Optimization And Case Study Of Transit Lines Based On Continuum Approximation

With the acceleration of the process of urbanization and motorization,the contradiction between the rapid increase in the number of car ownership and the limited capacity of urban roads has increased.Because of its high reliability,high traffic volume,and low utilization of urban road resources,large-capacity public transport has received attention from local governments and people’s love,setting off a construction boom.Under the premise of ensuring the completion of transit transportation requirements,it is particularly important to save the cost of users and operators to the utmost,and to optimize the layout of transit lines and headway.The key to the optimization of transit line is the setting of transit stations and the design of line’s headway.Among them,the influencing factors of station setting involve the macro,meso and micro levels.At the macro level,station setting should fully consider the land-use along the line,the convenience of transfer,and the demand for passenger flow in accordance with the requirements of the public transport network planning;at the meso level,the deployment of the station is related to its reasonable station distance and service radius;at the micro level,the establishment of station is closely related to the number of transit lines,which will stop at the station,the adjacent road sections and traffic conditions at the intersections.The methods of transit lines optimization include discrete modeling and continuous modeling.Although the former can take all factors above into account,it is difficult to obtain a global optimal solution.However,the continuous model can solve the deficiencies of the discrete model and has the advantages of low difficulty for giving global or local analytical solution.To solve the problem,this paper constructs a continuous model based on continuous approximation to optimize the transit line.In order to demonstrate the effectiveness of CA-based transit line optimization models in practical applications,constructing a discrete method based on continuous model to analyze the spatial offset effects of discrete results.The main research contents and conclusions are as follows:(1)From the perspective of travelers and transit operators,analyze the influencing factors of transit line costs,and build a transit line optimization CA-based model with station density function and headway as decision variables,and minimization of generalized system costs as the goal.Analytical solution of optimal station’s density and headway by using Lagrange Multiplier considering Karush–Kuhn–Tucker(KKT)conditions(2)Take Chengdu No.3 transit line(conventional transit)as an example,using the CA model constructed in the content(1)to obtain an optimization plan,and compare the gap between its system cost and actual plan to explore the possibility of optimization of the line.And then,the traffic travel/attracting demand of the line is adjusted in equal proportions.Using CA model to analyze the optimal schemes under the local bus and bus rapid transit(BRT).The research results show that: 1)The system cost can be saved by 12.37% through line optimization;2)When the demand for passenger flow on the line is 1.8 times the current status,it can be upgraded to the BRT mode.(3)Analyze the practical method of continuous model.A discrete method based on continuous scheme is constructed.Taking Chengdu No.3 transit line as an example,the influence of two typical discrete methods,namely the “integral endpoint” and “integral intermediate point” on the optimal scheme,is analyzed.Then,choose the discrete method with the least influence,and analyze the effect of single-station position offset impact analysis,the effect of station location offset analysis of different location attributes,impact analysis of sudden displacement of passenger flow station,and multi-station position shift analysis to discuss the impact of station location fine-tuning on the optimal plan.The results show that: 1)The two discrete methods both have less influence,which is less than 1%,on the optimal solution.The midpoint-based discrete method has the least impact on the optimal solution,and the system cost only increases by 0.6‰;2)The migration will increase the system cost,and is positively related to the offset distance,but its influence is less than 5‰;3)The impact of the offset of the intermediate station on the optimal scheme is greater than that of the first and the last station;4)The influence of the displacement of passenger demand mutation station on the optimal plan is greater than that of the ordinary station;5)The impact of short-distance offset of multiple stations is greater than that of single-station long-distance.The research results show that the design of transit line optimization CA model has a high degree of robustness,and in the implementation process,it is allowed to adjust the specific station location according to the actual conditions while still ensuring that the overall system performance is near the optimal value.