Multi-Scale Sponge Capacity Trading and SLSQP for Stormwater Management Optimization

Low-impact development (LID) facilities serve as a fundamental approach in urban stormwater management. However, significant variations in land use among different plots lead to discrepancies in runoff reduction demands, frequently leading to either the over- or under-implementation of LID infrastructure. To address this issue, we propose a cost-effective optimization framework grounded in the concept of “Capacity Trading (CT)”. The study area was partitioned into multi-scale grids (CT-100, CT-200, CT-500, and CT-1000) to systematically investigate runoff redistribution across heterogeneous land parcels. Integrated with the Sequential Least Squares Programming (SLSQP) optimization algorithm, LID facilities are allocated according to demand under two independent constraint conditions: runoff coefficient ( φ ≤ 0.49) and runoff control rate ( η ≥ 70%). A quantitative analysis was conducted to evaluate the construction cost and reduction effectiveness across different trading scales. The key findings include the following: (1) At a constant return period, increasing the trading scale significantly reduces the demand for LID facility construction. Expanding trading scales from CT-100 to CT-1000 reduces LID area requirements by 28.33–142.86 ha under the φ -constraint and 25.5–197.19 ha under the η -constraint. (2) Systematic evaluations revealed that CT-500 optimized cost-effectiveness by balancing infrastructure investments and hydrological performance. This scale allows for coordinated construction, avoiding the high costs associated with small-scale trading (CT-100 and CT-200) while mitigating the diminishing returns observed in large-scale trading (CT-1000). This study provides a refined and efficient solution for urban stormwater management, overcoming the limitations of traditional approaches and demonstrating significant practical value.