Improvement of Convergence in Frank-Wolfe Algorithm for Large Size Networks

Frank-Wolfe algorithm is the most practiced algorithm adopted by the planners to solve the traffic assignment problem. The algorithm has the advantage of being simple and modest in memory usage, but has the disadvantage of slow convergence, which is more significant forlarge size networks. To improve its convergence, various modifications have been suggested by many researchers. In this paper, an attempt has been made to improve its convergence rate and also to obtain a better solution. For this, three line search methods, namely, Bisection, Golden Section and Brent's algorithm (not mentioned before in the literature) have been used to solve the line search sub-problem in the Frank-Wolfe algorithm. Tests have been carried out on two large size networks to analyze the performance of the algorithms and Brent's algorithm has been found to converge well giving a better solution than the other two algorithms.