## 5 Improved SM-EMOEAs for MSIMP
### Adaptive Strategy Improvement
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Improvement Strategy** & **Specific Improvement Methods** & **Year** & **Main Ideas** \\ \hline \multirow{4}{*}{Adaptive sampling strategy} & \multirow{4}{*}{Probabilistic sampling strategy} & \multirow{4}{*}{2023} & The probability improvement criterion is used to adjust the sampling, the probability guidance algorithm is used to sample the candidate solution successfully, and the region with a high fitness value is sampled empirically. \\ \cline{2-4}  & \multirow{2}{*}{Dynamic sampling adjustment strategy} & \multirow{2}{*}{2023} & The radial basis function (RBF) network model for denoising is established according to the real-time feedback: noise level in the process of evolution, and dynamic adjustment of data sampling density is carried out. \\ \hline \multirow{4}{*}{Multi-population co-evolution strategy} & \multirow{4}{*}{Hierarchical co-evolution strategy} & \multirow{4}{*}{2022} & The Bayesian Gaussian process latent variable model is combined with adaptive sampling to iteratively select new partially observable training sample points. \\ \cline{2-4}  & \multirow{2}{*}{Hierarchical co-evolution strategy} & \multirow{2}{*}{2022} & In the stage of model training, a multi-classification model is constructed to divide the whole population into several classes to ensure diversity in the evolutionary phase, a coevolutionary framework is used to guide evolution according to the new selection criteria. \\ \hline \multirow{4}{*}{Domain knowledge strategy} & \multirow{4}{*}{Domain knowledge strategy} & \multirow{4}{*}{2024} & The schema layer is built based on domain knowledge, the query sentence is used to extract knowledge, and the knowledge graph is established to extract and reuse domain knowledge adaptively. \\ \cline{2-4}  & \multirow{2}{*}{Domain knowledge extraction strategy} & \multirow{2}{*}{2023} & A variable fidelity proxy model is established to obtain the low-fidelity undominated solution. A \\ \cline{2-4}  & \multirow{2}{*}{Domain knowledge extraction strategy} & \multirow{2}{*}{2023} & K-means clustering algorithm is used to extract knowledge from the low-fidelity undominated solution to search space. \\ \hline \multirow{4}{*}{Adaptive population size adjustment strategies} & \multirow{4}{*}{Population size adjustment strategy} & \multirow{4}{*}{2024} & The spatial determination mechanism and population size reduction strategy are implemented by improving the dimension between the best vector and the target vector. \\ \cline{2-4}  & \multirow{2}{*}{External file resource allocation strategy} & \multirow{2}{*}{2022} & An external archive is constructed to periodically add vectors from external archives to the population in the iterative process to achieve adaptive population size adjustment. \\ \hline \multirow{4}{*}{Multi-objective weight strategy} & \multirow{4}{*}{Inverse distance weighting strategy} & \multirow{4}{*}{2024} & Inverse distance weighting and radial basis function strategies are established to provide prediction target values and uncertainty, and an improved lower confidence boundary filling criterion is proposed. \\ \cline{2-4}  & \multirow{2}{*}{Weighted prediction variance strategy} & \multirow{2}{*}{2023} & The output fitting uncertainty index is calculated based on the weighted prediction variance strategy, and the uncertainty of sample dispersion and surrogate model fitting is taken into account. \\ \hline \multirow{4}{*}{Adaptive solution space partitioning strategy} & \multirow{4}{*}{Spatial hierarchical decomposition strategy} & \multirow{4}{*}{2019} & The object space is divided into multiple subspaces, and the best individual of adjacent estimates in each subset is selected. \\ \cline{1-1} \cline{2-4}  & \multirow{2}{*}{Adaptive interval decomposition strategy} & \multirow{2}{*}{2024} & The objective space is divided into a series of optimization subproblems, and a feasible solution of each subspace is saved to a feasible solution set of a partition. Once a subspace has a feasible solution, the search strategy is changed from a constrained search to unconstrained search. \\ \hline \hline \end{tabular}
\end{table}