## 5 Results
### Explainability Analysis  
By performing an explainability analysis on our neural network model, we may determine which of our extracted features strongly correlate with the predicted parameters of HGS. We chose to apply this analysis to the neural network over the KNN models, as KNN is a relatively transparent algorithm, while ANNs function as black box models.  
We applied SHapley Additive exPlanations (SHAP) [34] to our three neural network models (for 10, 30, and 60 s time limits). We considered an average of the three time limit results, to ease the visualization of the results. It is important to mention that this averaging did not substantially affect the ordering of features, as all three models presented similar results. SHAP values were computed with a sample size of 1000. Figures 12 and 13 show our extracted features ordered by relevance for each predicted parameter. The SHAP charts show that the features at the top are the ones that most strongly impact model output for a particular parameter. The strength of said impact is proportional to the dispersion of points such that low-impact features will present many points clustered around the  
Figure 11: Training and validation loss curves.  
center axis, and high-impact features will present values clustered far from it. We note that some clustering features, such as the outlier ratio, cluster ratio, and CV of nearest neighbor distances (cv_NN_distances), are the most relevant for predicting the generation size parameter (see Figure 12a), though most features perform similarly well, as can be seen from each feature's spread.  
Figure 12: SHAP values. (**a**) Generation size (gs); (**b**) Number of close solutions (nc); (**c**) Number of elite solutions (ne); (**d**) Population size (ps).  
Both the number of close solutions (_nc_) and the number of elite solutions (_nc_) seem to be strongly correlated to the capacity features (ratio of the CV and mean of client demand w.r.t capacity), as both features are strongly inversely correlated to the parameters, as can be seen in Figure 12b,c. Strong results can also be seen for features such as _CV of nearest neighbor distances_, _cluster ratio_, and _client number_.  
For the prediction of the minimum population size parameter (_ps_), Figure 12d shows the _CV of nearest neighbor distances_, _client number_, and _outlier ratio_ features to be most relevant. Moreover, when predicting the value for the target proportion of feasible solutions (_xi_), the model's output is most strongly impacted by the _outlier ratio_, _client number_, _cluster ratio_, and both capacity features (ratio of the CV and mean of client demand w.r.t capacity).  
The most frequently relevant features between parameters are the _cluster ratio_, _outlier ratio_, _client number_, and both capacity features, which seem to have the largest impact on overall parameter prediction. Regarding the time window-related features, we observe that some are among the ten most important compared to other classical spatial or clustering features. Moreover, the time windows features can be seen for the top ten features for _gs_ (sixth, ninth, and tenth place), for _nc_ (fifth, sixth, seventh, and tenth place), for the _ne_ (eight place), and for the _xi_ parameter (sixth and seventh place).