  Two major problems in modern cities are air contamination and road
congestion. They are closely related and present a similar origin: traffic
flow. To face these problems, local governments impose traffic restrictions to
prevent the entry of vehicles into sensitive areas, with the final aim of
dropping down air pollution levels. However, these restrictions force drivers
to look for alternative routes that usually generate congestions, implying both
longer travel times and higher levels of air pollution. In this work, combining
optimal control of partial differential equations and computational modelling,
we formulate a multi-objective control problem with air pollution and drivers'
travel time as objectives and look for its optimal solutions in the sense of
Stackelberg. In this problem, local government (the leader) implements traffic
restrictions meanwhile the set of drivers (the follower) acts choosing travel
preferences against leader constraints. Numerically, the discretized problem is
solved by combining genetic-elitist algorithms and interior-point methods, and
computational results for a realistic case posed in the Guadalajara
Metropolitan Area (Mexico) are shown.
