## 3 Model Construction and Solving Algorithm
### Solving Algorithm
#### 3.2.2 Application of NSGA-II-TOPSIS-GCA Algorithm for MOODPR Problem
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Scheme** \\ **Sets** \\ \end{tabular} } & \multirow{2}{*}{**Objectives**} & \multirow{2}{*}{\begin{tabular}{c} **Water** \\ **Demand** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Water** \\ **Supply** \\ \end{tabular} } & \multicolumn{2}{c}{**Guarantee Rate**} & \multirow{2}{*}{\begin{tabular}{c} **Water** \\ **Shortage** \\ **Depth** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Number of** \\ **Maximum** \\ **Continuous Water** \\ **Shortage Periods** \\ \end{tabular} } \\ \cline{3-3} \cline{5-10}  & & & **/10\({}^{8}\) m\({}^{3}\)** & **/10\({}^{8}\) m\({}^{3}\)** & _/\%_ & _/\%_ & _/10\({}^{8}\) m\({}^{3}\)_ & _/\%_ & _Shortage Periods_ \\ \hline \multirow{3}{*}{A} & Comprehensive & \multirow{3}{*}{\begin{tabular}{c} 0.931 \\ supply \\ \end{tabular} } & 4.828 & 4.577 & 94\% & 63\% & 0.251 & 5 & 1 \\  & & 0.931 & \(\begin{array}{c}0.906\\ (1.891)\end{array}\)\({}^{1}\) & 100\% & 61\% & 0.025 & 3 & 2 \\ \hline \multirow{3}{*}{B} & Comprehensive & \multirow{3}{*}{\begin{tabular}{c} 5.702 \\ water supply \\ \end{tabular} } & 5.702 & 4.996 & 89\% & 39\% & 0.706 & 12 & 3 \\  & & 0.813 & \(\begin{array}{c}0.813\\ (2.565)\end{array}\)\({}^{1}\) & 89\% & 44\% & 0.118 & 13 & 4 \\ \hline \multirow{3}{*}{C} & Comprehensive & \multirow{3}{*}{\
\begin{tabular}{c} 6.726 \\ water supply \\ \end{tabular} } & 6.726 & 5.563 & 78\% & 44\% & 1.163 & 17 & 3 \\  & & 0.931 & \(\begin{array}{c}0.804\\ (4.230)\end{array}\)\({}^{1}\) & 67\% & 39\% & 0.127 & 14 & 4 \\ \hline \multirow{3}{*}{D} & Comprehensive & \multirow{3}{*}{
\begin{tabular}{c} 6.726 \\ water supply \\ \end{tabular} } & 6.726 & 4.212 & 61\% & 39\% & 2.514 & 37 & 4 \\  & & 0.735 & \(\begin{array}{c}0.735\\ (4.953)\end{array}\)\({}^{1}\) & 50\% & 33\% & 0.196 & 21 & 6 \\ \hline \hline \end{tabular}

* The values in the brackets represent the ecological AAPFD values of different scheme sets.

\end{table} 
Table 6: Final decision schemes for four scheme sets. Figure 8: _Cont_. Figure 8: Ecological and comprehensive water supply processes: (**a**) P = 25%; (**b**) P = 50%; (**c**) P = 75%; (**d**) P = 95%. In the wet year, there was more upstream inflow in the flood season, which could meet the comprehensive and ecological water demand at the same time. There was less upstream inflow in early November, early and late December, mid-January, and early and late February, and the optimal operation of parallel reservoirs could not satisfy the comprehensive and ecological water demand. Among them, in early November, early and late December, mid-January, and early February, the available water supply of Jiaoyan reservoir was limited, and Shimen reservoir undertook the main water supply task. Except for an individual ten-day period in the non-flood season, the ecological water demand could essentially be met. The maximum ten-day water shortage of comprehensive and ecological water demand was 7.2 \(\times\) 10\({}^{6}\) m\({}^{3}\) and 1.0 \(\times\) 10\({}^{6}\) m\({}^{3}\), respectively. In the normal year, the upstream inflow was large in July, August, and September, which could meet the comprehensive and ecological water demand. The water shortage was mainly concentrated in mid-May, late June, late November, early December, mid-late January, February, early March, mid-March, early April, and mid-April. Among them, in late November, early December, early March, and early and mid-April, due to the limited water supply of Jiaoyan reservoir, Shimen reservoir was used to supplement the insufficient water supply. In the flood season, the satisfaction degree of the ecological water demand was 93.72% and the number of water shortage periods was two ten-day periods. In the non-flood season, the satisfaction degree was 70.86% and the number of water shortage periods was 10 ten-day periods.