A Continuum Model for Housing Allocation and Transportation Emission Problems in a Polycentric City

The effect of vehicle emissions on the global climate has prompted increasing concern in the past few decades. Housing development patterns determine people's travel behavior and related vehicle emissions. In this study, we consider a hypothetical city with several central business districts (CBDs) serving several classes of road users, which are continuously distributed over the city. The road network is relatively dense and can be approximated as a continuum. We establish a bi-level model to describe the relationships among housing allocation, traffic volume, and CO₂ emissions with a continuum modeling approach. At the lower level, the model achieves the user equilibrium condition of a transport system. At the upper level, it optimizes housing allocation to achieve minimum CO₂ emissions. The finite element method, Newton-Raphson algorithm, and convex combination approach are applied to solve the constrained optimization problem established in the bi-level model. A numerical example is then given to illustrate the effectiveness and efficiency of the proposed bi-level approach and solution algorithm in modeling transport demand, traffic intensity, and CO₂ emissions with an optimized housing development pattern.