W-SPSA : an Efficient Stochastic Approximation Algorithm for the off-line calibration of Dynamic Traffic Assignment models

Abstract

The off-line calibration is a crucial step for the successful application of Dynamic Traffic Assignment (DTA) models in transportation planning and real time traffic management. While traditional approaches focus on the separate or sequential estimation of demand and supply in a DTA system, a recently proposed framework calibrates the demand and supply models simultaneously by formulating the off-line calibration as a constrained optimization problem. Simultaneous Perturbation Stochastic Approximation (SPSA) has been reported in the literature to be the most suitable solution algorithm for this problem due to its highly efficient gradient estimation approach. However, it turns out that the performance of SPSA in terms of convergence rate and long run accuracy can deteriorate significantly when the physical network size and the number of considered time intervals increase. To overcome this problem, this thesis proposes a new algorithm, called Weighted SPSA, or W-SPSA. W-SPSA improves SPSA's gradient estimation process by effectively reducing the noise generated by irrelevant measurements. Synthetic tests are performed to systematically compare the performance of SPSA and W-SPSA. W-SPSA shows scalability and robustness in the tests and outperforms SPSA under different problem scales and characteristics. The application of W-SPSA in real world large-scale DTA systems is demonstrated with a case study of the entire Singapore expressway network. Results show that WSPSA is a more suitable algorithm than SPSA for the off-line calibration of large-scale DTA models. The contributions of the thesis include: 1) identifying limitations of a state-of-the- art solution algorithm for the DTA off-line calibration problem, 2) presenting rigorous definitions of an enhanced algorithm and proposing approaches to estimate the required algorithm parameters, 3) systematically comparing the performance of the new algorithm against the state-of-the-art, 4) demonstrating the characteristics of the new algorithm through experiments, and 5) discussing the general steps and empirical technical considerations when tackling real world DTA off-line calibration problems.