A methodology for solving the network toll design problem

Congestion pricing has been regarded as an efficient method to reduce network-wide travel cost. In this dissertation, a methodology for toll design is developed to provide policy-makers with suggestions on both where to charge tolls and how much the tolls should be. As opposed to the traditional approach of marginal social cost pricing, this methodology is capable of dealing with the more realistic case, in which only a small number of links can be tolled. Furthermore, this methodology is expanded to accommodate multiple user groups. The toll design problem can be formulated using both deterministic and stochastic route choice models. The most natural formulation of this problem in both cases is a bilevel formulation. Such formulations are very difficult to solve because of the nonconvexity and nondifferentiability of the constraint set. In this dissertation, the problem is converted into a single level, standard nonlinear optimization problem by making certain simplifying assumption. This single-level version of the toll design problem can be solved using a variety of well-developed algorithms. Tests show that this approach can be used to generate reasonable results and provide valuable decision support to policy-makers

Evaluation of advanced optimisation methods for estimating Mixed Logit models

The performances of different simulation-based estimation techniques for mixed logit modeling are evaluated. A quasi-Monte Carlo method (modified Latin hypercube sampling) is compared with a Monte Carlo algorithm with dynamic accuracy. The classic Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm line-search approach and trust region methods, which have proved to be extremely powerful in nonlinear programming, are also compared. Numerical tests are performed on two real data sets: stated preference data for parking type collected in the United Kingdom, and revealed preference data for mode choice collected as part of a German travel diary survey. Several criteria are used to evaluate the approximation quality of the log likelihood function and the accuracy of the results and the associated estimation runtime. Results suggest that the trust region approach outperforms the BFGS approach and that Monte Carlo methods remain competitive with quasi-Monte Carlo methods in high-dimensional problems, especially when an adaptive optimization algorithm is used