Optimize multi-objective transformation rules of water-sediment regulation for cascade reservoirs in the Lower Yellow River of China.

The Yellow River is characterized by water scarcity and high sediment load, leading to significant sedimentation issues in reservoirs. This severely restricts normal operation and contributes to frequent flooding, making it one of the most challenging problems in the Yellow River management. This study focuses on the operation of the Sanmenxia and Xiaolangdi cascade reservoirs, developing a multi-objective model (hydropower generation and sediment transport) and two single-objective models (hydropower generation only and sediment transport only). An innovative method (ESS-NSGA-II) is proposed, combining Efficient Search Space (ESS) with the Non-dominated Sorting Genetic Algorithm II (NSGA-II) to optimize cascade reservoirs operation. We analyzed the impact and transformation rules of multiple objectives under various optimization schemes. The results indicate a non-linear competitive relationship between the hydropower generation and sediment transport. An extreme case indicates an increase of 0.49 billion kWh in hydropower generation (4.08% increase) leads to greatly reduce the amount of sediment transport (96.25% decrease), while still meeting both water supply and flood control. The findings also indicate that Xiaolangdi reservoir plays a dominant role in the operation of the two reservoirs. The impact of different schemes is mainly reflected in the variation in Xiaolangdi's discharge, with the sediment transport maximization scheme offering greater flood control potential. Furthermore, the efficiency of sediment transport is closely related to hydropower generation: when hydropower is below 12.28 billion kWh, the conversion efficiency from hydropower generation to sediment transport increases significantly. This research reveals the transformation rules between multi-objectives in cascade reservoir operation, providing a scientific basis for water and sediment regulation in the Yellow River Basin and offering valuable insights into prolonging reservoir lifespans.