## 4 MSIMP Based on EMOEAs
### Flowchart of MSIMP Based on EMOEAs  
Classical expensive multi-objective evolutionary algorithms based on EMOEAs are used to solve the MSIMP problem. The flowchart of MSIMP based on EMOEAs is shown in Figure 5, which mainly includes MSIMP problem modeling, an optimal search, external population updating, and convergence judgment [75; 76; 77; 78; 79; 80; 81; 82].  
1. In the modeling of the MSIMP problem, information about the mission set and satellite resource set is obtained according to the application scenario. The objective functions, including the maximum mission benefit, minimum satellite resource consumption, and minimum response time, are constructed following the user's requirements. Moreover, the constraints, such as the mission uniqueness constraint, mission urgency constraint, and visible time window constraint, are set.
2. In the optimization search, a set of individuals is randomly generated to form the initial population, and the algorithm's parameters are configured. The fitness of each individual in the initial population is evaluated based on the objective function. High-quality individuals are selected through processes like crossover, mutation, and selection, which are then used to produce the next generation of the population.
3. In the external update and convergence evaluation steps, non-dominated solutions from the new population are stored in an external population, which is updated to preserve population diversity. Once the maximum number of iterations is reached, the final set of non-dominated solutions is produced as the optimal MSIMP scheme for the selected satellite control task [83].  
However, as the MSIMP scheme involves a large-scale task set and complex satellite resource allocation, tens of thousands of evaluations are required to find a high-quality task planning scheme. This leads to high computational complexity and consumes large amounts of computational resources. In addition, EMOEAs are prone to falling into local optimal solutions when facing complex multi-peak optimization problems, resulting in the algorithms not being able to effectively explore the global optimal solution space. In particular, in the context of the dynamically changing mission requirements and satellite resource state changes faced by MSIMP in complex environments, the response-ability is limited, making it difficult to solve the mission planning scheme in real scenarios [84].  
To solve the above problems, a surrogate model is introduced in the optimization search part of the algorithm. The surrogate model is a simplified mathematical model used to replace the high-dimensional objective function with constraints in the optimization search process, which helps to achieve rapid evaluation of the solution through approximating the real objective function and can identify a high-quality solution with a limited number of evaluations. It applies to complex optimization problems with large computational resource requirements or tight time constraints. Surrogate models include Gaussian process regression (GPR) [85], radial basis function networks (RBFNs) [86], support vector regression (SVR) [87], and neural networks (NNs) [88].  
Figure 5: Flowchart of MSIMP based on EMOEAs.