## 5 Case Study and Discussion
### Available Knowledge Acquisition
#### 5.2.2 Filtering Knowledge Genes by Calculating Synthetic Similarity  
According to the data in Table 7, in Equation (24), the values of \(l\) is 19, the values of \(l_{1}\) is 15, and that of \(l_{2}\) is 4. To further identify available diagnosis knowledge, the synthetic similarity is used to filter knowledge. To calculate the values of synthetic similarity between the target gene and knowledge genes as shown in Table 7, the PSO is applied to optimize the weights of elements of the target gene. **Optimizing weights. ** In the PSO, the initial values of weights corresponding to the initial position of a particle are set as the same value in this study. The related parameters of PSO are shown in Table 8. Besides, it will be initialized when a weight value is less than 0 or a single weight is 25% greater than the sum of all weights to guarantee the rationality of distribution of weights in the process of running PSO. The algorithm run 30 times, the evolutionary curves of the average value of the best fitnesses (\(f(x)\)) are shown in Figure 11. It can be easily observed that the fitness is optimized to a certain extent and the algorithm converges within 50 generations. So we can conclude that the PSO is effective in the weights optimization of this study. In particular, the solution that its best fitness is the closest to the average value of the best fitnesses is chosen to be a reasonable sequence of weights for further application. According to the results of PSO, the optimized solution is expressed by the sequence as follows:  
\[\begin{array}{l}[0.0359,0.0244,0.0432,0.0030,0.0032,0.0278,0.0135,0.0035,0. 0319,0.0345,\\ 0.0022,0.0318,0.0027,0.0158,0.0164,0.0001,0.0251,0.0063,0.0201,0.0081\\ -\\ 0.0022,0.0020,0,0,0.0131,0.0363,0.0152,0.0155,0.0408,0.0033,0.0452,\\ 0.0135,0.0401,0.0274,0.0093,0.0309,0.0142,0.0015,0.0075,0.0056\\ -\\ 0.0092,0.0205,0,0.0226,0.0078,0.0105,0.0017,0.0170,0.0625,0.0425,\\ 0.0050,0.0076,0.0035,0.0431,0.0490,0.0010,0.0148,0.0069,0,0.0022] \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline Index & 1 & 2 & 5 & 11 & 14 & 15 & 16 & 17 & 19 & **21** \\ \hline _SD_(_PG_, _KPG_) & 0.71 & 0.73 & 0.70 & 0.72 & 0.74 & 0.71 & 0.72 & 0.72 & 0.73 & 0.72 \\ _SD_(_PG_(_PE_), _KPG_(_PE_)) & 0.50 & 0.50 & 1.83 & 1.50 & 1.33 & 0.33 & 0.33 & 0.50 & 1.25 & **0.00** \\ \hline Index & 25 & **26** & 27 & 32 & **33** & 35 & **36** & 37 & 38 & \\ \hline _SD_(_PG_, _KPG_) & 0.71 & 0.70 & 0.73 & 0.72 & 0.73 & 0.71 & 0.70 & 0.74 & \\ _SD_(_PG_(_PE_), _KPG_(_PE_)) & 0.33 & **0.00** & 1.00 & 0.50 & **0.00** & 0.25 & **0.00** & 0.50 & 0.67 & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Values of direct similarity in relevant diagnosis knowledge pool. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{tabular}{c} **Number of** \\ **Dimensions** \\ \end{tabular} & \begin{tabular}{c} **Population** \\ **Size** \\ \end{tabular} & \begin{tabular}{c} **Number of** \\ **Iterations** \\ \end{tabular} & \
\begin{tabular}{c} **Self-Confidence** \\ \end{tabular} &
\begin{tabular}{c} **Swarm** \\ **Confidence** \\ \end{tabular} & **Inertia Weight** \\ \hline
59 & 200 & 200 & \(C_{1}=0.01\) & \(C_{2}=0.9\) &
\begin{tabular}{c} \(\omega_{min}=0.01\) \\ \(\omega_{max}=0.5\) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Related parameters of PSO. As shown in the expression (42), the array of weights is divided into three segments, which are separated by \"-\". Values in the first segment represent the weights of elements in \(GU\)(1). Values in the second segment represent the weights of elements in \(GU\)(2). Values in the third segment represent the weights of elements in \(GU\)(3). The result of weights shows that different elements have different correlations with the performance of product quality in this experiment.