Breast cancer has become a common malignancy in women. However, early detection and identification of this disease can save many lives. As computer-aided detection helps radiologists in detecting abnormalities efficiently, researchers across the world are striving to develop reliable models to deal with. One of the common approaches to identifying breast cancer is through breast mammograms. However, the identification of malignant breasts from mass lesions is a challenging research problem. In the current work, we propose a method for the classification of breast mass using mammograms which consists of two main stages. At first, we extract deep features from the input mammograms using the well-known VGG16 model while incorporating an attention mechanism into this model. Next, we apply a meta-heuristic called Social Ski-Driver (SSD) algorithm embedded with Adaptive Beta Hill Climbing based local search to obtain an optimal features subset. The optimal features subset is fed to the K-nearest neighbors (KNN) classifier for the classification. The proposed model is demonstrated to be very useful for identifying and differentiating malignant and healthy breasts successfully. For experimentation, we evaluate our model on the digital database for screening mammography (DDSM) database and achieve 96.07% accuracy using only 25% of features extracted by the attention-aided VGG16 model. The Python code of our research work is publicly available at: https://github.com/Ppayel/BreastLocalSearchSSD.