Scalable Computation of Dynamic Flow Problems via Multimarginal Graph-Structured Optimal Transport
Journal article, 2024

In this work, we develop a new framework for dynamic network flow pro-blems based on optimal transport theory. We show that the dynamic multicommodity minimum-cost network flow problem can be formulated as a multimarginal optimal transport problem, where the cost function and the constraints on the marginals are asso-ciated with a graph structure. By exploiting these structures and building on recent advances in optimal transport theory, we develop an efficient method for such entropy -regularized optimal transport problems. In particular, the graph structure is utilized to efficiently compute the projections needed in the corresponding Sinkhorn iterations, and we arrive at a scheme that is both highly computationally efficient and easy to implement. To illustrate the performance of our algorithm, we compare it with a state-of-the-art linear programming (LP) solver. We achieve good approximations to the solution at least one order of magnitude faster than the LP solver. Finally, we showcase the methodology on a traffic routing problem with a large number of commodities.

multimarginal optimal transport

dynamic network flow

Computational methods

traffic routing

multicommodity network flow

Sinkhorn's method

Author

Isabel Haasler

Swiss Federal Institute of Technology in Lausanne (EPFL)

Axel Ringh

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Yongxin Chen

Georgia Institute of Technology

Johan Karlsson

Royal Institute of Technology (KTH)

Mathematics of Operations Research

0364-765X (ISSN) 1526-5471 (eISSN)

Vol. 49 2 986-1011

Subject Categories

Computational Mathematics

Transport Systems and Logistics

Control Engineering

Computer Science

DOI

10.1287/moor.2021.0148

More information

Latest update

8/27/2024