An augmented Lagrangian origin-based algorithm for link-capacitated traffic assignment problem

The origin-based algorithm is embedded into the augmented Lagrangian method for the link-capacitated traffic assignment problem. In order to solve the nonexistence problem due to the second partial derivatives of the augmented Lagrangian function at some specific points, the approximate expressions of the second partial derivatives are amended in the origin-based algorithm. The graph of last common nodes is developed on the basis of the restricted single-origin network. A method is proposed for finding n-1 last common nodes of the restricted single-origin network, resulting in computational complexity of O(n(2)) in finding last common nodes. Numerical analysis on the Sioux Falls network and Chicago Sketch network demonstrated the effectiveness and characteristics of the proposed algorithm. Copyright (c) 2014 John Wiley & Sons, Ltd.