Bi-level Multi-objective Complex Regional Water Resources Optimal Allocation Model Under Hybrid Uncertainty - Wang, Tao; Duan, Jingjing; Jiang, Chenhui; Zhang, Zhaohan; Wang, Dangxian; Li, Xing; Guan, Ziyu; Zhao, Jing; Zhai, Jiaqi; Liu, Jingzhe; Gao, Yulong; Wang, Peiling (Water resources management, 2025)
To address the coordinated balance between ecological protection and economic benefits in water resources allocation under complex uncertain environments, this paper employs fuzzy random theory to quantify the uncertainty characteristics of the water resources system. Radial Basis Function Neural Networks (RBFNN) are introduced to characterize the nonlinear response relationship of water use benefits, and a bi-level multi-objective optimal allocation model for complex regional water resources systems is established. The model takes the objectives of the watershed water resources system manager as the core task, incorporating the responses of subregion managers to the optimization problem as constraints. The upper level, led by the watershed manager, comprehensively considers environmental and sustainable development goals while balancing water supply and demand for various users. The lower level, dominated by subregion managers, prioritizes resource allocation to high-benefit water use sectors. In terms of solution methodology, the bi-level model is transformed into an equivalent single-layer mixed-integer linear programming problem using the Karush–Kuhn–Tucker (KKT) optimality conditions for simplified computation. The Weihe River Basin is selected as the study area, and stochastic programming is applied to derive coordinated reservoir group scheduling and regional water resources allocation schemes under the average inflow scenario over multiple years. The results validate the significant effectiveness of the allocation scheme in reducing water shortage risks during dry periods and enhancing economic benefits. The findings demonstrate that the model provides an adaptive and robust decision-making approach for water resources conflict management under uncertain scenarios, while also offering technical reference for the subsequent operation of the Han-to-Wei Water Diversion Project. Highlight • Use fuzzy mathematics theory to describe the uncertainty in the water system • Using machine learning to describe economic benefits that are difficult to quantify • Construct a Bi-level multi-objective water resources optimal allocation model. • Apply model to the Shaanxi section of the Weihe River Basin.