Software defect prediction plays an important role in software quality assurance. However, the performance of the prediction model is susceptible to the irrelevant and redundant features. In addition, previous studies mostly regard software defect prediction as a single objective optimization problem, and multi-objective software defect prediction has not been thoroughly investigated. For the above two reasons, we propose the following solutions in this paper: (1) we leverage an advanced deep neural network-Stacked Contractive AutoEncoder (SCAE) to extract the robust deep semantic features from the original defect features, which has stronger discrimination capacity for different classes (defective or non-defective). (2) we propose a novel multi-objective defect prediction model named SMONGE that utilizes the Multi-Objective NSGAII algorithm to optimize the advanced neural network-Extreme learning machine (ELM) based on state-of-the-art Pareto optimal solutions according to the features extracted by SCAE. We mainly consider two objectives. One objective is to maximize the performance of ELM, which refers to the benefit of the SMONGE model. Another objective is to minimize the output weight norm of ELM, which is related to the cost of the SMONGE model. We compare the SCAE with six state-of-the-art feature extraction methods and compare the SMONGE model with multiple baseline models that contain four classic defect predictors and the MONGE model without SCAE across 20 open source software projects. The experimental results verify that the superiority of SCAE and SMONGE on seven evaluation metrics.