With the advancement in the field of Artificial Intelligence, there have been considerable efforts to develop technologies for pattern recognition related to medical diagnosis. Artificial Neural Networks (ANNs), a significant piece of Artificial Intelligence forms the base for most of the marvels in the former field. However, ANNs face the problem of premature convergence at a local minimum and inability to set hyper-parameters (like the number of neurons, learning rate, etc.) while using Back Propagation Algorithm (BPA). In this paper, we have used the Genetic Algorithm (GA) for the evolution of the ANN, which overcomes the limitations of the BPA. Since GA alone cannot fit for a high-dimensional, complex and multi-modal optimization landscape of the ANN, BPA is used as a local search algorithm to aid the evolution. The contributions of GA and BPA in the resultant approach are adjudged to determine the magnitude of local search necessary for optimization, striking a clear balance between exploration and exploitation in the evolution. The algorithm was applied to deal with the problem of Breast Cancer diagnosis. Results showed that under optimal settings, hybrid algorithm performs better than BPA or GA alone.