Bilevel optimal control of urban traffic-related air pollution by means of Stackelberg strategies

Air contamination and road congestion are two major problems in modern cities. Both are closely related and present the same source: traffic flow. To deal with these problems, governments impose traffic restrictions preventing the entry of vehicles into sensitive areas, with the final goal of decreasing pollution levels. Unfortunately, these restrictions force drivers to look for alternative routes that usually generate traffic congestions, resulting in longer travel times and higher levels of contamination. In this work, blending computational modelling and optimal control of partial differential equations, we formulate and analyse a bilevel optimal control problem with air pollution and drivers’ travel time as objectives and look for optimal solutions in the sense of Stackelberg. In this setting, the leader (local government) implements traffic restrictions meanwhile the follower (drivers set) acts choosing travel preferences against leader constraints. We discretize the problem and propose a numerical algorithm to solve it, combining genetic-elitist algorithms and interior-point methods. Finally, computational results for a realistic case posed in the Guadalajara Metropolitan Area (Mexico) are shown.