Background noise is a critical issue for hearing aid device users; a common solution to address this problem is speech enhancement (SE). In recent times, a novel SE approach based on deep learning technology, called deep denoising autoencoder (DDAE), has been proposed. Previous studies show that the DDAE SE approach provides superior noise suppression capabilities and produces less distortion than any of the classical SE approaches in the case of processed speech. Motivated by the improved results using DDAE shown in previous studies, we propose the multi-objective learning-based DDAE (M-DDAE) SE approach in this study; in addition, we evaluated its speech quality and intelligibility improvements using seven typical hearing loss audiograms. The experimental results of our objective evaluations show that our M-DDAE approach achieved significantly better results than the DDAE approach in most test conditions. Considering this, the proposed M-DDAE SE approach can be potentially used to further improve the listening performance of hearing aid devices in noisy conditions.