Investigating the quality of SPSA and Spiess-like approaches forDynamic OD Matrix Estimation

Abstract

Dynamic OD Estimation is usually formulated as bi-level problem where the objective function can not be evaluated analytically and thus the formulation relies on non-differentiable optimization methods that usually pivot on evaluating the objective function. Among these methods, SPSA (Stochastic Perturbation Stochastic Approximation) method has been widely used because it is a derivative-free method that can easily incorporate non conventional inputs as travel times provided by emerging sensors exploiting Information and Communication Technologies (ICT) and it is not limited to the inputs from conventional traffic counts. Analytical approaches have been proposed for the static OD matrix estimation case and for the dynamic case. The authors have conducted numerical experiments with several SPSA approaches and a modified dynamic Spiess-like method and the results have been analyzed from two different perspectives: performance and solution quality. While the goal of the authors in the past has been to address the performance and behavior of the algorithms and their sensibility to the initial historical matrix in previous works, the aim this work relies on comparing the estimated matrix to the initial historic matrix using some similarity measures. This paper will report on the comparison results of the numerical experiments, their analyses, conclusions and further research.