High levels of cognitive workload decreases human's performance and leads to failures with catastrophic outcomes in risky missions. Today, reliable cognitive workload detection presents a common major challenge, since the workload is not directly observable. However, cognitive workload affects several physiological signals that can be measured non-invasively. The main goal of this work is to develop a reliable machine learning algorithm to identify the cognitive workload induced during rescue missions, which is evaluated through drone control simulation experiments. In addition, we aim to minimize the computing resources usage while maximizing the cognitive workload detection accuracy for a reliable real-time operation. We perform an experiment in which 24 subjects played a rescue mission simulator while respiration, electrocardiogram, photoplethysmogram, and skin temperature signals were measured. State-of-the-art feature-based machine learning algorithms are investigated for cognitive workload characterization using learning curves, data augmentation, and cross-validation techniques. The best classification algorithm is selected, optimized, and the most informative features are selected. Finally, the generalization power of the optimized model is evaluated on an unseen test set. We obtain an accuracy level of 86% on the new unseen datasets using the proposed and optimized eXtreme Gradient Boosting (XGB) algorithm. Then, we reduce the complexity of the machine learning model for future implementation on resource-constrained wearable embedded systems, by optimizing the model and selecting the 26 most important features. Overall, a generalizable and low-complexity machine learning model for cognitive workload detection based on physiological signals is presented for the first time in the literature.