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Two major problems in modern cities are air contamination and roadcongestion. They are closely related and present a similar origin: trafficflow. To face these problems, local governments impose traffic restrictions toprevent the entry of vehicles into sensitive areas, with the final aim ofdropping down air pollution levels. However, these restrictions force driversto look for alternative routes that usually generate congestions, implying bothlonger travel times and higher levels of air pollution. In this work, combiningoptimal 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 ofStackelberg. In this problem, local government (the leader) implements trafficrestrictions meanwhile the set of drivers (the follower) acts choosing travelpreferences against leader constraints. Numerically, the discretized problem issolved by combining genetic-elitist algorithms and interior-point methods, andcomputational results for a realistic case posed in the GuadalajaraMetropolitan Area (Mexico) are shown.

Optimal control of atmospheric pollution because of urban traffic flow by means of Stackelberg strategies