Multi-system integration (e.g., high-speed rail, intercity rail, suburban rail, and metro) in regional rail transit has become an important strategy for enhancing regional travel quality. Nevertheless, optimizing line plans for such integrated networks remains a challenging task. Existing approaches are typically limited to dual-system integration and rely on pre-specified line pools, while often overlooking rolling stock heterogeneity. These limitations inevitably constrain the flexibility of stopping patterns and hinder the achievement of global cost optimality for the entire system. To address these challenges, this study proposes a comprehensive optimization framework for multi-system line plans. First, a hierarchical decoupling of the multi-system physical network is performed to identify candidate train service routes. Second, a deeply coupled network consisting of train service and passenger travel is developed. Subsequently, a multi-commodity flow model is established, incorporating critical constraints such as flexible stopping rules, rolling stock-system compatibility, and connecting line capacities. This framework integrates decisions regarding flow distribution, frequency, route design, stop patterns, and rolling stock assignment. Validated via a real-world case study using Gurobi, the results indicate that the through operation mode reduces operator costs by 20.4% and passenger costs by 6.5% compared to independent operations. This research offers a quantitative tool for developing coordinated plans that improve operator efficiency and passenger experience.
Lu et al. (Mon,) studied this question.