## Materials and Methods
### Multi-Objective Prediction Method Based on the Conditional Copula Function
#### 2.2.3 NSGA-II Multi-Objective Optimization Algorithm  
The NSGA (Non-dominated Sorting Genetic Algorithm) is derived from the Genetic Algorithm (GA) but is different from the traditional GA. The NSGA algorithm is based on a genetic algorithm, and its core technology lies in two aspects: one is to rank individuals in the population by using the non-dominated sorting principle; the other is to calculate the virtual crowding distance of each individual by the Niched Genetic Algorithms (NGR). Based on the above two technical principles, the NSGA algorithm evaluates and selects the population in the \"selection\" segment, thus achieving multi-objective optimization, and exhibits strong advantages such as strong searchability and robustness in the field of multi-objective optimization. However, with the increase in the complexity of problems, the NSGA algorithm also exposes the disadvantages of high computational complexity, the easy coverage of excellent individuals in the iterative process, and the need to manually specify shared parameters [37]. In view of the shortcomings of the NSGA algorithm, in 2002 [PERSON] and other scholars proposed NSGA-II algorithm, which is superior to the NSGA algorithm: it uses a fast non-dominated sorting algorithm, and the computational complexity is much lower than that of NSGA; the comparison operator of congestion degree and congestion degree is adopted to replace the shared radius: share Q that needs to be specified and serves as the winning criterion in the peer comparison after quick sorting. It extends the distribution range of the solution set in the Pareto frontier and distributes evenly, maintaining the diversity of the population. The elite strategy is introduced to expand the sampling space, prevent the loss of the best individual, and improve the computing speed and robustness of the algorithm [38]. In this paper, the two evaluation indexes consisting of PIAW and PICP are used as the adaptive function, \(K\) and \(t\) of copula interval prediction under the confidence level \(\beta\) are used as decision variables, according to the definition of \(K\) and \(t\)[32; 33], their value should be a positive integer. But the total number of subspaces of Equation (2) is \(K^{t+1}\), the subspace is too much. There will be no sample in the former N samples who fall within the same subinterval as Equation (4), so fail to construct the conditional matrix. Therefore, we first assume that \(t=1\), \(K\) gradually increases from 2, take obtain the condition matrix as the principle, and determine the value range of \(K\) when \(t=1\); then assume that \(t=2\), \(K\) gradually increases from 2, and determine the value range of \(K\) when \(t=2\). After such an exhaustive operation, the value range of all parameters (\(K\), \(t\)) is obtained. And then NSGA-II is used for multi-objective optimization to obtain a non-inferior solution set of the conditional copula prediction model. In order to better understand the specific process of this method, the specific implementation steps of the optimization method are given below, and the flowchart is shown in Figure 2:  
Step 1: Monte Carlo random sampling is carried out for two values of \(K\) and \(t\). Step 2: Coding. Adopt the real number coding method. Step 3: Set the population size \"Pop Size\" and generate the initial population, PO. Step 4: Conduct the fast-non-dominated sorting and virtual crowding distance calculation for the contemporary population, which is one of the core steps of this algorithm. The fast-non-dominated sorting is based on the two adaptability function values including PIAW and PICP, while the virtual crowding distance is obtained from the distance information of the individual vectors in the variable space. Step 5: Conduct a genetic operation, which includes selection, crossover, and mutation. The sub-population can be obtained in this step. Step 6: Conduct an elitist strategy.