Stochastic Origin Frank-Wolfe for traffic assignment
Igor Ignashin, Demyan Yarmoshik, Andrei Raigorodskii
TL;DR
This work addresses equilibrium flow computation in Beckmann's static traffic assignment model by introducing Stochastic Origin Frank-Wolfe (SOFW), a block-coordinate FW method that updates only a subset of OD pairs to dramatically reduce shortest-path computations. The authors provide a formal convergence framework, including a batched variant, and show that SOFW achieves comparable or superior convergence with lower per-iteration cost on large networks, at the cost of higher memory usage. Experimental results on multiple real-world and benchmark networks demonstrate substantial gains over classical Frank-Wolfe, especially in mega-scale graphs, while highlighting a trade-off between memory and speed. The approach offers a scalable option for traffic assignment in large urban networks and suggests avenues for future theoretical and algorithmic enhancements, such as batched analysis and hybrid stochastic methods.
Abstract
In this paper, we present the Stochastic Origin Frank-Wolfe (SOFW) method, which is a special case of the block-coordinate Frank-Wolfe algorithm, applied to the problem of finding equilibrium flow distributions. By significantly reducing the computational complexity of the minimization oracle, the method improves overall efficiency at the cost of increased memory consumption. Its key advantage lies in minimizing the number of shortest path computations. We refer to existing theoretical convergence guarantees for generalized coordinate Frank-Wolfe methods and, in addition, extend the analysis by providing a convergence proof for a batched version of the Block-Coordinate Frank-Wolfe algorithm, which was not covered in the original work. We also demonstrate the practical effectiveness of our approach through experimental results. In particular, our findings show that the proposed method significantly outperforms the classical Frank-Wolfe algorithm and its variants on large-scale datasets. On smaller datasets, SOFW also remains effective, though the performance gap relative to classical methods becomes less pronounced. In such cases, there is a trade-off between solution quality, iteration time complexity, and memory usage.