 \\
2 & \(-\)0.8519 & 0.0141 & 0.0557 & 0.0293 & \(-\)0.0554 & \(-\)0.0103 & \(-\)0.0219 \\
3 & \(-\)0.8674 & 0.1096 & \(-\)0.1195 & 0.0349 & 0.0632 & 0.0827 & \(-\)0.0021 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
43 & \(-\)0.7988 & \(-\)0.1222 & 0.0611 & \(-\)0.0322 & 0.0157 & 0.0015 & 0.0001 \\
44 & \(-\)0.7513 & \(-\)0.2207 & \(-\)0.0775 & \(-\)0.0538 & \(-\)0.1235 & 0.0368 & 0.0363 \\
45 & \(-\)1.0078 & 0.3870 & \(-\)0.0419 & \(-\)0.0675 & 0.0234 & \(-\)0.0227 & 0.0396 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: PC scores for representative samples. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**PC Number**} & **Proportion (\%)** & **Cumulative (\%)** \\ \hline PC 1 & 97.4588 & 97.4588 \\ PC 2 & 2.0882 & 99.5470 \\ PC 3 & 0.2039 & 99.7509 \\ PC 4 & 0.0946 & 99.8455 \\ PC 5 & 0.0645 & 99.9100 \\ PC 6 & 0.0290 & 99.9390 \\ PC 7 & 0.0233 & 99.9623 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Variance contribution rate of each principal component (PC). \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Sample**}} & \multicolumn{10}{c}{**Representative Adjectives**} \\ \cline{2-13}  & **Avant-grade** & **Dynamic** & **Eigen** & **Formal** & **Generous** & **Luxurious** & **Male** & **Modern** & **Simple** & **Smooth** & **Steady** & **Unique** \\ \hline
1 & 0.6686 & 0.8574 & 0.4882 & 0.0784 & 0.3729 & 0.7345 & 0.7345 & 0.9055 & 0.7849 & 0.6708 & 0.7843 & 0.7078 \\
2 & 0.5078 & 0.5561 & 0.4716 & 0.2980 & 0.4863 & 0.5667 & 0.7467 & 0.7604 & 0.5745 & 0.4205 & 1.0667 & 0.6667 \\
3 & 0.6853 & 0.8029 & 0.5142 & \(-\)0.2549 & 0.2696 & 0.6232 & 0.4332 & 0.9961 & 0.6265 & 0.7753 & 0.5196 & 0.5804 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
43 & 0.5852 & 0.2701 & 0.1657 & 0.2961 & 0.4243 & 0.5300 & 0.5400 & 0.7025 & 0.4875 & 0.5518 & 0.4892 & \(-\)0.2549 \\
44 & 0.6137 & 0.7123 & 0.4686 & \(-\)0.2308 & 0.5456 & 0.5376 & 0.4376 & 0.6951 & 0.5138 & 0.5726 & 0.7943 & 0.6235 \\
45 & 0.9510 & 0.5845 & 0.2269 & \(-\)0.2490 & \(-\)0.0746 & 0.4263 & 0.1963 & 0.6936 & 0.3857 & 0.5415 & 0.3676 & 0.5059 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Image evaluation mean scores (IEMs) matrix.