## 3 Results and Discussion
### Fitting of Model Parameters  
Multiobjective optimization is multiobjective function optimization. Using this method to obtain the parameter values to be solved is one of the engineering applications of multiobjective optimization. According to the built optimization function, it can quickly fit the optimal solution of each parameter in the target equation, and it has good applicability even under the condition of small samples [37]. Therefore, the multiobjective and multivariable optimization technique can solve the problem of insufficient data points under the IDC mechanism in this paper. The predicted life values under the same test boundary are compared with the test results, and finally, the optimal model parameter values can be obtained. The linear combination method is a branch of the evaluation function method, which belongs to the preference-based multiobjective optimization method [38]. This method can turn multiobjective optimization problems into single-objective ones, so it has the advantages of simple structure and efficient optimization, but the search preference determined in advance will directly affect the optimal solution [39; 40]. The weight of each data point in the creep test of CGI is equal, that is, the minimum creep rate under each test load point, the relative error between the test results and the model prediction results should be minimized, which just avoids the shortcomings of the linear combination method. Therefore, this paper adopted a relatively simple and commonly used linear combination method, and the general expression of its evaluation function was as follows:  
\[\left. \begin{array}{c}\min\text{U}(x)=\sum\limits_{i=1}^{p}w_{i}f_{i}(x)\\ x\in DR^{n}\\ D:g_{u}(x)\geq 0\\ \text{h}_{v}(x)=0\end{array} \right\} \tag{6}\]  
where \(w_{i}\) is the weighting coefficient, which is used to assign the importance of each objective function, \(f_{i}(x)\) is the subobjective function, \(R^{n}\) is an n-dimensional real Euclidean space, and \(g_{u}(x)\) and \(h_{v}(x)\) are constraints on design parameters. In this problem, the subobjective function was set as the minimum value function of the relative error between the model predicted value and the experimental value of the minimum creep rate under each test condition. The design parameters were activation energies Q\({}_{A}\), Q\({}_{B}\), and Q\({}_{C}\), stress exponents p, n, and m, and proportionality constants A\({}_{0}\), B\({}_{0}\), and C\({}_{0}\). According to experience, the optimization interval D\({}_{i}\) of each design parameter x\({}_{j}\) was determined, that was, the constraint condition of the design parameter. The objective function constructed in combination with Formula (6) was the following formula:  
\[\left. \begin{array}{c}\min f_{i}(x)=w_{i}\Big{|}\dfrac{e_{i}-p_{i}(x)}{e_{i} }\Big{|}\,,\,\,\,i=1,2,\ldots,11\\ \\ s.t.\,\,\,\,\,\,\,\,\,\,\,\,\,x_{j}\in D_{j}\,\,\,,\,\,\,j=1,2,3,4\end{array} \right. \tag{7}\]  
where \(e_{i}\) is the experimental value of the minimum creep rate, and \(p_{i}\) is the predicted value of the creep-constitutive model. The importance of each subobjective function is the same here, so the weight coefficient \(w_{i}=1/\text{N}\), N is the number of data points. The model parameter values obtained after multiobjective optimization are listed in Table 4. In order to verify the agreement between the model curve and the test data, according to the values in Table 4, the total minimum creep rate was calculated based on Equation (5). The predicted minimum creep rate stress curve of CGI was drawn into the same image as the test point (as shown in Figure 7a), and the comparison of the experimental value and the predicted value with twice the error band was plotted (asshown in Figure 7b). Since the creep time of CGI was very short under some conditions of high temperature and high stress, its minimum creep rate had a high sensitivity to the creep time.