Simulation-based optimization of toll pricing in large-scale urban networks using the network fundamental diagram: A cross-comparison of methods

Simulation-based optimization (SO or SBO) has become increasingly important to address challenging transportation network design problems. In this paper, we propose solve two toll pricing problems with different levels of complexity using the concept macroscopic fundamental diagram (MFD NFD), where a large-scale simulation-based dynamic traffic assignment model Melbourne, Australia is used. Four computationally efficient SBO methods are applied and compared, including proportional-integral (PI) controller, regressing kriging (RK), DIviding RECTangles (DIRECT), simultaneous perturbation stochastic approximation (SPSA). The comparison reveals that these work equally well on simple problem without exhibiting significant performance differences. But, for complex problem, RK manifests itself be best-performing method thanks its capability filtering out numerical noise arising from computer simulations (i.e. allowing non-smoothness objective function). While PI controller more competitive solution given faster rate convergence, poor scalability in results limited applicability. Two caveats, however, deserve emphasis: (i) chosen critical density NFD does not necessarily represent robust control threshold, as it might shift presence pricing; (ii) re-interpolation required part order achieve global convergence.