Simultaneous Control of Cost Dynamics and Transport in Network Systems

Transportation networks, including infrastructures such as roads and power transmission, are crucial for supporting modern society. However, these networks are frequently exposed to risks such as natural disasters, e.g., earthquakes and hurricanes. In the event of such an incident, efforts are made to maintain connectivity as much as possible while striving to restore the transportation network. The optimal transport (OT) problem, which can efficiently manage transportation networks, presents a promising approach to control such situations. Although there has been considerable progress in the application of OT to transportation research, studies addressing both the control of transport operations and network structure, such as network restoration, are limited. This paper introduces a novel formulation of OT that incorporates network structure control. Specifically, we optimize the routing and restoration of the network after the damage. The network damage is parameterized as a significant increase in cost, and the restoration process is formulated as the cost dynamics. Ultimately, this is framed as the OT on the network using costs that include these parameters. Additionally, we propose an efficient algorithm for this problem, which utilizes the Markov property and Schrödinger bridge. Through a post-disaster simulation of food transport across the European transportation network, we confirmed that our approach outperforms both the node-degree-based restoration strategy and the strategy that manages transportation and restoration separately. Our method shows promise as a more effective strategy for the initial response to a damaged network.