Previous methods of designing a bolt supporting network, which depend on engineering experiences, seek optimal bolt supporting schemes in terms of supporting quality. The supporting cost and time, however, have not been considered, which restricts their applications in real-world situations. We formulate the problem of designing a bolt supporting network as a three-objective optimization model by simultaneously considering such indicators as quality, economy, and efficiency. Especially, two surrogate models are constructed by support vector regression for roof-to-floor convergence and the two-sided displacement, respectively, so as to rapidly evaluate supporting quality during optimization. To solve the formulated model, a novel interactive preference-based multiobjective evolutionary algorithm is proposed. The highlight of generic methods which interactively articulate preferences is to systematically manage the regions of interest by three steps, that is, "partitioning-updating-tracking" in accordance with the cognition process of human. The preference regions of a decision-maker (DM) are first articulated and employed to narrow down the feasible objective space before the evolution in terms of nadir point, not the commonly used ideal point. Then, the DM's preferences are tracked by dynamically updating these preference regions based on satisfactory candidates during the evolution. Finally, individuals in the population are evaluated based on the preference regions. We apply the proposed model and algorithm to design the bolt supporting network of a practical roadway. The experimental results show that the proposed method can generate an optimal bolt supporting scheme with a good balance between supporting quality and the other demands, besides speeding up its convergence.