Finding the I mu-user Equilibrium Solution Using an Augmented Frank-Wolfe Algorithm

Abstract

The Frank-Wolfe algorithm has been extensively adopted in recent decades to solve the user-equilibrium problem because of its simple structure and low memory requirements. However, Dial observed that the results obtained by the Frank-Wolfe algorithm differed markedly from the B algorithm of Dial in terms of link flows, and the results obtained via Frank-Wolfe algorithm could be incorrect. This study attempts to provide a clear example showing that the Frank-Wolfe algorithm has difficulty in achieving an I mu-user equilibrium state when I mu is sufficiently small. An Augmented Frank-Wolfe algorithm is presented that overcomes the weaknesses of the conventional arc-based Frank-Wolfe algorithm.