Adaptive Partial Train Speed Trajectory Optimization

Abstract

Train speed trajectory optimization has been proposed as an efficient and feasible method for energy-efficient train operation without many further requirements to upgrade the current railway system. This paper focuses on an adaptive partial train speed trajectory optimization problem between two arbitrary speed points with a given traveling time and distance, in comparison with full speed trajectory with zero initial and end speeds between two stations. This optimization problem is of interest in dynamic applications where scenarios keep changing due to signaling and multi-train interactions. We present a detailed optimality analysis based on Pontryagin’s maximum principle (PMP) which is later used to design the optimization methods. We propose two optimization methods, one based on the PMP and another based on mixed-integer linear programming (MILP), to solve the problem. Both methods are designed using heuristics obtained from the developed optimality analysis based on the PMP. We develop an intuitive numerical algorithm to achieve the optimal speed trajectory in four typical case scenarios; meanwhile, we propose a new distance-based MILP approach to optimize the partial speed trajectory in the same scenarios with high modeling precision and computation efficiency. The MILP method is later used in a real engineering speed trajectory optimization to demonstrate its high computational efficiency, robustness, and adaptivity. This paper concludes with a comparison of both methods in addition to the widely applied pseudospectral method and propose the future work of this paper.

Integrated optimisation model for neutral section location planning and energy‐efficient train control in electrified railways

“…This model has non‐linear relationship between speed‐related variables on each distance interval for both directions, as a result, SOS2 (special ordered sets of type 2) is employed to realise the piecewise linear. SOS2 is a method proposed by IBM and is used in many other proposed models [25, 26]. The maximum train speed is set at 80 m/s (288 km/h).…”

“…Non‐linear programming methods based on the closed‐form expressions for optimal train control problem was proposed in [14] and more complex problems including train scheduling and controlling of leader–follower train pairs. In [25], a distance‐based mixed‐integer linear programming (MILP) model has once been applied to adaptive train trajectory optimisation problem, the results of which are compared and contrasted with the results obtained from the PMP. In addition, an integrated MILP model combining both train operation and on‐board energy storage management was proposed in [26].…”

Multi-Objective Shark Smell Optimization Algorithm Using Incorporated Composite Angle Cosine for Automatic Train Operation

“…Automatic train operation (ATO) target velocity trajectory optimization is a practical multiple optimization problem for railway transportation, the multiple performance indicators such as energy consumption, parking punctuality, comfort, accurate parking, and so on. Of particular note is the increasing energy demand, thus energy-saving is becoming a research hot spot in automatic train operation [2]. Many researchers' studies about energy efficiency or energy-saving have been proposed in recent literatures [3][4][5][6].…”

Computational load reduction of the agent guidance problem using Mixed Integer Programming

“…However, recent research on agent trajectory planning [1][2][3][4][5][6][7][8][9][10] shows that it is still possible to use linear programming subject to integer variables constraints to optimize the trajectory of an agent in such an environment. We use mixed-integer linear programming with the assumption that the totality of space available should not be considered as a valid possibility for an agent in a trajectory optimization problem at any and every moment.…”