Simultaneous Perturbation Stochastic Approximation Algorithm for Solving Stochastic Problems of Transportation Network Analysis

Abstract

Stochastic optimization has become one of the important modeling approaches in transportation network analysis. For example, for traffic assignment problems based on stochastic simulation, it is necessary to use a mathematical algorithm that iteratively seeks out the optimal, the suboptimal solution, or both, because an analytical (closed-form) objective function is not available. Therefore, efficient stochastic approximation algorithms that can find optimal or suboptimal solutions to these problems are needed. The method of successive averages (MSA), a well-known algorithm, is used to solve both deterministic and stochastic equilibrium assignment problems. As found in previous studies, the MSA has questionable convergence characteristics, especially when the number of iterations is not sufficiently large. In fact, the stochastic approximation algorithm is of little practical use if the number of iterations to reduce the errors to within reasonable bounds is arbitrarily large. An efficient method to solve stochastic approximation problems is the simultaneous perturbation stochastic approximation (SPSA), which can be a viable alternative to the MSA because of its proven power to converge to sub-optimal solutions in the presence of stochasticities and its ease of implementation. The performance of MSA and SPSA algorithms is compared for solving traffic assignment problems with varying levels of stochastic-ities on a small network. The utmost importance is given to comparison of the convergence characteristics of the two algorithms as well as to the computational times. A worst-case scenario is also studied to check the efficiency and practicality of both algorithms in terms of computational times and accuracy of results.

An Investigation of SPSA for Signal Timing Optimization at Isolated Intersections

“…Despite the SPSA-based traffic signal timing patent filed by Spall in 1995 [12], SPSA is receiving little if any attention by signal timing practitioners and product vendors. SPSA is rated highly by researchers of traffic demand matrices [13], traffic assignment [14], and traffic model calibration [15]. SPSA has been lauded by transportation researchers "for its proven performance and computational properties in large-scale problems" [16], and for its ability to "solve very large noisy problems in a computationally attractive fashion" [17].…”

Calibration of CORSIM models considering all model parameters simultaneously

“…The proposed calibration methodology is based on the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm [13,14], which has been proposed in the past for the calibration of microscopic traffic flow simulation models [11,12,[15][16][17][18]. Vehicular traffic systems modeled using microscopic traffic flow simulation models typically are characterized by a large number of parameters and stochasticities.…”

A secure and efficient inventory management system for disasters

“…The LM algorithm is a good choice for comparison with SPSA, as it appears to be the fastest method (up to ten to one hundred times faster than the standard back-propagation algorithms) for training moderate-sized feed forward neural networks. SPSA, on the other hand, has been successfully implemented for optimization in transportation network analysis problems (Ozguven and Ozbay, 2008). In the following subsections, we will show the comparative results of the proposed online control methodology based on these algorithms, namely the neural network approximation with Levenberg-Marquardt (LM) algorithm and SPSA algorithm.…”