Optimization Of Demand-response Container Train Timetables And Benders Decomposition

Inheriting the advantages of both railway transportation and container transportation,railway container transportation has huge development potential.It is an important task for railway container transportation organization to design reasonable timetables for container trains.Changing train service scheme per day is implemented.Designing the container train timetable not only requires the combination of the technical conditions of stations and the adjacent lines,but also the comprehensive consideration of the quantity and arrival times of container commodities.The schedule of trains should adhere to the characteristics of freight transportation.The matching relationship between container goods and container trains is considered from the aspects of both time and quantity.The integer programming models for the demand-response container train timetables are constructed,which integrate different factors such as stop planning,train overtakings and locomotive scheduling.An approach based on Benders decomposition is developed to solve these problems.The main contents are as follows:(1)The timetables of direct container trains is studied.A quadratic 0-1 programming model for optimization of train timetable is constructed with the minimum residence time of container goods set as the optimization goal.By linearizing the objective function and supplementing the corresponding inequalities,an equivalent 0-1 linear programming model is obtained.On account of the characteristics of the model,the Benders decomposition method is employed to solve the problem.The original problem is decomposed into the master problem of optimizing the train timetables,and the sub-problem of determining the assignment of container goods to trains.The cuts can be gradually obtained through solving the separated sub-problem.(2)The train timetable for loading and unloading containers on the way is performed.Considering the departure station,destination station and arrival time of each freight demand,a mathematical model for optimizing container train timetable is constructed with given skip-stop patterns.The model also considers the constraints such as the uniqueness of freight loading,the number of containers carried by train,the working time,and the departure interval.The model is solved by using Benders decomposition algorithm.Valid Inequalities are added to the master problem to avoid infeasible solutions,which improves the efficiency of the algorithm.(3)An integrated optimization method for container train timetable and stop planning is proposed.The analysis focuses on the correlation between stop plan and timetable,and the influence of changing stop planning on the demand assignment.With the goal of minimizing residence time and transportation time of container goods,the integrated optimization model for container train timetable and stop planning is built.The Benders decomposition algorithm is applied to the proposed model.The purpose of integrated optimizing train scheduling,stop planning and container cargo distribution is achieved.(4)The container train timetables on shared-use corridors are optimized.In the condition of shared-use corridors,the schedule of container trains is designed based on the fixed and unchanged passenger train timetable.Considering the constraints of container cargo arrival time,train overtakings,stop time and safety interval,an optimization model of container train schedule is established,Benders decomposition method is used to solve it.The genetic algorithm is designed to solve the master problem model containing a large number of integer variables.The obtained satisfactory solution is substituted into the sub-problem to generate the cut.The effectiveness of the proposed method is verified experimentally.(5)A collaborative optimization method for container train timetable and locomotives scheduling is postulated.Considering costs of container transportation and locomotive operating,an integrated optimization model for container train and locomotive scheduling is established.The Benders decomposition is involved.The original sub-problem is separated into three independent sub-problems to generate multiple non-aggregating cuts and add them to the master problem.The method can more effectively limit the solution space of the master problem,and the effectiveness is verified in numerical experiments.