Speed Curve Optimization for Virtual Coupling Operation of Multiple Trains Based on an Improved Interior-Point Algorithm

The concept of Virtual Coupling improves the utilization of transportation infrastructure capacity and train operation efficiency. This study proposes a speed curve optimization model for the Virtual Coupling operation of multiple trains, focusing on energy consumption, running time, tracking capability, and service quality. Different objectives and constraints for the leading and following trains are presented, respectively. An improved interior-point algorithm is designed with an adaptive update strategy, which realizes accelerated convergence and improves computational efficiency. This algorithm integrates an inertia correction strategy to deal with non-convex issues. Finally, the viability and effectiveness of the proposed model and improved algorithm are demonstrated by numerical examples based on real subway data. The results show that the model realizes the efficient operation of train formations, and the improved algorithm shows better performance than the conventional methods.