Breast cancer is a very prevalent illness worldwide in which abnormal growth of breast tissue occurs, predominantly in women. Early diagnosis is of foremost importance for successfully treating this disease. However, traditional pathology tests typically consume a substantial amount of time and money. Hence, the automation of cancer classification through computer-aided deep learning techniques is imperative as it can significantly improve the efficiency of the process. Our study proposes an approach to efficiently classify histopathology images of breast tumor cells using ResNet50, a popular convolutional neural network (CNN), implemented for extracting deep features. Principal component analysis (PCA) is employed to reduce dimensionality, i.e., to reduce the feature space and its computational complexity. Feature optimization is performed via gray wolf algorithm, a nature-inspired optimizer well known for its novel population updating strategy. BreakHis, a well-studied dataset, has been used to assess the proposed methodology. The proposed model achieved a training and testing accuracy of 99.95% and 97.47%, respectively, throughout the experiment. The reported results are suggestive of the fact that this approach can be employed for precise categorization of breast cancer tissues from histology images.