## 4 Results and Discussion
### Description of the ANN Model  
Figure 2 illustrates the framework of the ANN model determined in this study. The framework is divided into input, hidden and output layers. The default type of transfer function is selected for hidden and output layers in MATLAB. The hyperbolic tangent sigmoid transfer function (tansig) for the hidden layer, and the log-sigmoid transfer function (logsig) for output layer. Backpropagation is used to train the ANN. The input layer is where the sports shoe design factors are input, and can be further divided into discrete and continuous factor types. The discrete factors can be further classified as form or color factors (Table 5). The hidden layer mainly serves to increase the complexity of the ANN and represents the interaction between inputs. The hidden layer is a structure describing the complex interactions among various variables in the ANN structure. The number of neurons and hidden layers cannot be known in advance. This study determined an appropriate number of hidden layers through trial and error. The output layer expressed the scores which the respondents gave for the perceived adjective-based scale anchors. ANN can be simulated using these data to establish a nonlinear relationship between shoe design factors and Kansei adjectives.  
First, a 10 \(\times\) 10 ANN structure was used to build the correlations between shoe design factors and adjectives in this experiment. Because the ANN structure could not be easily determined, and there were no specific sets of rules to follow, trial and error was used to decide the structure. Figure 3 plots the preliminary training results for the three sets of adjectives, where the horizontal axis indicates the experimental value, and the vertical axis indicates the predicted value. The \(R^{2}\) for Adjs.1-3 were 0.536, 0.555 and 0.757, respectively. The results indicated, that except for Adj3 (like-dislike), which obtained relatively satisfactory prediction results through training, the other two adjective pairs [i.e., Adj1 (elegant-artless) and Adj2 (rare-common)], did not achieve satisfactory prediction results through training. Therefore, this study inferred that building an ANN framework with complicated relationships for the experimental factors might be relatively difficult. Using trial and error was not effective enough to rapidly identify valid model-building parameters and generate accurate predictions. Therefore, the GA was employed to find the optimal structure and build a more accurate ANN model.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Population size** & 100 \\
**Maximum number of generations** & 100 \\
**Termination criterion** & Meet the maximum number of generations (100) or tolerance (\(10^{-6}\)) \\
**Selection function** & Roulette wheel \\
**Crossover function** & Discrete method \\
**Mutation function** & (0.65 probability of crossover) \\  & Real valued (0.05 probability of mutation) \\ \hline \hline \end{tabular}
\end{table}
Table 6: Genetic algorithm (GA) structural parameters.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{5}{c}{**\(\mathbf{x_{1}}\)**} & \multicolumn{5}{c}{\(\mathbf{x_{2}}\)} & \(\mathbf{x_{3}}\) & \(\mathbf{x_{4}}\) & \multirow{2}{*}{\(\mathbf{x_{5}}\)} & \multirow{2}{*}{\(\mathbf{x_{6}}\)} & \multirow{2}{*