# An Evolutionary Neural Network Approach for Slopes Stability Assessment
## 4 Results and Discussion
### Feature Selection  
Figure 4 depicts the trade-off between recall values for each one of the four EHC class for all Pareto optimal solutions covering the three case studies, that is, rock and soil cuttings and embankments. Although putting all this information in a single graph is somewhat confusing, for the purposes of analysis, its more than enough, as it aims at providing an overview of the performance for each EHC class.  
From its analysis, and as expected, the best solution is always a performance commitment between all EHC classes. This commitment is particularly evident between class \"A\" and classes \"B\", \"C\", and \"D\". For example, to obtain a high performance for class \"A\", the response for the other classes must be compromised in some way. The same behavior is also observed for the other possible EHC class combinations, although in some instances, specifically between the \"B\" and \"C\" classes, commitment is not as evident. In fact, there are some solutions that maximise the response for such classes. In addition to the performance commitment between EHC classes, Figure 4 also demonstrates the inferior performance of all Pareto optimal solutions for classes \"C\" and \"D\", namely for rock cuttings (below 0.4) when compared to class \"A\" (above 0.9).  
As previously stated, GAs were applied in this study for feature selection purposes; in other words, they were used to find the best model (set of input variables) that maximized EHC prediction. However, some additional and useful information was extracted from the achieved results, which was useful to obtain a better understanding of the behavior of the stability of slopes. Specifically, they provided information regarding the optimal number of inputs for the accurate determination of slope stability, as well as the variables that should be used as model attributes.  
Figure 5 demonstrates that, with the exception of embankments, all Pareto optimal solutions evaluated fewer than ten features and no more than forty inputs. There are some  
Figure 4: Recall correlation matrix for each Pareto-optimal solution.  
solutions for embankments that considered fewer than ten inputs, with a minimum of five attributes. Still, in regards to embankments, it is interesting to observe that most of the solutions have considered, on average, 15 or 34 inputs. Moreover, for the rock and soil cuttings' slopes, although this was not so evident, the number of variables considered by a significant part of the solutions ranged between 10 and 20 or between 30 and 40. These observations indicate that only about half of the more than 50 features available for model training were simultaneously considered as input to a model. In fact, the majority of Pareto optimal solutions in the study of rock cuttings considered between sixteen and seventeen features, while some were fed by as many as thirty-one features. Regarding soil cutting, the most frequent number of variables taken by the Pareto optimal solutions was 12, and for embankments, that number was 15.  
From Figure 6, which shows the variables present in at least half of all Pareto optimal solutions, it can be observed that slopes categorized as \"high\" and \"angle\" are common to the three types of slopes. Moreover, it can also be observed that only three variables were considered as model attributes by all Pareto optimal solutions among the three slope types. Comparing the three slope types, higher variability was observed for embankments in terms of the model attributes considered by any Pareto optimal solution. In fact, only a restricted group of 14 variables are present on 50% of all Pareto optimal solutions. When considering rock and soil cuttings, this number becomes almost twice higher, particularly for soil cuttings, where a group of 23 variables were used by 50% of all solutions.  
Figure 5: Number of features used as model attributes over all Pareto optimal solutions.