Train Trajectory Optimization with Random Initial States under Multiple Constraints

In urban rail transit, the train trajectory is a set of the operational conditions, including acceleration, cruising, coasting, and deceleration, that capture the dynamics of the train’s movement. The train trajectory optimization problem aims at searching an optimal combination of the operational conditions and thus improving the energy efficiency of the whole operation process. It is difficult to obtain the optimal solution of train trajectory optimization by traditional methods because the train operation is a multi-state procedure and suffers to multiple constraints. In this paper, railway line division rules in both micro and macro scopes are presented for quickly generating the train trajectory under multiple constraints, which fits the actual situation of the line better. Furthermore, the Elitist Non-Dominated Sorting Genetic Algorithm (NSGA-II) is used to automatically determine the number and location of coasting points under multiple constraints of the speed limits, grade profiles and curve radius, which is more suitable for solving train trajectory optimization than traditional cases. Finally, some experiments results are given to demonstrate the effectiveness of the proposed searching algorithm by a better performance upon the optimization of energy-efficient train trajectory.