Study On Optimization Of Formation Plan Of Single Group Trains At Technical Service Stations By Using Lagrange Algorithm

Freight train formation plan, which can be called as train formation plan or formation plan, is an important part of science production management method of railway transportation. It is also a technical document of freight cars flow organization. An optimal freight train formation plan not only can well-organize the station’s work, but also lay the foundation of improving the level of the use of locomotives and freight cars. Therefore, well-making the freight train formation plan is an importation work for railway plan transportation, and accomplishing the work of organizing railway transportation is significant. The rain formation plan at technical service stations is an important part of the entire freight train formation plan, and train formation plan at technical service stations is composed with the formation plan of single group trains and the formation plan of multi-group trains. The research object of this paper is the former, formation plan of single group trains at technical service stations.The thesis research area of this paper is the national railway of China, and the optimization research is under the determinate condition of freight cars flow volume between technical service stations, freight cars flow running path, assembly parameter and so on. The research of this paper is on the base of lots of previous relevant research results, this paper translates the freight cars organization problem into the mathematical programming problem, and it establishes the organization model by using railway organization theory and optimization theory, then it solves this problem by using mathematical algorithm theory.The research contents of the thesis can be concluded as follows:(1) It elaborates the background and the meaning of formation plan of single group trains at technical service stations, and it respectively introduces the research situations in domestic and abroad.(2) It explains how to make the formation plan, including the formation plan of direct trains, the formation plan of trains at technical service stations, and the formation plan of trains within the district. It mainly elaborates the formation plan of single group trains at technical service stations.(3) It introduces the organization theory of formation plan of single group trains at technical service stations, and it respectively analyses three kinds of model of formation plan of single group trains, they are the linear 0-1 planning model, the quadratic 0-1 planning model and the linear integer planning model. At the meantime, it simply recommends the solving algorithm of these models, using the branch and bound method to solve the linear 0-1 planning model and using the Gomory cutting plane algorithm to solve the linear integer planning model. And it also recommends using the genetic algorithm to solve the quadratic 0-1 planning model.(4) It firstly explains the complexity of formation plan, and then it analyses the constraint which influents the formation plan. Also, it defines the decision variable and all the parameters, it establishes the optimization model of formation plan of single group trains at technical service stations by taking the minimization of assembly time and reorganization time as the objective function, and taking the reorganization ability, the number of shunting tracks, and the car flows joining as the constraints.(5) It explains the meaning of lagrange algorithm and it also introduces the functional form of lagrange algorithm. At the part of updating the lagrange multiplier, it introduces the subgradient algorithm. It also elaborates how to apply the lagrange algorithm into this paper’s model. At the part of calculating-example, it calculates the results of a simple railway network with eight technical service stations by using Matlab. It respectively calculates the results of formation plan with the constraints and without the constraints of reorganization ability and the amount of shunting tracks.This paper solves the optimization problem of formation plan of single group trains at technical service stations by using lagrange algorithm, and it also testifies the availability of lagrange algorithm. The goal of this paper is to offer a new perspective to solve the optimization problem of formation plan of single group trains at technical service stations at some extent.