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Recent decades have seen increasing concerns regarding air quality in housing locations. This study proposes a predictive continuum dynamic user-optimal model with combined choice of housing location, destination, route, and departure time. A traveler’s choice of housing location is modeled by a logit-type demand distribution function based on air quality, housing rent, and perceived travel costs. Air quality, or air pollutants, within the modeling region are governed by the vehicle-emission model and the advection-diffusion equation for dispersion. In this study, the housing-location problem is formulated as a fixed-point problem and the predictive continuum dynamic user-optimal model with departure-time consideration is formulated as a variational inequality problem. The Lax-Friedrichs scheme, the fast-sweeping method, the Goldstein-Levitin-Polyak projection algorithm, and self-adaptive successive averages are adopted to discretize and solve these problems. A numerical example is given to demonstrate the characteristics of the proposed housing-location choice problem with consideration of air quality and to demonstrate the effectiveness of the solution algorithms. 

In recent decades, the effects of vehicle emissions on urban environments have raised increasing concerns, and it has been recognized that vehicle emissions affect peoples’ choice of housing location. Additionally, housing allocation patterns determine people's travel behavior and thus affect vehicle emissions. This study considers the housing allocation problem by incorporating vehicle emissions in a city with a single central business district (CBD) into a bilevel optimization model. In the lower level subprogram, under a fixed housing allocation, a predictive dynamic continuum user‐optimal (PDUO‐C) model with a combined departure time and route choice is used to study the city's traffic flow. In the upper level subprogram, the health cost is defined and minimized to identify the optimal allocation of additional housing units to update the housing allocation. A simulated annealing algorithm is used to solve the housing allocation problem. The results show that the distribution of additional housing locations is dependent on the distance and direction from the CBD. Sensitivity analyses demonstrate the influences of various factors (e.g., budget and cost of housing supply) on the optimized health cost and travel demand pattern.