## 4 Conclusions  
This paper developed a multi-surrogate-assisted multi-tasking optimization algorithm (MSAMT) in the framework of the G-MFEA for the expensive optimization problems. The proposed MSAMT first divides the space into several disjoint regions using a decision space partition strategy and then builds an RBF model on each region. A new dynamic ensemble of surrogates is then suggested, constructed using the samples with the optimal fitness values. Several RBF models and a surrogate ensemble are then optimized simultaneously as tasks in multi-tasking optimization using the generalized multi-factorial evolutionary algorithm. To evaluate the performance of the proposed approach, algorithm analyses of the MSAMT were first carried out on fourteen test functions, analyzing the parameters, the decision space partition strategy, the dynamic ensemble of surrogates, and the computational complexity. Finally, fourteen 10- to 100-dimensional test functions and a spatial truss design problem were used to compare the proposed approach with several recently proposed SAEAs. The results show that the proposed MSAMT exhibits a superior performance compared to comparison algorithms in most of the test functions and an engineering real-world problem. The present study shows that the surrogate models can greatly affect the optimization results as they are utilized to select the samples that need to be evaluated exactly. Furthermore, as the modality of the optimization problem is increasing, both global and local searches may be unable to identify better individuals. Therefore, the proposed MSAMT enhances the population diversity through strategies such as the new dynamic ensemble of surrogates, the decision space partitioning, and the combination of local and global search under the G-MFEA framework to improve the performance of the algorithm. In this work, the components used for constructing the ensemble surrogate are RBF, PRS, and SVR, and more components such as Kriging and the response surface model (RSM) could be further investigated to improve the ability of the MSAMT to handle various optimization problems. In addition, the control functions in the formula for calculating the weight coefficients (Equation (10)) can be adaptively selected according to different model combinations to further explore more reasonable weighting factors. Finally, it is possible to consider how the suggested MSAMT makes trade-offs between different objectives, thereby extending it to multi-objective optimization. Methodology, investigation, software, writing--original draft, data curation, and formal analysis, H.L. ; conceptualization, methodology, supervision, project administration, and writing--review and editing, L.C. ; methodology, supervision, validation, funding acquisition, and writing--review and editing, J.Z. ; visualization and writing--review and editing, M.L. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (grant No. 11872190). Data Availability Statement: Data will be made available on request. The authors declare no conflicts of interest. **Figure A1. **_Cont._Figure A1: Convergence curves of the MSAMT, HSAOA, DSP-SAEA, BiS-SAHA, and FSAPSO on test problems with 10 dimensions (From (**a**) to (**n**) are the convergence curves of F1 to F14, respectively). Figure A2: Convergence curves of the MSAMT, HSAOA, DSP-SAEA, BiS-SAHA, and FSAPSO on test problems with 20 dimensions (From (**a**) to (**n**) are the convergence curves of F1 to F14, respectively). Figure A4: _Cont._  
Figure A4: Convergence curves of the MSAMT, HSAOA, DSP-SAEA, BiS-SAHA, and FSAPSO on test problems with 50 dimensions (From (**a**) to (**n**) are the convergence curves of F1 to F14, respectively). Figure A5: Convergence curves of the MSAMT, HSAOA, DSP-SAEA, BiS-SAHA, and FSAPSO on test problems with 100 dimensions (From **(a)** to **(n)** are the convergence curves of F1 to F14, respectively).