Analysis of Gradient-Based Minimization with Finite Difference Method and Automatic Differentiation on Double-Lane Roundabout

Abstract

To ensure that the double-lane four-arm roundabout model can represent the real traffic performance, parameter estimation is carried out using two optimization approaches: partial exact gradient minimization via the Finite Difference Method and full exact gradient minimization via Automatic Differentiation, a built-in tool in MATLAB for machine learning applications. In the partial gradient approach, linear interpolation is applied to generate new data for the Finite Difference Method, due to the mismatch between data set sizes caused by varying time steps determined by the Courant-Friedrichs-Lewy (CFL) condition. To better reflect real traffic conditions, the model considers the entry and exit rates for both the inner and outer lanes. As a result, a total of sixteen parameters are estimated. Six pseudo-experiments are initially conducted for result analysis, acknowledging the potential non-uniqueness of the estimated parameters. Simulation results are evaluated based on two key criteria: computational time and accuracy. The partial exact gradient minimization shows strong accuracy but is time-consuming due to slower convergence. In contrast, the full exact gradient minimization demonstrates both faster convergence and higher robustness, making it more suitable for the fitting process when estimating a large number of parameters. Finally, the fitting process is successfully implemented, enabling the roundabout model to study the real traffic flow performance when actual Total Travel Time and Total Waiting Time data are available.