Network design with an embedded traffic assignment (TA) to model user equilibrium principle, sometimes expressed as bi-level problems or mathematical programs with equilibrium constraints (MPEC), is at the heart of transportation planning and operations. For applications to large-scale multimodal networks with high dimensional decision variables, the problem is nontrivial. This paper proposes an efficient gradient estimation method called Iterative Backpropagation (IB), which exploits the iterative structure of the TA solution procedure and simultaneously calculates the gradients while the TA process converges. We apply the proposed approach to origin-destination (OD) estimation, an MPEC problem, of the Hong Kong multimodal network with 49,806 decision variables, 8,797 nodes, 18,207 links, 2,684 transit routes, and 165,509 OD pairs, among the largest networks ever solved for this type of problem. The calibrated model performs well in matching the link counts. The framework, even though applied to OD estimation in this paper, is applicable to a wide variety of optimization problems with an embedded TA model, opening up an efficient way to solve large-scale MPEC or bi-level problems.  

暂无