## 4 Results and Analysis
In this paper, under the existing forecast level, the runoff forecast error is set to follow the normal distribution \(\varepsilon\sim N(-2.2,19.71^{2})\) and the downstream flood control acceptable risk is 0.075; the upper limit of flood limit water level control can be obtained as 695.12 m, where the simulated polynomial mutation (PM) and the binary crossover operator (SBX) of the MOEA/D-GABS algorithm are used to generate offspring individuals [36]. The implementation of the algorithm is completed on a ThinkPad T440p (4-core i5-4210M CPU 2.60 GHz frequency, 8 G running memory) notebook. The TCH aggregation method is used for decomposition [37]. The total population size N is set to 500; the number of decision variables is n; and the crossover probability \(\rho_{c}\) and mutation probability \(\rho_{m}\) are set to 1.0 and \(1/n\), respectively. For the SBX operation, the distribution index \(\eta_{c}\) is 30, the mutation distribution index \(\eta_{m}\) is 20, the control parameter \(topK\) is 3, and the algorithm termination condition Fmax is 1000. In addition, the optimization algorithm obtains a set of non-inferior sets. When determining the optimal scheduling scheme, the hedging mechanism in time space established in this paper is needed to determine the optimal point in the Pareto front. It can be seen from Figure 12 that, with the increase in pre-storage capacity, the target value of benefit difference decreases, the target value of downstream flood control risk increases, the hydropower generation decreases in the current period, and the ability of hydropower to regulate photovoltaic power generation decreases, which indirectly leads to the increase in system volatility. Therefore, there is an inverse proportional relationship between the reservoir benefit difference target and the flood control risk target, as well as between the benefit difference target and the joint output fluctuation target, while there is a positive proportional relationship between the flood control risk target and the joint output fluctuation target. According to the hedging mechanism decision strategy of the above joint scheduling, the intersection of the marginal benefit curves of the hydropower station and the photovoltaic power station is obtained through the hydropower-photovoltaic joint scheduling system as the optimal decision scheme under the hedging mechanism. Table 3 shows the target values of the optimal decision schemes under the optimal water storage benefit, optimal flood control risk, optimal joint output fluctuation, and optimal hedging mechanism. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Target**} & **Optimal Water** & \multirow{2}{*}{\
\begin{tabular}{c} **Optimal Flood Risk** \\ **Decision Scheme** \\ \end{tabular} } & **Optimal Volatility** & \multirow{2}{*}{
\begin{tabular}{c} **Under Hedging** \\ **Decision Scheme** \\ \end{tabular} } \\  & **Storage Benef** & & & \\  & **Decision Scheme** & & & \\ \hline Water storage benefit & \multirow{2}{*}{\(1.24\times 10^{-3}\)} & \multirow{2}{*}{\(1.16\times 10^{-2}\)} & \multirow{2}{*}{\(2.57\times 10^{-3}\)} & \multirow{2}{*}{\(1.92\times 10^{-3}\)} \\ difference & & & & \\ Flood risk value & \(9.07\times 10^{-3}\) & \(3.04\times 10^{-3}\) & \(6.47\times 10^{-3}\) & \(4.11\times 10^{-3}\) \\ Joint output fluctuation value & \(6.67\times 10^{-0}\) & \(9.59\times 10^{0}\) & \(2.38\times 10^{0}\) & \(5.64\times 10^{0}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The comparison of the optimization goal in the Pareto frontier. In order to verify the effectiveness of the hedging mechanism, a compromise optimization strategy is used to compare the effects. The compromise optimization strategy is solved by selecting the fuzzy membership function of the optimal solution on the Pareto front, and the solution with the highest satisfaction will be analyzed as a compromise solution.