**6. Conclusions**

In this paper, the multi-objective optimization algorithm is applied to solve the different models by GA and optimized NSGA-II. The results of the single-objective and multi-objective calculation are compared and analyzed, and the following conclusions are obtained.

(1) Compared with the GA, MOPSO, and NSGA-II algorithms, the feasibility and effectiveness of the optimized NSGA-II are verified.

(2) With the single-objective model of maximum power generation, the total power generation is 8.84 billion kW·h, and the guarantee rate of ecological water demand is 74.43%; the single-objective model considering ecological constraints has a total power generation of 8.759 billion kW·h, and increases the ecological guarantee rate to 93.18%, which basically meets the ecological requirements. The comparison of the results of the two models reveals the degree of impact of ecological goals on dispatching.

(3) The single-objective typical annual optimal value basically falls on the multi-objective Pareto-front curve, which is in good agreement with the Pareto-front curve, further demonstrating the accuracy and reliability of each model and algorithm. With the decrease in incoming water, the ecological security situation in the lower reaches of the Yellow River is poor. The multi-objective model gives a global equilibrium solution set of power generation and ecology, which provides the best coordination scheme for the decision makers of reservoir actual operation and river basin management.

(4) In the multi-objective power generation and ecological sensitivity, the weakest year is in the dry year, and the strongest in the wet year, which is the contradiction between the ecological and the power generation in the dry year. To improve the same ecological benefits, it is bound to sacrifice greater power generation benefits. As the situation of ecological security in the dry years is more severe, stage-by-stage measures should be taken to ease the deterioration of the ecological environment.

In this paper, the different ecological water demand processes of each typical year is regarded as the ecological target. The influence of water quality factors such as water and sediment from alluvial water and algae on the ecological flow in Xiaolangdi is neglected. The next step is to establish an ecological and discharge flow response model to determine the process of integrated ecological water demand for the lower reaches of the Yellow River, and then improve the multi-objective optimization scheduling model.

**Author Contributions:** T.B, J.-x.C. and J.L. provided the writing ideas and supervised the study; Y.-p.H. conceived and designed the methods; T.B. and X.L. wrote the paper, and all the authors were responsible for data processing and data analysis. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Acknowledgments:** This study is supported by the National Key R&D Program of China (2017YFC0405900), the China Postdoctoral Science Foundation (2017M623332XB), the Postdoctoral Research Funding Project of Shaanxi Province (2017BSHYDZZ53), the Basic Research Plan of Natural Science in Shaanxi Province (2018JQ5145), the Natural Science Foundation of China (51879213), Guangdong Province Water Conservancy Science and Technology Innovation Project (2017-09).The authors would like to thank the Editors and anonymous Reviewers for their valuable and constructive comments on this manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

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