Virtual Coupling-Enabled Trajectory Optimization for Heavy-Haul Train Group: A Goal-Oriented MADDPG Approach

The virtual coupling-based train group operation presents promising prospects to enhance the capacity of freight railways. Adopting a leader-follower control mechanism enables coordinated multi-train operations. However, inhomogeneous environmental disturbances demand-optimized group-level operational states and trajectories during emergencies, particularly on heavy-haul lines. This paper addresses this challenge by developing a mixed-integer quadratic programming (MIQP) model that incorporates safety constraints, train dynamics, speed limits, and tracking interval requirements. A goal-oriented reinforcement learning method based on Multi-Agent Deep Deterministic Policy Gradient (GO-MADDPG) is proposed to achieve the train group's safe, efficient, energy-saving, and stable trajectories. Agents output continuous acceleration and deceleration control actions, while a cooperative collision avoidance mechanism and action masking ensure both safety and feasibility. Numerical experiments demonstrate that the proposed method can efficiently derive efficiency-enhanced solutions within short computation times.