Correct understanding of the characteristics of breast tumors is important to help identify cancer types, providing a more accurate diagnosis, and directing appropriate treatment. In this context, the objective of this work is to apply machine learning and deep learning methods to multiclass classification of genes associated with breast cancer, using gene expression databases, and to evaluate the predictive performance of the used methods. The dataset is obtained from the Gene Expression Omnibus repository and the pre-processing is performed especially to reduce its dimensionality, since it has a high number of variables. Thus, the Principal Component Analysis method is initially applied to reduce the data dimensionality. Next, machine learning methods, such as Logistic Regression, Support Vector Machine, and Random Forest, and deep learning models like Multilayer Perceptron (MLP) and Convolutional Neural Network (CNN) are applied. To improve the performance of the models, the Optuna library is used to optimize the hyperparameters values and the algorithms are then evaluated with and without this optimization method. The analyzes show that Logistic Regression and Support Vector Machine obtained high accuracy. Regarding the deep learning, the MLP and CNN models, especially when optimized with Optuna, also provided competitive results. The optimization process fitted key parameters such as the learning rate and the number of layers, obtaining significant performance improvements. The results show that hyperparameter optimization can improve classifier accuracy and help diagnose breast cancer subtype and clinical outcomes.