Computational graph-based mathematical programming reformulation for integrated demand and supply models

As transportation systems grow in complexity, analysts need sophisticated tools to understand travelers’ decision-making and effectively quantify the benefits of the proposed strategies. The transportation community has developed integrated demand–supply models to capture the emerging interactive nature of transportation systems, serve diverse planning needs, and encompass broader solution possibilities. Recently, utilizing advances in Machine Learning (ML) techniques, researchers have also recognized the need for different computational models capable of fusing/analyzing different data sources. Inspired by this momentum, this study proposes a new modeling framework to analytically bridge travel demand components and network assignment models with machine learning algorithms. Specifically, to establish a consistent representation of such aspects between separate system models, we introduce several important mathematical programming reformulation techniques—variable splitting and augmented Lagrangian relaxation—to construct a computationally tractable nonlinear unconstrained optimization program. Furthermore, to find equilibrium states, we apply automatic differentiation (AD) to compute the gradients of decision variables in a layered structure with the proposed model represented based on computational graphs (CGs) and solve the proposed formulation through the alternating direction method of multipliers (ADMM) as a dual decomposition method. Thus, this reformulated model offers a theoretically consistent framework to express the gap between the demand and supply components and lays the computational foundation for utilizing a new generation of numerically reliable optimization solvers. Using a small example network and the Chicago sketch transportation network, we examined the convergency/consistency measures of this new differentiable programming-based optimization structure and demonstrated the computational efficiency of the proposed integrated transportation demand and supply models.