## 3 Optimization Methods
### Improved Decomposition Optimization Algorithm  
The classic MOEA/D works well for general MOP problems [34], but for complex multi-objective problems such as hydropower- photovoltaic joint scheduling, its replacement strategy may lose some characteristic solutions in the feasible region. Aiming at this problem, this paper adopts MOEA/D-GABS [35], a multi-objective evolutionary algorithm based on the greedy strategy. Different from the previous optimization methods, the framework of this algorithm adopts MOEA/D, including greedy-based selection (GBS) and angle-based selection (ABS). The greedy-based selection aims mainly to minimize the fitness function value of each sub-problem. In order to prevent over-optimization problems, a parameter is used to control the search depth of each sub-problem. The angle-based selection aims mainly to select a relatively sparse regional solution to maintain the distribution of the population when the maximum population number is not reached. The MOEA/D-GABS Algorithm 1 framework is as follows:  
```
Input: MOP, population size N; Output: pareto non-dominated solution; step 1: initialize. Weight vector \(T=\lambda^{1},\lambda^{2},\cdots,\lambda^{N}\), set of domains \(B(i)=(i_{1},i_{2},\cdots,i_{T})\), initial population \(P_{0}\), ideal point \(Z^{*}\), mean \(EP=\Phi\); Step 2: update; 2.1:\(topK=1\), \(t=0\), while \(t<MaxIteration\), do; 2.2:\(Q_{t}=\text{Recombination}+\text{mutation}(P_{t})\);//Crossover, variation generate individual; 2.3:\(R_{t}=P_{t}\cup Q_{t}\); 2.4:\(P_{t+1}=GBS(R_{t},topK)\); 2.5:\(P_{t+1}=ABS(R_{t},P_{t+1})\); 2.6:\(t=t+1\); Step 3: judging termination conditions; if the termination condition is satisfied, output EP, otherwise continue to execute Step 2.
```  
**Algorithm 1 MOEA/D-GABS algorithm framework**  
In fact, for some confusing POF regions, general MOEA/D is difficult to obtain, but because MOEA/D-GABS solves the sub-problems in the whole process, the diversity distribution of POF will be better. The process of the MOEA/D-GABS algorithm is shown in Figure 9.  
Figure 9: The flow chart of the MOEA/D-GABS algorithm.  
Obviously, the MOEA/D-GABS algorithm completely abandons the concept of non-dominant ordering and is an approximation to solving according to the decomposition method. At the same time, the idea of region division is also involved in each sub-problem. The solution is matched with its nearest sub-problem by ABS. The GBS algorithm guarantees the convergence of the solution as much as possible by sorting the aggregation function values of each sub-problem. In fact, in the early stage of evolution, the number of solutions selected by GBS is often lower than the population size N because of the extremely induced POP in some regions. Therefore, the ABS algorithm is used to enhance the distribution of the solution, which is also in line with the original intention of the algorithm design.  
Solving the Process of Combined Hydropower-Photovoltaic Operation Based on an Improved Optimization Algorithm  
In this paper, according to the possible inflow and photovoltaic output conditions, the high-dimensional MOEA/D-GABS optimization algorithm is used to obtain the non-inferior solution set. On this basis, the hedging mechanism decision is made for each feasible solution in the non-inferior solution set, and the hedging marginal benefit corresponding to each non-inferior solution is obtained. According to the optimal conditions of the hedging mechanism, all feasible states and schemes under constraints are decided, and finally the hydropower-photovoltaic joint scheduling scheme is formed. The solution process of hydropower-photovoltaic joint scheduling considering hedging rules is shown in Figure 10.  
Figure 10: Hydropower photovoltaic joint dispatch in a flow chart based on the MOEA/D-GABS algorithm.