Inverse demand tracking in transportation networks

TL;DR

This paper introduces a method for reconstructing desired transportation demand profiles over a network by formulating and solving an inverse optimal control problem, accommodating fluctuations and noise in demand data.

Contribution

It develops a hierarchical inverse control framework for demand reconstruction on tree-shaped networks, ensuring solution existence and computational tractability.

Findings

Effective demand reconstruction under noisy data

Hierarchical inverse control framework demonstrated

Numerical experiments validate approach robustness

Abstract

This paper deals with the reconstruction of the desired demand in an optimal control problem, stated over a tree-shaped transportation network which is governed by a linear hyperbolic conservation law. As desired demands typically undergo fluctuations due to seasonality or unexpected events making short-term adjustments necessary, such an approach can exemplary be used for forecasting from past data. We suggest to model this problem as a so-called inverse optimal control problem, i.e., a hierarchical optimization problem whose inner problem is the optimal control problem and whose outer problem is the reconstruction problem. In order to guarantee the existence of solutions in the function space framework, the hyperbolic conservation law is interpreted in weak sense allowing for control functions in Lebesgue spaces. For the computational treatment of the model, we transfer the hierarchical problem into a nonsmooth single-level one by plugging the uniquely determined solution of the inner optimal control problem into the outer reconstruction problem before applying techniques from nonsmooth optimization. Some numerical experiments are presented to visualize various features of the model including different types of noise in the demand and strategies of how to observe the network in order to obtain good reconstructions of the desired demand.