Trajectory Optimization for Heavy Haul Train With Pneumatic Braking via QCMIP

Heavy haul train manipulation is extremely challenging due to cyclic pneumatic brake application and safe operation demand. To reduce the driving difficulties and enhance transportation efficiency, this article proposes a trajectory optimization method to conduct optimal speed profile with pneumatic brake application regimes. The discontinuous characteristics and safe guidelines of cyclic pneumatic brake application are fully included in trajectory optimal model to find out optimal brake regimes without stopping release, which ensures transportation efficiency to the largest extent. Integer variables and convex relaxation are introduced in optimal model construction process to linearize time-accumulated constraints of cyclic pneumatic brake application and regularize the nonconvex relationship between operation time and speed. With the aforementioned deduction and matrix construction, the trajectory optimization problem can be constructed as mixed integer programming model with quadratic constraints (QCMIP) and solved by mature solvers. Finally, simulation experiments with commercial freight line data are carried out to verify the effectiveness of the proposed optimal method. Comparisons with the piecewise affine (PWA) linearization method and dynamic programming (DP) method verify the superior performance of the proposed optimal method.