# An Evolutionary Neural Network Approach for Slopes Stability Assessment
## 3 Methodology
### Modelling Procedure  
A nominal classification approach showed the highest overall response on EHC prediction during the first attempt [30,31]. Accordingly, the same modelling strategy was adopted in this new attempt. In addition, as mentioned before, only ANN algorithms were trained, as they showed superior performance in the EHC problem. SMOTE, oversampling, and no resampling were also tested in these new experiments (only during the modelling step) in order to address the issue of imbalanced data [70,71], as no conclusive conclusion could be drawn from the first attempt regarding the optimal resampling technique. We note that the three resampling approaches are reasonably diverse. The no resampling option did not change the training data; thus, it was used as a baseline to check if the other resampling approaches provided a modelling value. Since the minority classes occurred very infrequently, it made more sense to apply oversampling rather than undersampling (if this last method was applied, the training data would be too small). Finally, SMOTE is a state-of-the-art resampling technique that generates synthetic samples for minority classes. The overall proposed procedure was comprised of two main steps, as illustrated in Figure 3 and as described below:  
1. **Optimization:** The objective of applying GA is to identify the optimal set of variables that minimizes the objective function. Consequently, our GA began by randomly defining an initial population in which each individual (a sequence of 1 and 0 indicating whether a feature was included or not) represented a potential solution (set of variables) to the problem. The objective function corresponded to the maximization of the recall metric for all four EHC classes (a multi-objective problem). The fitness function corresponded to an ANN algorithm-based predictive model. Two ANNs were fitted to the database using the methodology outlined in Section 3.1 (i.e., a feedforward network with one hidden layer, a logistic function for hidden nodes, and a grid search of \(\{0,2,4,6,8\}\) for \(H\) definition using a 3-fold cross-validation schema as the validation procedure). Then, for each EHC class, a recall metric (the average of both ANNs) was calculated, which was then utilized by the GA to optimize the optimal set of attributes for EHC identification. 2. **ANN training:** After optimization, five ANNs were fitted to the database for each Pareto optimal solution (set of optimal variables) using the methodology described in Section 3.1. Here, in addition to the standard approach (no resampling), ANNs were trained with a resampled database using the SMOTE and oversampling approaches. Notably, the various sampling methods were only applied to the training data, which were used to fit the data-driven models, and the test data (as provided by the 5-fold cross-validation procedure) were not altered. This means that \(3\times(5\times 5)=75\) ANNs were trained for each Pareto optimal solution. Each model was then subjected to a sensitivity analysis to determine the relative relevance of each attribute for EHC prediction. As presented and discussed in the next sections, it was possible to identify the average number of input variables considered for EHC prediction. In addition, the variables selected more frequently by the GA were determined. In the end, based on the overall performance of each model (measured by the recall, precision, and F\({}_{\rm 1-score}\) for all four EHC classes) and the results of the sensitivity analysis, a single model was chosen and thoroughly analyzed. Although not presented in the paper, it should be mentioned that some other experiments were also carried out following a regression strategy, where, in addition to the optimization of the best set of attributes, a numeric regression scale was also optimized at the same time. The R statistical environment [58] was adopted to implement all experiments conducted in this research.