以黄河上游多年调节水库龙羊峡及下游刘家峡水库为研究对象，考虑来水不确定性影响，建立梯级水库群多目标随机优化模型，并基于理想点法（technique for order preference by similarity to an ideal solution，TOPSIS）决策方法，求解当年发电量与年末水位Pareto方案集中最佳方案，探讨来水频率及起调水位对年末水位和发电量的影响，验证年末期望水位保证多年调节水库发电效益的可靠性。结果表明：在不确定来水条件下，龙羊峡水库年末期望水位与龙羊峡水库、刘家峡水库年期望发电量之间存在竞争关系；龙羊峡水库来水频率越低、起调水位越高时，龙羊峡水库年末水位越高，龙羊峡水库、刘家峡水库发电量越大；基于提出的年末水位优化方法可大幅缩减龙羊峡水库现行调度方式下年末水位范围，且保障发电效益的可靠性在98%以上。

Multi-year regulation reservoirs are used to regulate the unbalanced water volume within and between years, and year-end water level control is linked to the overall benefits of the current year and the following several years. The water level at the end of the year is typically not fixed because of the unpredictability of natural inflow. It is worth studying how to optimize the year-end water level of multi-year regulation reservoirs based on the uncertainty of inflow to ensure their long-term comprehensive benefits.Taken the multi-year regulating Longyangxia Reservoir and Liujiaxia Rservoir in the upper reaches of the Yellow River as a case study, the year-end water level is optimized under uncertain inflow conditions. The Latin Hypercube Sampling-Monte Carlo (LHS-MC) method was applied to generate random reservoir inflows. On this basis, a multi-objective stochastic optimization model for cascade reservoirs considering the uncertain inflow was established. The best scheme from the Pareto solution set of the current-year power output and the year-end water level was obtained based on the TOPSIS decision-making method. The effects of runoff frequency and initial water level on year-end water level and power output were investigated, and the reliability of year-end expected water level on multi-year power output was verified.The results show that the initial water levels of Longyangxia Reservoir and Liujiaxia Reservoir are 2,590 m and 1,728 m, respectively, the total expected power output ranges from 9.514 billion kW?h to 9.689 billion kW?h, and the year-end water level of Longyangxia Reservoir ranges from 2,586.45 m to 2,587.41 m. The higher the year-end water level, the less power is generated. The water level of Longyangxia Reservoir and the power generation of the cascade reservoirs differ greatly from June to October under different inflow frequencies. The lower the frequency of runoff and the higher the initial water level of Longyangxia Reservoir, the higher the year-end water level of Longyangxia and the higher the power output of Longyangxia Reservoir and Liujiaxia Reservoirs. The optimal year-end water level of Longyangxia Reservoir should be controlled between 2,580 m and 2,590 m based on the stochastic optimization model, which is a significant reduction from the actual operation. When the optimal year-end expected water level obtained by stochastic optimization is used to control Longyangxia Reservoir, the reliability of guaranteeing the power output benefit is above 98%.Overall, under the uncertainty inflow scenarios, there is a competitive relationship between the annual estimated power output of Longyangxia Reservoir and Liujiaxia Reservoir and the year-end expected water level of Longyangxia Reservoir. The main determinants of Longyangxia Reservoir's year-end water level are the reservoir's inflow frequency and initial water level. This approach has a high degree of reliability and significantly narrows the range of year-end water level under the existing dispatching mechanism.