## 5 Conclusions  
The main goal of this study was to present and discuss a semi-automatic and unbiased procedure to select the most reliable ANN model for a given predictive modeling problem, which can overcome the limitations of conventional approaches. In particular, the focus was on predicting at once volumetric properties and mechanical characteristics of bituminous mixtures prepared using different types of bitumen and aggregate, binder content and maximum nominal grain size, to support the mix design phase, providing numerical estimations of the investigated parameters without any other costly laboratory test. The study results can be summarized as follows:  
* To perform proper neural modeling, the evaluation of the several network structures resulting from the selection of different model hyperparameters values is required. The procedure developed in this article allowed the limitations of the most widely used ANN toolbox to be overcome. * The proposed approach with the k-fold CV produces more reliable results in terms of model validation error, with respect to the standard grid search based on a random data set partition: in fact, if the procedure were based on a fixed random split of the available data set, different results are possible, worse (R4 = 0.829) or better (R3 = 0.906) than the most likely situation represented by the k-fold CV (RCV = 0.868), due to the different distribution of the training and validation data. * The BO algorithm has shown to be successful in solving the challenging problem of properly setting the model hyperparameters: it has identified the optimal solution, in terms of algorithmic and structural configuration of the ANN, in only 54 iterations. The hallmark of such a technique lies in the ability to take past evaluations into account so as to limit the loss function recalls. Nonetheless, the reader should be aware that the BO procedure results may be linked to the constraints set by the research engineer in terms of hyperparameters' variability. * In the current paper, Marshall parameters, ITSM, as well as AV content have been determined simultaneously by a single multi-output ANN, unlike previous studies; therefore, such approach represents an integrated predictive model of the selected mechanical and volumetric properties. * The neural network structure best suited (MSECV = 0.249, RCV = 0.868) to model experimental mixtures data is defined by 5 layers, 37 neurons in each hidden layer and _tanh_ transfer function. A learning step size \(\alpha\) equal to 0.01 and weight decay \(\beta\) equal to 1\(\times\)10\({}^{-6}\) are implemented in the Ranger training algorithm. * The algorithms applied and the analytical steps taken by the artificial networks have been illustrated in detail to make the procedure followed replicable to the reader. If it is desired to put the proposed model into service for the designed application (e.g., use in a laboratory or plant for estimates of mechanical parameters and volumetric properties of bituminous mixtures), then the optimized ANN must be trained with all available data. It is worth recalling that the proposed model is applicable only to the specific types of aggregate, bitumen and mixture structure considered. This study did not account for the influence of different aggregate gradation on the results for a specific bitumen content. An interesting further development would be to investigate such an effect, integrating new input variables related to aggregate gradation or mix proportioning. Alternatively, the modeling variables relating to the mechanical characteristics of the mixture could be replaced by those relating to the road pavement performance, such as fatigue and permanent deformation resistance. This replacement would represent further progress towards a performance-based mix design.