Driving responses and synergistic-competitive relationships within the complex multi-objective system of the Yellow River Basin.

Effective river basin management demands balancing sediment regulation, ecological protection, and economic development. However, the nonlinear and spatially heterogeneous responses of these objectives to reservoir operations have remained poorly understood. To address this gap, a novel integrated framework is developed, incorporating Analytic Hierarchy Process (AHP)-based multi-objective functions, Non-dominated Sorting Genetic Algorithms II (NSGA-II) for optimization, and Copula function analysis. This approach enables a systematic assessment of synergy-competition dynamics among multiple objectives under varying hydrological conditions and operational scenarios. The results showed that sediment and economic benefits increased by 18.7 % and 24.1 % on average, particularly in the middle and lower reaches. Ecological benefits exhibited an "inverted U-shaped" response, declining by up to 36.5 % beyond a certain threshold, becoming increasingly pronounced downstream. During dry years, sediment benefits increased by 1.5-2.4 times, while ecological-economic competition intensified by a factor of ten. Upstream cascade operations promoted sediment-economic synergy, whereas downstream regulation alleviated ecological-economic conflicts. These findings provide quantitative evidence and theoretical support for adaptive, resilient water resource management in complex, multi-objective basin systems.