City-scale optimal location planning of Green Infrastructure using piece-wise linear interpolation and exact optimization methods

Green Infrastructure (GI) location planning involves multi-objective spatial analysis considering simultaneous benefits. Fast optimization results are often required (e.g., collaborative modeling exercises and stakeholder involvement workshops), while the simulation-optimization approach is impractical for these cases if it relies on time-consuming simulations of complex drainage system models. This paper proposes a new method using a surrogated model based upon targeted executions of a more complex urban drainage model. This method uses a piece-wise linear interpolation to predict the hydrological impact of individual impervious-to-pervious area changes and the Mixed Integer Linear Optimization to find the optimal location of GI practices. We applied the methodology to the capital city of Colombia, Bogotá, with the objectives of reducing runoff, combined sewer overflows (CSOs), and separate sanitary overflows (SSOs). Two multi-objective optimization approaches (i.e., a lexicographic and a weighted-sum model) were explored, showing the high efficiency of this approach in building Pareto Fronts and rapidly suggesting alternative solutions for different budgets. It was found that by implementing GIs on one-third of the city's GI-feasible public areas (2.2% of city area), under a 10-year 6-h rainfall event, the total reduction on runoff, CSO, and SSO are 0.9%, 1.8%, and 2.4%, respectively. These results show the importance of promoting GI among private-land owners, especially in cities with land predominantly private-owned. This new approach is particularly useful for applications under data scarcity and high-uncertainty scenarios.