A mathematical approach for designing speed-limit and low/zero emission zones in urban areas

Urban policies like Low-Emission Zones (LEZs) and Zero-Emission Zones (ZEZs) are crucial for accelerating pollutant reduction. This paper introduces a numerical multi-objective optimization framework to determine the optimal spatial extent of these restricted areas by balancing environmental benefits and economic costs. The methodology integrates the finite element method with a semi-implicit time scheme to efficiently compute coupled traffic and emission dynamics. We address two scenarios: a single-control problem identifying the optimal radius of a Zone 30 via exhaustive search, and a multi-control problem defining a combined LEZ (outer annulus) and ZEZ (inner disk). The latter employs a hybrid Genetic Algorithm and Pattern Search to compute the Pareto front. Applied to the Guadalajara Metropolitan Area (Mexico), this framework successfully identifies Pareto-optimal solutions, providing a robust decision-making tool to evaluate the trade-offs between air quality and economic constraints in urban planning.