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Voice analysis and classification for biomedical diagnosis purpose is receiving a growing attention to assist physicians in the decision-making process in clinical milieu. In this study, we develop and test deep feedforward neural networks (DFFNN) to distinguish between healthy and unhealthy newborns. The DFFNN are trained with acoustic features measured from newborn cries, including auditory-inspired amplitude modulation (AAM), Mel Frequency Cepstral Coefficients (MFCC), and prosody. The configuration of the DFFNN is optimized by using Bayesian optimization (BO) and random search (RS) algorithm. Under both optimization techniques, the experimental results show that the DFFNN yielded to the highest classification rate when trained with all acoustic features. Specifically, the DFFNN-BO and DFFNN-RS achieved 87.80% ± 0.23 and 86.12% ± 0.33 accuracy, respectively, under ten-fold cross-validation protocol. Both DFFNN-BO and DFFNN-RS outperformed existing approaches tested on the same database.