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Deep convolutional neural networks (DCNNs) have demonstrated promising performance in classifying breast lesions in 2D ultrasound (US) images. Exiting approaches typically use pre-trained models based on architectures designed for natural images with transfer learning. Fewer attempts have been made to design customized architectures specifically for this purpose. This paper presents a comprehensive evaluation on transfer learning based solutions and automatically designed networks, analyzing the accuracy and robustness of different recognition models in three folds. First, we develop six different DCNN models (BNet, GNet, SqNet, DsNet, RsNet, IncReNet) based on transfer learning. Second, we adapt the Bayesian optimization method to optimize a CNN network (BONet) for classifying breast lesions. A retrospective dataset of 3034 US images collected from various hospitals is then used for evaluation. Extensive tests show that the BONet outperforms other models, exhibiting higher accuracy (83.33%), lower generalization gap (1.85%), shorter training time (66 min), and less model complexity (approximately 0.5 million weight parameters). We also compare the diagnostic performance of all models against that by three experienced radiologists. Finally, we explore the use of saliency maps to explain the classification decisions made by different models. Our investigation shows that saliency maps can assist in comprehending the classification decisions. [ABSTRACT FROM AUTHOR]