Line Planning And Simultaneous Optimization With Differential Pricing Of High Speed Railway

Line plan determines the operating sections,stopping patterns and frequencies of the trains,which is one of the core problems of the product design of high speed railway.Differential pricing determines different prices for HSR transportation products,enriching the choices of travel paths for passengers.Both are an important part of the high speed rail passenger transportation product.Line plan is to provide transportation services to passengers of multiple ODs using the limited high speed rail transportation resources,which on one hand affects the efficiency of the railway operation and on the other affects the level of service to passengers.Therefore,in the design process of line planning,the accurate portrayal of passengers’ travel behavior is of great significance,which cannot be separated from the study of passenger assignment.For the simultaneous optimization of line plan and differential pricing,the problems that need to be solved include not only the stop patterns and frequencies,but also the differential fares paid by passengers of the same OD who choose different paths and travel on different trains.Therefore,it is a necessary means to improve railway passenger services and enhance the competitiveness of HSR in the passenger transportation market.At the same time,under the combined effect of line plan and differentiated prices,the attributes of the train service network are more complex,which places higher demands on the accurate portrayal of the travel behavior of passengers in the service network.Therefore,this paper starts with the issue of passenger assignment and then conducts a series of studies on the design of high speed railway line plan and its joint decision with differential pricing.This paper first focuses on a space-time-dimension-based approach to allocate passengers.Passenger travel behavior is studied from the two dimensions of spatial travel path selection and temporal travel demand arrival.Then a passenger assignment method based on space and time dimensions is proposed,also deconstructing the passenger assignment problem into two dimensions of passenger assignment strategy and passenger loading method.Passenger assignment strategy is to express passengers’ travel path selection behavior.Passenger loading method is the way to describe the priority of passengers’ travel demand when occupying transportation resources.In this paper,MNL models and user equilibrium are highlighted in the dimension of passenger assignment strategy.The loading order of OD importance,demand arrival order,and two loading granularities with different levels of fineness are discussed in the dimension of passenger loading method.On the basis of the space-time-dimension-based passenger assignment,this paper proposes a decision model for the core elements of the train line plan and constructs a design process for the line planning with passenger assignment as feedback.An improved particle swarm algorithm for solving the model is also proposed.The decision model of the core elements of the train line plan is based on a certain set of possible trains to solve the problems of the train operating sections,stopping patterns and frequencies.In the process of the improved particle swarm algorithm,the space-time-dimension-based passenger assignment method is used as a feedback to guide the updating of the line plan.And some of the constraints related to the frequencies of the trains in the model are transformed in the steps of particles’ initialization and updating.Finally,different kinds of space-time-dimension-based passenger assignment methods are used in the designing of the line plan.The impact of different passenger assignment strategies,passenger loading methods and their combinations is measured by comparing the results of the line plans.In order to make a simultaneous decision on the line plan and differential pricing,starting with passenger assignment,this paper proposes a differential pricing theory based on passenger flow distribution and a user equilibrium condition for high speed rail passengers based on price differences.A user equilibrium-based differential pricing and passenger assignment model is then built.And the Frank-Wolfe algorithm for price adjustment and passenger assignment is designed to solve the model.Finally,a simultaneous optimization model for the line plan and differential pricing is developed by combining the decision model for the core elements of the line plan with a user equilibrium-based differential pricing and passenger assignment model.The improved particle swarm algorithm combined with the Frank-Wolfe algorithm for price adjustment and passenger assignment together form the hybrid algorithm for solving the model.Finally,through small-scale calculations and real background cases,this paper verifies the validity and feasibility of the simultaneous optimization model and algorithm for the line plan and differential pricing and analyzes the impact of the key parameters.It is proved that the simultaneous optimization method for the line plan and differential pricing proposed in this paper can increase revenue and reduce operating costs of high speed railway while ensuring trains’ utility,thereby significantly improving the profit of the HSR operating department.