Comparative Performance Analysis of Speed Trajectory Optimization Algorithms for Metro and High-speed Railways

With the increasing concerns about railway energy efficiency, researchers have developed various approaches to optimize train trajectories for energy savings. However, these methods often rely on different models, and most studies validate their effectiveness on a single type of railway system, making it challenging for readers to compare them effectively. To address this, our paper introduces a novel comparative framework that evaluates three distinct optimization methods: nondominated sorting genetic algorithm (NSGA-II), convex optimization (CO), and mixed integer linear programming (MILP). We develop a continuous train trajectory optimization model, tailored to each method. Comprehensive asymptotic analyses of the computational complexity for NSGA-II and CO are performed, along with an in-depth examination of MILP’s NP-hard problem complexity. Additionally, we analyze the distinct characteristics of metro and high-speed railways to assess the applicability and performance of these methods under varied operational conditions. Our comparative analysis reveals that while all methods effectively achieve significant energy savings, they display distinct profiles in terms of computational demand and operational stability. These differences are crucial for practitioners when selecting the most appropriate method for specific railway research and operational needs.