| China’s high-speed railway network has been continuously developed,and passenger transport capacity has gradually increased.As the operator of Chinese railway,China Railway Corporation is also seeking ways to further increase the profit of the passenger rail while realizing the railway’s public value.In the future,for the diverse passenger demand of different lines and different times,high-speed rail tickets will be discounted to increase the placing rate and passenger revenue will be a common means of sales.The issue of railway booking problem in the case of discounts is also a problem worth studying.Railway booking problem is a problem of how to set the maximum number of tickets sold in each route(OD)to increase ticket revenue under passenger demand.Base on the existing literature,the thesis proposes the research scenario of this paper:railway booking problem under the condition of multi-level fare,as known as discounts,and the situation of multiple trains with mutual substitution.The paper then analyzes the relevant theories of the railway booking problem,and points out the similarities and differences between the issue of aviation booking problem which is well studied and the railway booking problem.And then the thesis analyzes the characteristics of passenger demand with different attributes,and the different influences of different passenger demand on railway booking problem.Secondly,the thesis points out the necessity of the booking problem,and points out that reasonable booking scheme can improve the income of passenger rail.Then thesis claims that different booking scheme will result in different revenues while multiple trains which are alternative to each other have different skip-stops.Finally,claims the impact of different booking scheme on railway booking problem under multi-level fare conditions.The thesis constructs a nonlinear integer programming model and related constraints for the problem in order to solve the problem based on the existing literature,makes mathematical description of practical problem.Due to the structural characteristics of the model,exact algorithms are ineffective in solving the problem,the paper uses particle swarm optimization algorithm which has characteristic of better global searching ability to solve the problem.In the process of particle swarm optimization,the initial solution has a great influence on the algorithm.In order to obtain the initial solution of the algorithm,the paper analyzes the model and processes the nonlinearity and integerity of the model to obtain the initial solution of the particle swarm algorithm.Based on the research problem,the paper constructs examples of different scales for analysis.For the integral calculation process in the algorithm implementation process,the paper compares four different implementation methods based on Python language,and compares its calculation accuracy,computational efficiency and computational resources,and comprehensively selects the most suitable calculation method.In the solution process of the small-scale example,the algorithm obtains the result through the calculation time of 24s.The small-scale example has four stations A,B,C,D and four trains.Taking train 4 as an example,all tickets assigned to OD(A,B)are discounted tickets,totaling 396;all tickets assigned to(A,C)are full-price tickets,totaling 164;and all tickets assigned to(B,C)、(B,D)、(C,D)are full-price tickets,364,32 and 382,respectively.The results conform to the model constraints.The calculation results show that the GAP of the algorithm is less than 5%,and the solution quality is stable under different parameters.The correctness of the model and the validity of the algorithm are verified.A large-scale numerical examples are set up based on actual data.In the solution process of large-scale example,the calculation time of the algorithm is 105s.The calculation results show that the GAP of the algorithm under different parameters is less than 5.5%,and the solution quality is stable.At the end of the paper,the performance analysis of the related parameters affecting the performance of the algorithm is carried out.The numerical experiments show the correctness and validity of the design idea of the algorithm. |
