## 4 Experimental Environment and Preliminaries
### Experimental Setup  
Experiments included comparing the performance of several well-established optimization algorithms to the introduced metaheuristic. Each algorithm was tasked with selecting a set of parameters yielding the best-performing model. Alongside the introduced metaheuristics, the original PSO [17] and GA [19] were also evaluated. Additionally, well-known optimizers were also subjected to a comparative analysis, including the ABC [21], BA [22], WOA [23], HHO [20], and the relatively newly introduced ChOA [24]. For the classification experiment, metaheuristics were allocated a population size of 10, allowed 10 iterations, and tasked with optimizing XGBoost hyperparameters and improving outcomes. Parameters were chosen for optimization due to their high influence on model performance. The parameters and their respective ranges included: learning rate \([0.1,0.9]\), min child weight \([1,10]\), subsample \([0.01,1]\), subsample by tree \([0.01,1]\), max depth \([3,10]\), and gamma \([0,0.8]\). The dataset used for classification was divided, with an initial 70% used to train the models, the following 10% for validation, and the final 20% for testing. A flowchart is shown in Figure 2 left. For trajectory forecasting, models were provided with the vessel latitude, longitude, speed over ground, course over ground, and heading, and tasked with forecasting the latitude and longitude of the vessel. The LSTM models were provided with 16 lags (samples considered as inputs for a network) of data as inputs and a batch size of 20, using the Keras library TimeSeriesGenerator to facilitate model training. The number of lags was empirically determined as a trade-off between the memory and computational demands and the accuracy, to give the best results. The training was carried out with 50% of the available data, and 50% was used for testing. Metaheuristics were tasked with selecting optimal LSTM network parameters and architecture. The parameters selected for optimization were, once again, selected due to their significant influence on model performance. The parameters and their respective ranges included the learning rate within the range \([0.0001,0.01]\), dropout \([0.05,0.2]\), and a number of training epochs \([30,50]\). Finally, the network architecture was also optimized, and the number of layers was selected between \([1,3]\). The number of neurons in each layer was also optimized, and the number of neurons per layer was selected from a \([16,32]\) range. However, the constraints depended on the number of lags utilized. Neuron constraints were considered in a range of \([lags,lags\cdot 2]\). A validation set was not employed, and the dataset was grouped into training and testing sets, in a 50/50 ratio. A flowchart is shown in Figure 2 right. Metrics Used for Validation and Comparative Analysis  
Two sets of evaluation metrics were used to facilitate experimentation and to provide a fair comparison between the optimization metaheuristics. For the classification experiment, the standard classification metrics, including the accuracy shown in Equation (24), precision Equation (26), recall Equation (25), and \(F_{1}\) score Equation (27) were recorded and presented. Additionally, [PERSON]'s Kappa metric shown in Equation (28) was also utilized, due to the ability of the metric to provide a better evaluation of methods for imbalanced data, such as the one utilized in this work. \[Accuracy=\frac{TruePositives+TrueNegatives}{TruePositives+True Negatives+FalsePositives+FalseNegatives}, \tag{24}\]  
\[Recall=\frac{TruePositives}{TruePositives+FalseNegatives}, \tag{25}\]  
\[Precision=\frac{TruePositives}{TruePositives+FalsePositives}, \tag{26}\]  
\[F_{1}\ Score=2\times\frac{Precision\times Recall}{Precision+Recall}, \tag{27}\]  
\[Cohen^{\prime}skappa=\frac{ObservedAgreement-ExpectedAgreement}{1-ExpectedAgreement}, \tag{28}\]  
For the time series forecasting experiments for the vessel trajectories, regression metrics were utilized.