Multi-objective Trajectory Optimization For Freight Trains

Rail freight has the advantages of low cost,large volume,safety and reliability,and has become one of the main development directions of railway transportation in modern countries.The future freight railway system,especially freight trains,will be more automated and intelligent.Trajectory optimization for freight trains is a key technology for intelligent train equipment such as advisory driving and automatic driving systems.It aims to optimize train speed and control trajectories,which can effectively improve the quality of railway operation services,including enhancing safety,improving driving smoothness,reducing energy consumption,and promoting punctuality.Therefore,this dissertation focuses on the multiobjective trajectory optimization for freight trains,and generates driving trajectories and optimization algorithms,which are of great significance to the high-efficiency and sustainable development for freight railways.First of all,based on the theoretical basis of train traction calculation and existing train models,this paper analyzes the forces of the train in the journey,and the energy consumption calculation methods and operation constraints are summarized and expanded.Then,a continuous-time model of multi-objective trajectory optimization for freight trains is established.The evaluation function is based on the energy consumption,desired speed tracking and the change in train forces,and the constraints include external environmental constraints and the characteristics of the freight trains.By discretization and linear approximation,the proposed model is converted into a quadratic programming(QP)problem with sparse matrix which can be solved rapidly and robustly,and a weight selection algorithm based on the desired speed is designed to meet the travel time in a single section,saving the need for manual parameter selection.A mathematical derivation is made for explaining the deviation of the optimization speed from the predefined desired speed in the case of constant driving,and corrected desired speeds are obtained,thereby eliminating the speed deviation in constant driving.Then,taking into account that running time is a high-order nonlinear function of the train speed,a multi-objective optimization model reconstruction based on mixed-integer quadratic programming(MIQP)is carried out,which solves the problem that QP cannot handle the multi-section travel constraints for freight trains.The multi-section trajectory optimization model for freight trains is established considering multiple section travel time constraints.With the help of piecewise affine functions and propositional logic for linear approximation,logic variables and auxiliary continuous variables are introduced to restate the optimization problem as a mixed logic dynamic(MLD)model,which can be solved through MIQP.It also expands the derivation process for the linear expression of the piecewise affine function with many pieces to improve the applicability of the linear approximation to any nonlinear model.Finally,simulation verification using QP and MIQP is carried out based on actual operation environment: the Shuozhou-Huanghua railway line and a kind of freight train.The error by linear approximation for the nonlinear model is calculated,and the small difference proves the applicability of the model parameters.Then the single-and multi-section trajectory optimization are performed,and the differences in speed fluctuations and operation strategies between the proposed methods and the comparison data are analyzed from the global and local aspects.With the same journey time,the optimized trajectories obtained by the two methods are better than the actual operation data in terms of energy consumption(reduced by more than20%)and driving smoothness.In addition,MIQP can simultaneously optimize the trajectories and timetabling,further reducing the energy consumption.