A Smoothing Approach to the Optimisation of Traffic Networks
R. Connors (Institute for Transport Studies, University of Leeds, UK)
Transport planners routinely use mathematical models to predict the impacts of network improvements and policy interventions. Methodologies adopted in practice are those available in established software; for urban network analysis this continues to be User Equilibrium (UE).
Unfortunately, network optimisation with UE flows is a systematically non-differentiable problem, preventing application of gradient based methods. We consider a sequence of smoothed versions of the UE network optimisation problem, where successive iterations converge to the original non-smooth problem. We discuss this smoothing as a model of traveller behaviour, and connections with merit-function smoothing techniques for nonlinear complementarity problems.