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

Stochastic optimization has become one of the important modeling approaches in the 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 and/or suboptimal solution because an analytical (closed-form) objective function is not available. Therefore, there is a need for efficient stochastic approximation algorithms that can find optimal and/or suboptimal solutions to these problems. Method of Successive Averages (MSA), a well-known algorithm, is used to solve both deterministic and stochastic equilibrium assignment problems. As stated in previous studies, MSA has questionable convergence characteristics, especially when number of iterations is not sufficiently large. In fact, 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 MSA due to its proven power to converge to suboptimal solutions in the presence of stochasticities and its ease of implementation. In this paper, we compare the performance of MSA and SPSA algorithms for solving traffic assignment problem with varying levels of stochasticities on a small network. The outmost importance is given to comparison of the convergence characteristics of two algorithms as well as 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. INTRODUCTION A problem of great practical importance in transportation engineering field is the problem of stochastic optimization and approximation. Many problems in this field can be expressed as finding the setting of certain adjustable parameters so as to minimize an objective function. Most of the real world problems of this kind have to be considered as stochastic optimization problems to capture random nature of real-world occurrences. To make this discussion more concrete, consider the problem of setting traffic light timing schedules to minimize the total time spent by vehicles in that area waiting at intersections during rush hour (1). Typically, the aim is to minimize the objective function, like the average total delay time in signal timing problem (2). Stochastic optimization and approximation techniques are discussed by Spall (3), and Gelfand and Mitter (4) where a survey of several important algorithms is given. Early work in this field begins with the …