This paper proposes a multi-objective optimization-based approach to identify critical elements, including units and interactions within and between systems, in a high-speed train (HST). In the framework, network theory is used to model the HST as an interdependent machine-electricity-communication network (IMECN) composed of a machine network (MN), an electricity network (EN) and a communication network (CN). Cascading failure models for the subnetworks and IMECN, and topological and functional metrics for robustness are developed. We then formulate a multi-objective optimization model for maximizing the impact of the failure of critical elements on the topological and functional robustness of the IMECN and minimizing their number. We use NSGA-II to solve the optimization problem. Considering a practical HST as a case study, we apply the multi-objective optimization framework to search the groups of critical nodes, intra-links and inter-links. The results show that critical nodes, intra-links and inter-links of the IMECN are within the MN and CN. In particular, end nodes of the critical intra-links and inter-links may also be critical, and the critical elements of subnetworks tend to also be critical for the IMECN. In addition, we find that the critical nodes, intra-links and inter-links are not related to their topological importance.