Origin-Based Partial Linearization Method for the Stochastic User Equilibrium Traffic Assignment Problem

Abstract

This paper proposes a modified origin-based partial linearization method for solving the logit-based stochastic user equilibrium traffic assignment problem formulated by a strictly convex minimization model in terms of origin-based link flows. As a feasible descent direction method, it first generates a feasible descent direction in terms of the origin-based link flows by Bell’s second logit-based stochastic network loading algorithm without path enumeration, and it proceeds to improve the descent direction according to the Fukushima’s strategy and the PARTAN technique which haven been successfully applied to accelerate convergence of the link-based Frank-Wolfe method for solving the deterministic user equilibrium traffic assignment problem. To tackle the numerical overflow or underflow issue of the exponential function calculation arising in the computerized logit-based stochastic network loading algorithms, this paper develops a scientific notation based engineering approach for large-scale problems. Two numerical examples are carried out to compare the proposed solution method with the conventional origin-based partial linearization method and the method of successive averages in computational time and accuracy of solution.