Device-to-device-based heterogeneous cellular networks (HCNs) have received considerable attention recently. However, connectivity optimization is a challenging problem for the existing network architecture that remains open in the literature because it is affected by many uncertain real-life factors, such as locations of femtocell base stations (FemtoBSs), the trust relationships among user equipments (UEs), and the dynamic characteristics of spectrum. In this paper, we propose a connectivity optimization method that jointly considers the influence of these factors. In this method, we first build a new framework called the trusted device-to-device-based HCN to capture the stochastic characteristics of the above factors through three models: the dynamic FemtoBS employment architecture, the trust-based directed graph model, and the dynamic spectrum graph model. Based on this framework, we then formulate the connectivity optimization problem as the maximization of the average number of connected UEs in a given time by selecting the optimal FemtoBSs. Since the maximization problem is proven to be NP-hard, we propose three heuristic algorithms, namely, the simple greedy algorithm, the submodular greedy algorithm, and the particle swarm optimization based FemtoBSs selection algorithm to obtain the suboptimal solutions. The effectiveness of the proposed algorithms is justified through extensive simulations with differently parameterized factors.