Bilevel Optimization in Flow Networks -- A Message-passing Approach

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.