Surrogate modelling-based multi-objective optimization for best management practices of nonpoint source pollution.

The integrated application of hydrological models and best management practices (BMPs) serves as a pivotal decision-making tool for managing nonpoint source (NPS) pollution in watersheds. Optimizing and selecting BMP options are critical challenges in managing NPS pollution, as these processes are typically computationally expensive and involve mixed discrete-continuous decision variables. Our study integrated a novel method, the multi-objective adaptive surrogate modeling-based optimization for constrained hybrid problems (MO-ASMOCH), with the distributed Soil and Water Assessment Tool (SWAT) model to efficiently optimize the deployment of BMPs in the Four Lakes watershed of China. We compared the optimization results with those obtained using the traditional non-dominated sorting genetic algorithm (NSGA-II) method. Our results demonstrate that MO-ASMOCH significantly outperforms NSGA-II in computational efficiency, achieving comparable Pareto-optimal solutions with just 1,150 model evaluations compared to NSGA-II's requirement of 10,000 model evaluations. This demonstrates that MO-ASMOCH is a more efficient optimization algorithm for BMP optimization problems with both discrete and continuous decision variables. We selected representative scenarios to calculate in-lake concentrations of total phosphorus (TP) and total nitrogen (TN) pollutant loads. The largest reduction scenario could reduce TN and TP loads by 18.3 % and 20.7 %, respectively, at a cost of 1.54 × 10 Chinese Yuan. Under this scenario, the water quality classification level of TN improves from inferior Class V to Class IV-V, while TP attains Class III throughout the year. The methods of this study could enhance our capability to manage NPS pollution in watersheds effectively and provide targeted decision-making insights for environmental management practices.