Exploring trust region method for the solution of logit-based stochastic user equilibrium problem

• Showing that the trust region Steihaug-Toint (TRST) algorithm is inappropriate.
• The proposal of the modified trust region (MTRN) algorithm.
• The proof of the convergence and superlinear convergence rate of MRTN.
• Implementation issue on computation of the trial step.
• The proposal of the basic route choice principle.

In this research paper, we explored using the trust region method to solve the logit-based SUE problem. We proposed a modified trust region Newton (MTRN) algorithm for this problem. When solving the trust region SUE subproblem, we showed that applying the well-known Steihaug-Toint method is inappropriate, since it may make the convergence rate of the major iteration very slow in the early stage of the computation. To overcome this drawback, a modified Steihaug-Toint method was proposed. We proved the convergence of our MTRN algorithm and showed its convergence rate is superlinear.For the implication of our algorithm, we proposed an important principle on how to select the basic route for each OD pair. We indicated that it is a crucial principle to accelerate the convergence rate of the minor iteration (i.e. trust region subproblem-solving iteration). In this study, other implication issues for the SUE problem are also considered, including the computation of the trial step and the strategy to ensure strict feasibility iteration point. We compared the MTRN algorithm with the Gradient Projection (GP) algorithm on the Sioux Falls network. Some results of numerical analysis are also reported.