The COVID-19 pandemic has shown the importance of using face masks, avoiding the spread of the virus, and preventing the infection of millions of people ^[1][2][1,2]. However, it is important to mention that various studies on its use were performed several years before the COVID-19 pandemic, where the importance and efficacy of its use to prevent other respiratory infections were demonstrated ^[3][4][3,4]. Two of the most widely used subsets of artificial intelligence related to face masks are deep learning (DL) and machine learning (ML). Different works on the detection of the facial mask using pre-trained models of convolutional neural networks can be found in ^[5][6][7][5,6,7], which allowed us to observe the potential of this technique in the detection and classification of facial masks ^[8][9][10][8,9,10]. In Ref. [11], the authors studied the architectures of different pre-trained models such as EfficientNet, InceptionV3, MobileNetV1, MobileNetV2, ResNet-101, ResNet-50, VGG16, and VGG19. Based on their study, they proposed a model for face mask detection based on MobileNetV2, applying data augmentation techniques to increase the number of images for the training phase. In Ref. [12], an application for mobile devices was developed to identify face masks using the Google Cloud ML API, while analyzing the progress of cloud technology and the benefits of machine learning. In Ref. [10], the authors developed five ML models for face mask classification. The developed models were Naïve Bayes (NB), Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF), and K-Nearest Neighbors (KNN). The test of the models was performed using 1222 images, where the results demonstrated the effectiveness of the DT over the other models. The use of neural networks is related to metaheuristics, which are utilized to find the optimal architectures that improve the results depending on the application for which the network is used [13]. Metaheuristics are a great option for finding optimal parameters in applications in different areas. These algorithms have been classified according to their inspiration: based on evolutionary algorithms, physics-based algorithms, and algorithms based on swarm intelligence ^[14][15][16][14,15,16]. Nature-inspired algorithms are mainly inspired by collective behavior, where the main characteristics of a particular species are analyzed and represented in a computational way to be used in solving complex problems in the search for optimal solutions ^[17][18][17,18]. In recent works, comparisons have been made between metaheuristics to compare the performances applied to find CNN hyperparameters. Some of these metaheuristics are grey wolf optimizer (GWO), whale optimization algorithm (WOA), salp swarm algorithm (SSA), sine cosine algorithm (SCA), multiverse optimizer (MVO), particle swarm optimization (PSO), moth flame optimization (MFO), and bat algorithm (BA), to mention a few. The authors have concluded the advantages of combining convolutional neural networks and metaheuristics for the search of hyperparameters ^[19][20][21][19,20,21]. These techniques have been combined to solve applications related to pattern recognition ^[19][22][23][19,22,23], image classifications ^[18][24][18,24], and medical diagnosis ^[21][25][26][21,25,26], among other applications.

Convolutional neural network hyperparameters are optimized by different nature-inspired algorithms ^[27][28][29][27,28,29]. The optimized hyperparameters are the number of convolutional layers, filters, fully connected layers, neurons, batch size, and epochs. The contribution of this woresearchk includes the optimal design of the convolutional neural network architectures to increase classification accuracy and its application to face mask classification: no mask, incorrect mask, and mask. Recent works applied to face mask classification based their model architectures on pre-trained models, which does not guarantee optimal architecture. As a novelty, this researchpaper proposed optimizing CNN architectures instead of basing them on other architectures. The optimal hyperparameters are found using four metaheuristics used in recent works to make a statistical comparison and analysis, providing better accuracy for face mask classification.

2. Convolutional Neural Networks Applied to Face Mask Classification

The optimal design of architectures and models has allowed the realization of important practical applications. In Ref. [30], optimal convolutional neural network architectures was designed to identify various types of damage on reinforced concrete (RC) to avoid further structure deterioration. The results achieved show good accuracy of six types of damage. The design of convolutional neural network architectures using a particle swarm optimization algorithm was proposed and applied to sign language recognition using three study cases of sign language databases: the Mexican Sign Language alphabet, the American Sign Language MNIST, and the American Sign Language alphabet [31]. In Ref. [32], the authors proposed face detection and face classification by developing adaptive sailfish moth flame optimization (ASMFO) to the parameter optimization using a deep learning approach. In Ref. [19], the authors analyzed the importance of the CNN hyperparameters, such as filters, kernel, epoch, batch size, and pooling size of the convolutional neural networks applied to classify human movements. They compared seven metaheuristic algorithms: GWO, WOA, SSA, SCA, MVO, PSO, and MFO, concluding the advantages of the metaheuristics to optimize the hyperparameters of CNNs. The results led the authors to the conclusion that the implementation of GWO achieved higher accuracy than the other metaheuristics. In Ref. [20], the authors proposed a PSO to determine optimal hyperparameters of convolutional neural networks. They used the simplest CNN model as a base: LeNet. Their results achieved better results when the PSO designed the CNN architectures. The results achieved by their study were obtained using MNIST, Fashion-MNIST, and CIFAR-10 datasets. In previous works ^[33][34][33,34], nature-inspired algorithms have optimized modular neural network architectures applied to human recognition using different biometric measures. In those works, comparisons using genetic algorithms (GAs) and swarm intelligence algorithms were performed, and significant evidence of the advantage of the swarm intelligence algorithms was proven. More recently, in [22], and based on the advantages offered by the swarm intelligence algorithms, the architecture of convolutional neural networks was optimized and applied to face recognition. Algorithms such as particle swarm optimization and grey wolf optimizer offer advantages when designing convolutional neural network architectures. It is important to mention that the databases used for this work were small, with 400 and 165 images. In Ref. [35], the non-optimized design of convolutional neural network architectures applied to the facial mask classification was performed, and the best architecture was implemented in a real-time system using a Raspberry Pi 4 in combination with a camera to obtain the image in real time. The Raspberry Pi 4 sends a signal through its GPIO Board, and a result is provided by lighting an LED. If the mask is correctly used, the green LED is turned on. If the mask is incorrectly used, the yellow LED is turned on, and if a mask is not used, the red LED is turned on.