Incorporating an Adaptive Adjusting Scheme into Method of Successive Averages for Solving Stochastic User Equilibrium Problem

Abstract

The method of successive averages (MSA) is the most widely used algorithm for solving the stochastic user equilibrium (SUE) problem. It avoids the step size optimization subproblem by using a predetermined step size sequence. However, as is known, its convergence in the latter iterations is quite slow. In this study, we develop an adaptive adjusting scheme to enhance the computational efficiency of the MSA. The features of the proposed scheme are twofold: (1) The step size is adjusted according to the current and previous iterative solutions. Thus, the iterative information is more fully used to determine the step size. In contrast, the step sizes in the MSA are independent of the iterative information. In addition, the step size sequences from the proposed adaptive adjusting scheme satisfy the Blum theorem, which guarantees its convergence. (2) Similar the MSA, the objective function is not used in this scheme, making it useful for solving other more advanced forms of traffic assignment problems (e.g., variational inequality, fixed point problem). Finally, numerical examples on several large-size realistic networks are provided to demonstrate the efficiency of the proposed scheme.