A spectral clustering enabled SPSA algorithm for dynamic origin-destination demand matrix estimation

Abstract

The simultaneous perturbation stochastic approximation (SPSA) algorithm has been widely employed in the dynamic origin-destination demand estimation (DODE) problem. However, SPSA results in the inaccurate estimation of the dynamic OD matrices when the magnitudes of OD flows in the OD matrix are uneven. This paper proposes an enhanced SPSA algorithm, named SNMF-SPSA, to improve the estimation accuracy. The SNMF-SPSA algorithm innovatively leverages the potential spatial–temporal information in the dynamic OD matrices to guide the gradient approximation, without introducing substantial computational burden. Furthermore, the macroscopic fundamental diagram (MFD) is also considered in the objective function to capture the non-linear network traffic dynamics, thereby enhancing the estimation consistency. Two real urban networks with different scales were used to validate the performance of SNMF-SPSA. The results demonstrate that SNMF-SPSA can achieve the optimal result in fewer iterations, and the results of OD flows estimation are more accurate.

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