Towards the Solution of Large-Scale and Stochastic Traffic Network Design Problems

Abstract

This thesis investigates the second-best toll pricing and capacity expansion problems when stated as mathematical programs with equilibrium constraints (MPEC). Three main questions are rised: First, whether conventional descent methods give sufficiently good solutions, or whether global solution methods are to prefer. Second, how the performance of the considered solution methods scale with network size. Third, how a discretized stochastic mathematical program with equilibrium constraints (SMPEC) formulation of a stochastic network design problem can be practically solved. An attempt to answer these questions is done through a series ofnumerical experiments. The traffic system is modeled using the Wardrop’s principle for user behavior, separable cost functions of BPR- and TU71-type. Also elastic demand is considered for some problem instances. Two already developed method approaches are considered: implicit programming and a cutting constraint algorithm. For the implicit programming approach, several methods—both local and global—are applied and for the traffic assignment problem an implementation of the disaggregate simplicial decomposition (DSD) method is used. Regarding the first question concerning local and global methods, our results don’t give a clear answer. The results from numerical experiments of both approaches on networks of different sizes shows that the implicit programming approach has potential to solve large-scale problems, while the cutting constraint algorithm scales worse with network size. Also for the stochastic extension of the network design problem, the numerical experiments indicate that implicit programming is a good approach to the problem. Further, a number of theorems providing sufficient conditions for strong regularity of the traffic assignment solution mapping for OD connectors and BPR cost functions are given.

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