## 3 The Proposed Method
### Dpga
#### 3.1.1 Chromosome Representation  
In a GA, a solution is represented by a chromosome. Table 2 shows a chromosome in DPGA, which is implemented by a one-dimensional list consisting of categorical and continuous variables to represent algorithm-selection and parameter-specification. Specifically, it is composed of four parts corresponding to data rebalancing, feature extraction, feature reduction, and learning subtasks as follows: \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline The number of solutions in a population (\(|P|\)) & 20 \\ \hline Stopping-patience & 50 \\ \hline The crossover probability (\(p_{c}\)) & 0.5 \\ \hline The mutation probability (\(p_{m}\)) & 0.1 \\ \hline The algorithm-change mutation probability & 0.3 \\ \hline The parameter-change mutation probability & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameter values used in DPGA. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Field** & **Description** & \multicolumn{4}{c}{**Range of Values**} \\ \hline DR algo. & A data rebalancing algorithm & One of [None, RDUP, SMOTE, BSMOTE1, BSMOTE2, \\ SSMOTE, RREM, NCL] \\ \hline DR para. & A parameter value of the rebalancing algorithm & Balancing ratio \(r\in[0.75\)–\(1]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Chromosome representation in DPGA. DR: Data rebalancing, FFE: Filtering-based feature extraction, RFE: Reduction-based feature extraction, LM: Learning model. Figure 2: Overall framework of DPGA. * Data rebalancing--This part is only applicable in the fault-types classification. As explained in Section 2.1, the 'DR algo.' field in a chromosome indicates one among five over-sampling and two under-sampling algorithms, or none of them. In addition, the 'DR para.' field represents the threshold parameter of the rebalancing ratio (see Section 2.1 for details). * Feature extraction--To generate latent features, our GA employed two groups of approaches, filtering-based (available only for time-series datasets, see Section 2.2) and reduction-based (see Section 2.3) approaches. The 'FFE algo.' field represents the subset of five filtering-based feature extraction algorithms (SMA, CMA, EMA, ES, and LFS). In addition, the 'FFE para.' field includes the corresponding parameters that are necessary to run the selected feature extraction algorithms (for example, the number of time points in SMA or CMA). Similar to filtering-based feature extraction, the 'RFE algo.' and 'RFE para.' fields represent the combinatorial selection among five reduction-based feature extraction algorithms (PCA, LSA, FAG, GRP, and SRP) and the corresponding parameters (for example, the number of principal components), respectively. We note that if none are selected in 'FFE algo.' and 'RFE algo.,' only the original variables are used as input variables in the learning algorithm. * Dimension-reduction by PCA--Before executing the learning method, the dimension of the input space consisting of all of the newly constructed features and the original variables can be finally reduced by the PCA [41, 42, 43]. The 'PCA flag' and 'PCA para.' represent whether PCA is applied or not, and the threshold parameter (\(\epsilon\)) with respect to the desirable explained variance, respectively. In other words, when the 'PCA flag' turns on, the set of highest-order principal components that