Research On Path-based Multiclass Multicriteria Traffic Assignment Problem With A Continuous Distribution

User Equilibrium(UE),the result of traffic assignment models,is one of the main methods for estimating and predicting travelers’ route choices on road networks.The traffic assignment model requires less input information,the output is stable,and it is able to solve large-scale problems.The algorithms for solving traffic assignment problems can be classified into link-based,path-based and bush-based algorithms according to the degree of decomposition of the network topology,and different algorithms are derived from models with different expressions.The infinite dimensional multi-class multi-criteria traffic assignment problem is an extension of the standard traffic assignment problem,in which the homogeneity assumption in the standard traffic assignment problem is relaxed and travelers use multiple criteria such as time,money,etc.to inscribe a generalized cost to measure their cost of travel,and travelers view these criteria with different degrees of importance.If coefficients are used to portray the importance of different criteria,then in an infinite dimensional problem,the coefficients can be portrayed using a continuous distribution.To facilitate the study,this study assumes that the O-D pair demand is fixed and the link cost is divisible.Considering the two criteria of time and money and using the time-equivalent value of money(TEM)value to portray people’s weight on the two criteria,the traveler’s cost on the path can be viewed as a linear combination of time and money.We also call this problem the continuous bi-criteria traffic assignment(C-BiTA)problem,which aims to find the distribution of travelers with heterogeneous preferences in the network,where travelers can be viewed as playing a congestion game.First,I analyze and integrate the existing research in this direction(Chapter 1),and review the bi-criteria traffic assignment problems into discrete and continuous problems.In fact,the difficulty and key point of modeling and solving continuous problems is how to find the endogenous relationship to finitely split the continuous distribution.Existing research on the C-BiTA problem is mainly conducted at the model level,and little research has been done on the algorithm,and the FW algorithm is mainly used for solving the C-BiTA problem.Further,I effectively integrate the background knowledge required to model the C-BiTA problem(Chapter 2)by first introducing the basic concept definitions and important properties at the optimization theory level and the network construction level,further introducing the standard traffic assignment model and algorithms,then extending to the multi-class multicriteria problem formulation in existing studies,and finally describing the key problems in solving the C-BiTA problem.The algorithm is able to find the efficient paths that lie on the Pareto frontier among all O-D pairs from an origin to all destinations at a certain amount of time and money level,and the algorithm is constructed with the help of the network simplex method,which improves the efficiency of the algorithm and also lays the foundation for solving the C-BiTA problem efficiently.The existing C-BiTA model is mainly constructed for link volumes,while in this study,the C-BiTA problem is viewed from the path perspective.In Chapter 3,since there exists a fixed ordering of the monetary cost of each path connecting an O-D pair,it is observed that the travelers who choose each path are divided by the inverse monetary cost order and form the feature of path division boundaries,I use the path division TEM boundaries boundaries to model the C-BiTA problem,and the constraint then inscribes the relative size relationship of the boundary values.Subsequently,the equivalence of the boundary-based model and the C-BiTA equilibrium condition is proved,and the model is further decomposed by O-D pairs and then by a single-boundary value,and the decomposed subproblem can be regarded as moving the current boundary under the condition of fixing the adjacent boundary values to make the objective function fall,so the single-boundary adjustment(SBA)algorithm is constructed based on the principle of gradient projection.This chapter further provides the derivation of the algorithm methodologies,process explanation,convergence proof,etc.,and uses a small case to explain the model and algorithm process.In Chapter 4,I construct a model based on path flow to find a suitable form to portray the total money cost part of the objective function and provide an explanation of the physical meaning of the money part of the objective function.Using a similar approach as in Chapter 3,I decompose the problem into O-D pairs,and then use the reference path to remove the flow conservation constraint to derive the flow adjustment(FA)algorithm form,and further provide the algorithm process and case explanation.In Chapter 5,we compare the convergence of the SBA and FA algorithms with the existing FW algorithm for two models and two corresponding algorithms,based on path division TEM boundaries and path flow,and discuss the impact of the number of toll links,magnitude of tolls,demand and PDF distribution type on the algorithm and equilibrium results.For example,we find that in solving a large network such as Chicago regional,FW takes more than 24 hours to reach the relative error of 10-4(which is considered to be an allocation result that can be used for practical applications,such as making decisions for infrastructure construction),while the SBA and FA algorithms achieve that accuracy in less than two hours.Experiments show that C-BiTA poses a greater computational challenge than the standard assignment problem,and in addition,solving the C-BiTA problem becomes more time-consuming when(ⅰ)more links of the network are affected by monetary costs,(ⅱ)the magnitude of the monetary costs of the links increases,and(ⅲ)the network becomes more congested.