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.

空气污染和道路拥堵是现代城市中的两个主要问题。两者密切相关，并具有相同的来源：流量。为了解决这些问题，政府实施了交通限制措施，以防止车辆进入敏感区域，最终目标是降低污染水平。不幸的是，这些限制迫使驾驶员寻找通常会引起交通拥堵的替代路线，从而导致更长的行驶时间和更高的污染水平。在这项工作中，将计算模型与偏微分方程的最优控制相结合，我们以空气污染和驾驶员出行时间为目标，制定并分析了双层最优控制问题，并从Stackelberg的角度寻找最优解决方案。在这种情况下，领导者（当地政府）实施交通限制，而跟随者（驾驶员组）则根据领导者的约束来选择出行偏好。我们将问题离散化，并提出了一种数值算法来解决，它结合了遗传精英算法和内点方法。最后，显示了在瓜达拉哈拉大都会区（墨西哥）提出的一个实际案例的计算结果。