## 5 Improved SM-EMOEAs for MSIMP
### Adaptive Strategy Improvement

Table 5: Improved adaptive strategies based on EMOEAs. 1. The adaptive sampling strategy improves the accuracy of surrogate model evaluation by dynamically adjusting the density of sampling. In the early stage of the optimized search, coarse sampling is used to cover the search space quickly. Meanwhile, in the middle and late stages of the optimized search, the sampling density is gradually increased to improve the local accuracy of the surrogate model. The adaptive sampling strategy ensures that the sampling density is adaptively adjusted at different stages of the optimal search, thus balancing the needs of the global search and local fine search. Common approaches include the dynamic sampling adjustment strategy [119] and the probabilistic sampling strategy [120]. 2. The multi-population co-evolution strategy divides the population into multiple sub-populations that are co-evolving; each sub-population independently evolves to explore different solution spaces and exchanges information at the appropriate time, improving the diversity and adaptability of the algorithms through co-evolution and enhancing the overall planning effect. Common approaches include adaptive variable grouping strategies [121] and hierarchical co-evolutionary strategies [122]. 3. The domain knowledge strategy adaptively selects the knowledge transfer strategy by calculating the difference between the current domain knowledge and the historical knowledge. When the similarity between the two types of knowledge is high, the direct transfer method is used to directly invoke the historical knowledge. The knowledge is adjusted and corrected when the similarity between the two types of knowledge is low, thus helping the algorithm to identify and exploit the properties of the problem during the optimization process and to quickly locate the area covered by the high-quality solution. Common approaches include domain knowledge adaptive strategies [123] and domain knowledge extraction strategies [124]. 4. The adaptive population size adjustment strategy dynamically adjusts the population size according to the problem convergence speed and complexity to ensure that the algorithm maintains efficient search capabilities at different optimization stages. If the algorithm converges too quickly, it indicates that the algorithm may be trapped in a local optimum and that it is necessary to adaptively increase the population size to increase the diversity of the search space. If the convergence of the algorithm stagnates, the population size needs to be reduced to improve the optimization efficiency. Common methods include the population size adjustment strategy [125] and external file resource allocation strategy [126]. 5. The multi-objective weighting strategy adjusts the weights of multiple objective functions according to the real-time feedback information obtained during the optimization process. If the prediction error of the surrogate model of the objective function is large, its weight can be temporarily reduced to avoid misleading the optimization. If the prediction error of the surrogate model of the objective function is small, its weight can be increased to effectively advance the optimization process. Commonly used methods include the inverse distance weighting strategy [127] and weighted prediction variance strategy [128]. 6. The adaptive solution space division strategy dynamically divides the solution space based on the feedback information from the optimal search process, constantly monitors the quality of the candidate solutions and their distribution in the space, and achieves a trade-off between the exploration of new regions and the refinement of the known regions by conducting local and global searches in different solution space regions. Commonly used methods include the spatial hierarchical decomposition strategy [129] and adaptive interval decomposition strategy [130].