This research presented a hybrid methodology for feature selection aimed at predicting breast cancer, which integrated Genetic Algorithm (GA) and Simulated Annealing (SA) with various machine learning classifiers. The dataset underwent pre-processing that included standardizing features and encoding the target variable. GA was utilized to generate and optimize feature subsets based on classification accuracy, specifically using XGBoost. Subsequently, SA was applied to further refine the selected feature subset. The chosen features were then deployed to train and evaluate a range of models, such as XGBoost, Random Forest, Logistic Regression, SVM, K-Nearest Neighbors (KNN), Gradient Boosting, AdaBoost, and ExtraTrees. The performance of each model was measured using accuracy and ROC-AUC metrics. Logistic Regression has been performed well, achieved an accuracy of 0.9825 and a ROC-AUC score of 0.9971. To enhance interpretability, SHAP (SHapley Additive exPlanations) was applied to XGBoost, providing visual insights into the importance of features. Overall, the results indicated that the hybrid approach combining GA and SA significantly enhanced the accuracy of breast cancer classification through effective feature selection.