In this article, an adaptive learning framework is established for a deep weighted sparse autoencoder (AE) by resorting to the multiobjective evolutionary algorithm (MOEA). The weighted sparsity is introduced to facilitate the design of the varying degrees of the sparsity constraints imposed on the hidden units of the AE. The MOEA is exploited to adaptively seek appropriate hyperparameters, where the divide-and-conquer strategy is implemented to enhance the MOEA's performance in the context of deep neural networks. Moreover, a sharing scheme is proposed to further reduce the time complexity of the learning process at the slight expense of the learning precision. It is shown via extensive experiments that the established adaptive learning framework is effective, where different sparse models are utilized to demonstrate the generality of the proposed results. Then, the generality of the proposed framework is examined on the convolutional AE and VGG-16 network. Finally, the developed framework is applied to the blind image quantity assessment that illustrates the applicability of the established algorithms.