# A Machine Learning Predictive Model for Ship Fuel Consumption
## 3 Analysis of Results
Thus, a long-distance trip or a vessel built of wood or of great length are factors that will certainly cause greater fuel consumption by the vessel, while the reverse is also true. In order to optimize the hyperparameters of the model, the Grid Search Method was adopted, as advocated by [PERSON] et al. (2018) and [PERSON] et al. (2018). The values that best fit the model and provide greater efficiency are achieved through a step-by-step increment, that is, through an iterative feature in which the machine changes the hyperparameters until the stopping criterion is reached when the model is no longer capable of presenting more assertive predictions [25]. To define the winning model, which obtained the best performance in predicting in a more satisfactory way the vessels' fuel consumption during the training stage, the performance metrics Mean Absolute Error (MAE), Mean Square Error (MSE), Root Mean Square Error (RMSE), Coefficient of Determination (R\({}^{2}\)), and Computational Processing Time (CPT) were evaluated, as proposed by [PERSON] et al. [25] in their study. Through the Cross-Validation Method applied by [PERSON] et al. [32], each model participated in nine training rounds and one test round, and the performance was evaluated from the average of these ten rounds. The performances of each model are presented in Table 5.  
The model with the highest performance score was CatBoost, achieving 0.852. This was due to its unique technique for handling categorical variables, its robustness to outliers, and its advantages when dealing with tabular data, aligning with the approach applied by [PERSON] et al. [34]. In second, third and fourth places, Extreme Gradient Boosting [26], Random Forest [30], and Gradient Boosting [33], whose Coefficient of Determination (R\({}^{2}\)) values were 0.797, 0.790 and 0.787, respectively. The last positions were presented: Extra Tree [32] with 0.751 and Decision Tree [25] with 0.669; the latter had the lowest R\({}^{2}\) among the six models considered. For the performance parameters MSE and RMSE, employed by [PERSON] et al. [82], it remains the same performance order of the models generated in the function of the determination coefficient (R\({}^{2}\)) in which the predictions made by CatBoost were the most assertive and, therefore, presented lower MSE and RMSE when compared to the other models. On the other hand, the evaluation of the MAE shows that CatBoost presented the lowest error (348.48), followed by Extra Tree (352.67), Random Forest (387.08), Gradient Boosting (406.33), Extreme Gradient Boosting (409.23), and Decision Tree (433.02). The MAE and MSE values have the same units as the measured variables [83]. From the point of view related to computational time, as done by [PERSON] et al. [25], the Decision Tree stood out as the fastest one to process the data and reach a result, even if, as seen, presenting a higher error and, consequently, divergent predictions from the observed data. CatBoost, in turn, due to its complexity in working with categorical records, presented the longest processing time, about 3.80 s. In the subsequent positions, emphasis is given to the Extreme Gradient Boosting and Random Forest models that obtained an excellent performance in the predictions, although they also spent a longer processing time. CatBoost was chosen as the winning model due to satisfactory performance evaluations for data processing and target variable prediction. Hyperparameter adjustment was performed once again with the goal of making the model even more effective, refining its treatment of residuals and, consequently, achieving a higher R\({}^{2}\), according to [PERSON] et al. [35]. The hyperparameters found via application of the Random Search Method [27; 34] generated final values that can be checked in Table 6, which ensure the generated model a more effective predictive performance among the sets of hyperparameters tested.