## 3 Model Construction and Solving Algorithm
### Solving Algorithm
#### 3.2.2 Application of NSGA-II-TOPSIS-GCA Algorithm for MOODPR Problem
With the continuous advancement of ecological civilization construction, many comprehensive utilization reservoirs no longer simply pursue the maximization of economic benefits in actual operation. The benefit orientation focuses on ecological benefits and sometimes even sacrifices some economic benefits, which leads to the lack of enthusiasm of reservoir managers. In order to ensure the real implementation of the decision schemes, it is necessary for governments at all levels and water administrative departments to give full play to their social service and public management functions and to formulate and implement some practical and feasible security systems as soon as possible, such as clarifying the subjects of economic compensation, the standards of economic compensation, the sources of funds, the forms of compensation, and the corresponding accounting and supervision system. This will ensure the decision schemes are put into practice and produce benefits as soon as possible and play an active role in promoting the creation of a harmonious society of humans and water in the Hanjiang River Basin and ensuring the sustainable utilization of water resources. ## 5 Conclusions

The MOODPR is of great importance for the efficient utilization of hydropower resources, the protection of the ecological environment of river channels, and the improvement of the management level of parallel reservoirs. To solve the MOODPR problems, a new method of multi-objective optimal operation decision of parallel reservoirs was proposed. Taking Jiaoyan-Shimen parallel reservoirs as an example, the conclusions are as follows:

(1) Problem identification, model construction, optimization solution, and scheme evaluation are combined to build the MOOM and NSGA-II-TOPSIS-GCA algorithm. The decision schemes can be obtained from the alternative scheme sets, which can provide theoretical guidance for decision makers. (2) By combining the Euclidean distance with the grey correlation degree, a new hybrid closeness degree considering the correlation among attribute indexes and the implicit relationship among the data is constructed, which makes the decision method more scientific and reasonable. (3) Through the implementation of the new method of Jiaoyan-Shimen parallel reservoirs, this study explores the significant competition between the comprehensive water supply and ecology. The results provide scientific support for the planning, operation, and management of Jiaoyan-Shimen parallel reservoirs. The multi-objective optimal operation of a reservoir group is a complicated dynamic decision-making process in essence, with dynamic changes among various water processes. The existing optimal operation of a reservoir group finds it difficult to cope with the complex and changeable operation environment and operation requirements, resulting in a large deviation between the operation effect and the expected effect. Most studies lack the compensation and economic incentive mechanism after operation, which affects the enthusiasm of various stakeholders. In addition, the multi-objective optimal operation of a reservoir group often pursues the optimal benefit of each objective such as the maximum water supply and the minimum ecological AAPFD value and pays insufficient attention to the key periods or key indicators of different objectives. We will consider the above problems in the follow-up study and constantly improve the theory and practice of the optimal operation of reservoir groups. Conceptualization, N.W. ; preparation, X.G. ; methodology, N.W. and Y.P. ; data analysis, Y.P., K.L. and X.G. ; writing--original draft preparation, N.W. and K.L. ; writing--review and editing, G.Z., X.G. and M.N. ; supervision, M.N. and G.Z. All authors have read and agreed to the published version of the manuscript. This research was supported by the Key Scientific Research Program of Education Department of Shaanxi Provincial Government (Grant No. 22 JT029), the Science and Technology Program of Shaanxi Province (Grant No.