## 5 Discussion  
This section presents the results of the GA-ANN modeling using scatter plots. Figure 5 displays the detailed results of models with 1-3 training layers. Figure 5a presents the training results of the model with one hidden layer. The hidden layer contained 16 nodes. The \(R^{2}\) of the adjective sets were 0.633, 0.665 and 0.824; these results are superior to those obtained with an arbitrarily selected ANN structure. Figure 5b reveals that when the model comprised two hidden layers and \(35\times 5\) nodes, the \(R^{2}\) of the adjective sets were 0.652, 0.683 and 0.829, respectively, whereas when the model comprised three hidden layers and \(28\times 38\times 19\) nodes, the \(R^{2}\) of the adjective sets were 0.668, 0.674 and 0.843 (Figure 5c). The data distribution was relatively highly concentrated, suggesting that the GA-ANN under these conditions is the optimal model. In particular, the highest correct prediction rate was found for Adj3 (like-dislike), which indicates respondents' preference. Tables 8 and 9 present the shoe color schemes and types that resulted in relatively small and large prediction errors using the GA-ANN, respectively. These prediction data were compared with statistics obtained from the original questionnaire responses, which revealed that for shoe types for which the predictions were accurate, the questionnaire investigation results were comparably coherent, and the trends were identifiable. A review of these samples suggested that the prediction results for casual and running shoes were the most accurate, whereas the prediction results for shoes with a shape that is relatively difficult to identify were the least accurate. Regarding shoes with two colors, the prediction accuracy for shoes with black soles was relatively higher than for single-color shoes. Therefore, the effect of color could not be predicted; the prediction accuracy for different colors varied randomly. This was found by plotting the colors with high and low prediction accuracies on the color wheel, in which no identifiable trend could be observed. This study inferred that the respondents had relatively similar opinions of the different shoe shapes, so trends in their perceptions were easily identified. By contrast, the opinions of the respondents regarding the color schemes were different, so no obvious trend could be identified. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{\
\begin{tabular}{c} **Hidden** \\ **Layers** \\ \end{tabular} } & \multirow{2}{*}{**Hidden Nodes**} & \multicolumn{4}{c}{**MSE**} & \multicolumn{4}{c}{\(\boldsymbol{R^{2}}\)} & \multirow{2}{*}{
\begin{tabular}{c} **Overall** \\ **\(R^{2}\)** \\ \end{tabular} } \\ \cline{3-3} \cline{5-10}  & & & **Adj1** & & & & & & & \\ \hline ANN & 2 & \(10\times 10\) & 0.549 & 0.308 & 0.536 & 0.556 & 0.555 & 0.757 & 0.627 \\ ANN & 2 & \(50\times 50\) & 0.524 & 0.259 & 0.469 & 0.550 & 0.619 & 0.782 & 0.662 \\ ANN & 2 & \(100\times 50\) & 0.690 & 0.340 & 0.552 & 0.441 & 0.496 & 0.755 & 0.569 \\ ANN & 2 & \(50\times 100\) & 0.828 & 0.417 & 0.967 & 0.34 & 0.4 & 0.61 & 0.357 \\ ANN & 3 & \(50\times 50\times 50\) & 0.480 & 0.312 & 0.531 & 0.61 & 0.51 & 0.72 & 0.624 \\ GA-ANN & 1 & 16 & 0.419 & 0.231 & 0.403 & 0.633 & 0.665 & 0.824 & 0.713 \\ GA-ANN & 2 & \(35\times 5\) & 0.393 & 0.222 & 0.417 & 0.652 & 0.683 & 0.829 & 0.724 \\ GA-ANN & 3 & \(28\times 38\times 19\) & 0.381 & 0.239 & **0.367** & 0.668 & 0.674 & **0.843** & **0.733** \\ GA-ANN & 4 & \(30\times 46\times 30\times 46\) & **0.360** & **0.209** & 0.472 & **0.699** & **0.703** & 0.806 & 0.720 \\ \hline \hline \end{tabular} Adj1 (elegant–artless); Adj2 (rare-common); Adj3 (like–dislike). Bold numbers indicates the optimal value.  
\end{table} 
Table 7: Predictive performance of different GA-based ANN models. In addition to th configurations of solid colors (color = hue), this study included gradient color effects, because these more closely reflect product designs currently on the market.