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.