Gene expression data is very essential to breast cancer analysis. It gives information on the molecular mechanisms of different types of cancers. The approaches used to analyze the cancer data suffer from problems, such as high dimensionality, small sample sizes, noisy data, and class-imbalanced data. Traditional machine learning fails to properly select the most informative genes, which consequently results in lower accuracy and poor generalization. Moreover, in the case of limited information, deep learning techniques will suffer from overfitting and can be easily stuck in local minima during training. The more complex relationships between genes cannot be captured. These problems necessitate more complex techniques in order to efficiently deal with high dimensions without suffering from overfitting, underfitting, or suboptimal convergence. The proposed Hybrid Deep Neural Network with Attention-Based Feature Selection (HDNN-AFS) addresses these limitations by integrating a hybrid feature selection mechanism that combines Genetic Algorithm and Particle Swarm Optimization, and an attention-based feature fusion module for dynamic feature weighting. The architectures of the HDNN integrate CNN, Transformer, and Maxout layers into multiscale learning in order to more adequately model complex gene interactions as well as spatial expression patterns. An adaptive focal loss function can be effectively used in order to handle class imbalance. In addition, Bayesian optimization, along with transfer learning, helps to avoid overfitting to local minima for better performance. The model achieves a 98.7% accurate rate in classification and attains a minimum False Negative Rate (FNR) of 19.6% along with a True Positive Rate (TPR) of 97.8% for the classification of cancer.