## 5 Improved SM-EMOEAs for MSIMP
### Surrogate Model Improvement  
Regarding the improved SM-EMOEAs for MSIMP, improved surrogate models are crucial to ensure the efficiency and accuracy of the solution of the MSIMP scheme, and suitable improved surrogate models can enable SM-EMOEAs to better adapt to MSIMP problems in different scenarios. They also improve the adaptability of the algorithms to dynamic problems [107; 108; 109]. The improvement of the surrogate model depends on the MSIMP problem's characteristics. For example, for MSIMP problems applied to environmental monitoring and weather forecasting in large-scale scenarios, it is required to plan satellites and target missions globally and as a whole. The introduction of a global surrogate model can assist the algorithm in searching the distribution characteristics of the candidate solutions in the solution space and thus quickly identifying high-quality task planning solutions. Figure 7 summarizes the methods used to improve the surrogate model in MSIMP-oriented SM-EMOEAs, including the global surrogate model, local surrogate model, two-layer surrogate model, and aggregation surrogate model. 1. The global surrogate model aims to cover the global characteristics of all satellites and missions by modeling the whole MSIMP problem, mainly by using Gaussian process regression, radial basis functions, support vector regression, and so on. Through collecting global data to train the model, the global surrogate model can capture global trends for optimization to find an excellent solution for overall mission planning. It is suitable for mission planning scenarios that require global coverage, such as the monitoring of the global forest cover, through SM-EMOEAs based on global surrogate models. The global multi-satellite coverage area target task is optimized to search and  
Figure 7: Approaches to surrogate model improvement. capture the global trends of the forest cover so as to find an excellent overall mission planning solution [110; 111; 112]. 2. The local surrogate model focuses on the optimization properties of a specific region, divides the optimal MSIMP problem into several sub-problems, and performs the fine optimization of a specific region by collecting data from this region for training so as to improve the quality of the local solution. Common local surrogate models include local weighted regression, local Gaussian processes, and local radial basis function networks. They are applicable to high-frequency imaging missions in a specific area that requires delicate tuning. For example, after a natural disaster, SM-EMOEAs using local surrogate models are applied to divide the MSIMP into multiple sub-problems for focused local-scale observation. Frequent high-resolution imaging of the affected city is conducted to enhance observation efficiency, monitor the disaster's impact, and track recovery progress [113; 114]. 3. The two-layer surrogate model first uses the global surrogate model for the initial optimization of the MSIMP problem. It then selects specific regions for local optimization, stores global and local data for the training of the global and local surrogate models, and uses them for different levels of optimization. The two-layer surrogate model mainly includes a two-layer Gaussian process, a hierarchical radial basis function network, and hierarchical support vector regression. It is suitable for complex tasks that require both global and local optimization. For example, in an agricultural monitoring project, multiple satellites are required to monitor crop growth in different agricultural zones. The global surrogate model is used in the initial stage to globally optimize the imaging tasks for the whole agricultural area, and then the local surrogate model is used to assign high-resolution imaging tasks to specific areas. This achieves fast and accurate agricultural monitoring imaging, task assignment, and execution [115; 116]. 4. An aggregate surrogate model involves the integration of artificial neural networks, deep learning, decision tree regression, and other surrogate models.