Convolutional neural networks (CNN) have been increasingly popular in image categorization in recent years. Hyperparameter optimization is a critical stage in enhancing the effectiveness of CNNs and achieving better results. Properly tuning hyperparameters allows the model to exhibit improved performance and facilitates faster learning. Misconfigured hyperparameters can prolong the training time or lead to the model not learning at all. Manually tuning hyperparameters is a time-consuming and challenging process. Automatically adjusting hyperparameters helps save time and resources. This study aims to propose an approach that shows higher classification performance than unoptimized convolutional neural network models, even at low epoch values, by automatically optimizing the hyperparameters of AlexNet and DarkNet19 with equilibrium optimization, the newest metaheuristic algorithm. In this respect, the proposed approach optimizes the number and size of filters in the first five convolutional layers in AlexNet and DarkNet19 using an equilibrium optimization algorithm. To evaluate the efficacy of the suggested method, experimental analyses were conducted on the pneumonia and COVID-19 datasets. An important advantage of this approach is its ability to accurately classify medical images. The testing process suggests that utilizing the proposed approach to optimize hyperparameters for AlexNet and DarkNet19 led to a 7% and 4.07% improvement, respectively, in image classification accuracy compared to non-optimized versions of the same networks. Furthermore, the approach displayed superior classification performance even in a few epochs compared to AlexNet, ShuffleNet, DarkNet19, GoogleNet, MobileNet-V2, VGG-16, VGG-19, ResNet18, and Inceptionv3. As a result, automatic tuning of the hyperparameters of AlexNet and DarkNet-19 with EO enabled the performance of these two models to increase significantly.