Scalable Computation of Dynamic Flow Problems via Multimarginal Graph-Structured Optimal Transport
Artikel i vetenskaplig tidskrift, 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

Författare

Isabel Haasler

Ecole Polytechnique Federale de Lausanne (EPFL)

Axel Ringh

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Yongxin Chen

Georgia Institute of Technology

Johan Karlsson

Kungliga Tekniska Högskolan (KTH)

Mathematics of Operations Research

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

Vol. 49 2 986-1011

Ämneskategorier

Beräkningsmatematik

Transportteknik och logistik

Reglerteknik

Datavetenskap (datalogi)

DOI

10.1287/moor.2021.0148

Mer information

Senast uppdaterat

2024-08-27