Hitherto, there has been insufficient work to quantify the degree of mutual feedback among the different objectives of multi-objective reservoir operation. The purpose of this study is to use a Multi-objective Correlation Index (MCI) to quantitatively analyze the complicated relationship of a multi-objective reservoir operation under changing inflow and water demands. First, an improved maximum probability density function method has been used to generate the adaptive ecological flow thresholds in long-term, wet-year, normal-year and dry-year inflow scenarios. Based on these ecological flow thresholds, a multi-objective reservoir optimal operation including the three objectives of power generation, water supply and ecology is constructed to research the tradeoff relationship among the objectives. Moreover, using the optimal solution set as determined by the Progressive Optimality Algorithm-Particle Swarm Optimization (POA-PSO) algorithm, the MCI is used to quantify the degree of the tradeoffs and their trends in responding to the changing conditions. The results show that the synergistic degree between the water supply and ecological objective decreases when the climatic condition changes from wet years to dry years, while the conflicting degree of power generation with respect to water supply or ecological objectives increases. Furthermore, the major degree of tradeoffs changes from the power generation-ecological flow objective pair to the power generation-water supply objective pair. In general, the MCI is able to quantify the extent and characteristics of the tradeoffs between different objectives. Hence, this index is useful for managers to make more informed and transparent decisions.

迄今为止，还没有足够的工作来量化多目标水库调度的不同目标之间的相互反馈程度。这项研究的目的是使用多目标相关指数（MCI）定量分析在流入量和需水量变化的情况下多目标水库作业的复杂关系。首先，一种改进的最大概率密度函数方法已被用于在长期，湿润年，正常年和干旱年流入情况下生成自适应生态流量阈值。基于这些生态流量阈值，构造了包括发电，供水和生态三个目标的多目标水库优化运行，以研究目标之间的权衡关系。而且，使用由渐进最优算法-粒子群优化（POA-PSO）算法确定的最优解集，MCI用于量化权衡的程度及其在响应不断变化的条件时的趋势。结果表明，当气候条件从湿年转变为干旱年时，供水与生态目标之间的协同度降低，而发电与供水或生态目标之间的冲突程度则增加。此外，主要的权衡程度从发电-生态流量目标对变为发电-供水目标对。通常，MCI能够量化不同目标之间权衡的程度和特征。因此，该索引对于管理者做出更明智，更透明的决策很有用。