Bilevel optimization in flow networks: A message-passing approach

TL;DR

This paper introduces a message-passing approach for bilevel optimization in flow networks, effectively optimizing network parameters to improve global objectives in complex systems like traffic and network control.

Contribution

It presents a novel message-passing algorithm tailored for bilevel optimization in sparse flow networks, enhancing computational efficiency and applicability.

Findings

Effective optimization on randomly generated graphs

Improved efficiency over traditional methods

Applicable to traffic and network control scenarios

Abstract

Optimizing embedded systems, where the optimization of one depends on the state of another, is a formidable computational and algorithmic challenge, that is ubiquitous in real world systems. We study flow networks, where bilevel optimization is relevant to traffic planning, network control and design, and where flows are governed by an optimization requirement subject to the network parameters. We employ message-passing algorithms in flow networks with sparsely coupled structures to adapt network parameters that govern the network flows, in order to optimize a global objective. We demonstrate the effectiveness and efficiency of the approach on randomly generated graphs.