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In order to improve the search efficiency of the NSGA-Ⅱ algorithm, this paper introduced an arithmetic crossover operator with stronger global search ability and faster convergence speed to replace the simulated binary crossover operator used in the original NSGA-Ⅱ algorithm. Based on this, an improved NSGA-Ⅱ algorithm was proposed, the G_D index was used to evaluate the convergence capability of the multi-objective Pareto solution set. The method was applied to the research of Fenhe Reservoir water supply and ecological collaborative optimal scheduling to verify its effectiveness. By comparing the Pareto solution sets generated by different algorithms and various indicators of reservoir operation, and compared with the traditional algorithm, the number of iterations to reach the convergence state after the improved algorithm was reduced by 100 generations and the convergence time is shortened by 7.76%. The water shortage rate of each department under the condition of non-optimization was decreased, of which the effect of agricultural water shortage rate is the most significant, decreasing by 13.20% to 14.52%, and the total water supply increased by 0.268 to 0.303 million cubic meters. This paper verified the effectiveness of the improved algorithm and optimized scheduling, and provides an optional new idea for multi-objective optimal scheduling of reservoirs.

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为进一步提高NSGA-Ⅱ算法搜索效率，引进全局搜索能力更强、收敛速度更快的算术交叉算子改进原始算法中采用的模拟二进制交叉算子（SBX）。据此提出一种改进NSGA-Ⅱ算法，同时采用GenerationalDistance（G_D）指标评价多目标Pareto解集的收敛状态，并将该方法应用于汾河水库供水及生态协同优化调度研究中以验证其有效性。对比不同算法运行产生的Pareto解集及水库运行各项指标表明，与传统算法相比，算法改进后达到收敛状态的迭代次数降低了100代且收敛时间缩短7.76%；较不优化条件下的各部门缺水率均有所降低，其中农业缺水率效果最为显著，降低13.20%~14.52%，总供水量增加0.268×10⁸~0.303×10⁸m³。验证了改进算法及优化调度的有效性，为水库多目标优化调度提供了一种新思路。

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董领（1995-），男，硕士研究生，研究方向为水文水资源，E-mail：1819594278@qq.com

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董领（1995-），男，硕士研究生，研究方向为水文水资源，E-mail：1819594278@qq.com

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