Train energy-efficient speed profile generation under various track alignments: a quantum evolutionary algorithm with cosine annealing

The optimization of train speed profiles is an effective method for reducing energy consumption and operating costs for urban rail transit (URT). In recent years, numerous intelligent optimization algorithms have been employed to generate high-quality solutions for speed profile optimization models. However, most previous studies preset the train operation sequence, overlooking the complex impacts of track alignment diversity on train operation modes. This limitation hinders the applicability of these findings across multiple inter-stations within the URT network. Moreover, there has been insufficient validation of the proposed optimization algorithms under diverse train operation scenarios. This study reformulates the generation of train speed profiles as a multi-stage decision-making problem within a continuous speed space. By applying the law of conservation of energy, a dynamic model of the train operation process is established and the decision evolution of the train speed is mapped into a high-dimensional quantum space. Subsequently, an improved quantum evolutionary algorithm with adaptive rotation strategies is designed using the cosine annealing function (CA-QEA). Furthermore, a conditional quantum collapse mechanism is introduced to enhance the global search capability of the algorithm. Utilizing actual URT data from Tianjin, China, three test scenarios featuring various track alignments, including gentle slopes, energy-saving slopes, and multiple continuous steep slopes, are constructed. The results demonstrate that the proposed method can effectively reduce the traction energy consumption (TEC) in three different track alignment. The Friedman non-parametric test results indicate that the performance of CA-QEA surpasses that of several mature intelligent optimization algorithms.