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An ideal synthetic population, a key input to activity-based models, mimics the distribution of the individual- and household-level attributes in the actual population. Since the entire population's attributes are generally unavailable, household travel survey (HTS) samples are used for population synthesis. Synthesizing population by directly sampling from HTS ignores the attribute combinations that are unobserved in the HTS samples but exist in the population, called 'sampling zeros'. A deep generative model (DGM) can potentially synthesize the sampling zeros but at the expense of generating 'structural zeros' (i.e., the infeasible attribute combinations that do not exist in the population). This study proposes a novel method to minimize structural zeros while preserving sampling zeros. Two regularizations are devised to customize the training of the DGM and applied to a generative adversarial network (GAN) and a variational autoencoder (VAE). The adopted metrics for feasibility and diversity of the synthetic population indicate the capability of generating sampling and structural zeros -- lower structural zeros and lower sampling zeros indicate the higher feasibility and the lower diversity, respectively. Results show that the proposed regularizations achieve considerable performance improvement in feasibility and diversity of the synthesized population over traditional models. The proposed VAE additionally generated 23.5% of the population ignored by the sample with 79.2% precision (i.e., 20.8% structural zeros rates), while the proposed GAN generated 18.3% of the ignored population with 89.0% precision. The proposed improvement in DGM generates a more feasible and diverse synthetic population, which is critical for the accuracy of an activity-based model.