Investigating Path-Based Algorithms For Logit Stochastic User Equilibrium Problem

Logit based Stochastic User Equilibrium (SUE) model is widely used in transportation planning. This model has simple structure. It can be explicitly formed and well explained. Therefore, it has received great attention in the research community. This dissertation investigates path-based algorithms for Logit SUE model in urban transportation networks. Gradient Projection (GP) method is one of the most efficient algorithms that currently exist for the model. In order to solve the Logit SUE model more efficiently, this dissertation proposes 4 new methods. The main research contents and results are as follows:(1) A two level partial linearization method is proposed. This method consists of two phases:The outer level iteration phase applies a second order partial linearization method to the Logit SUE model, and creates a linearly-constrained entropy maximization subproblem with quadratic cost. The inner level iteration phase uses a first order partial linearization method to solve the subproblem approximately. According to different characteristics of the outer and inner phase, different step size rules are chosen, which improves the computation efficiency.(2) A dual method is proposed. This method transforms the Logit SUE model to its dual, and uses a scaled steepest ascend method to solve the dual problem.(3) A modified truncated Netwon method is proposed. In this method, the search direction is generated by solving the reduced Newton equation inexactly, and the step size is chosen according to the Armijo rule. During the iterative process, the reduced variable can be changed from one iteration to the other.(4) It is shown that the well-known Steihaug-Toint method is inappropriate to solve the trust region SUE subproblem, and a modified trust region Newton method is proposed. This method determines the search direction and the trial step in sequential order (not at the same time), which overcomes the drawback of the Steihaug-Toint method method.In this dissertation, the convergence and convergence rate of the newly proposed methods are analyzed in detail. Numerical results indicate that each of the proposed methods has specific features, and outperforms GP method in some aspects. Therefore, this dissertation provides new insights and perspectives for Logit SUE model. The research results have both theoretical value and practical signifcance.