## 4 Conclusions  
In this paper, a scale-separated design of the Voronoi-GSCS for the heat transfer problem was proposed. On the microscale, the offline calculation proceeded. The stochastic Voronoi microstructure was generated and homogenized. The relative density of the microstructure was calculated and the mapping relationship among the relative density, the average aspect ratio of the struts, and the heat conductivity matrix were established. On the macroscale, online optimization was carried out to solve the heat transfer problem. The optimized relative density distribution of the design domain was obtained. On the full scale, the Voronoi-GSCS was reconstructed based on the mapping relationship built on the microscale and the relative density distribution obtained on the macroscale. The body heat source with uniform-distributed heating (I and II) and the gradient-distributed heat transfer problems were considered to demonstrate the effectiveness of the developed multiscale method for designing the Voronoi-GSCS. The results showed that the scale-separated multiscale could ensure good connectivity of the adjacent microstructure. The size effect was surveyed by changing the width of the struts. It could be seen that the size effect has little influence on the obtained graded cellular structure. The heat conductivity of the cellular structure was enhanced considerably compared to the single-scale structure obtained by the SIMP method, showing that the Voronoi-GSCS has great advantages in heat transfer. Additionally, the strut size of the Voronoi-GSCS was larger than the minimum print size of additive manufacturing. Admittedly, much work remains to be performed: (1) the model with arbitrary boundaries should be developed; (2) the graded stochastic cellular structure could be produced with the aid of additive manufacturing, and an experiment could be conducted to verify the properties of the Voronoi-GSCS; (3) the proposed multiscale method could be extended to 3D optimization problems.  
Figure 11: Iteration history: (**a**) compliance convergence history of the SIMP method and the multiscale method for gradient distributed heating; (**b**) compliance convergence history of the SIMP method and the multiscale method for uniform distributed heating (II).  
**Author Contributions:** Conceptualization, H.L. and L.C.; software, L.C.; validation, L.C. and R.Z.; formal analysis, L.C.; investigation, L.C.; resources, L.C.; data curation, R.Z.; writing--original draft preparation, L.C.; writing--review and editing, L.C.; visualization, H.L.; supervision, X.C.; project administration, H.L.; funding acquisition, H.L. and X.C. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research work was supported by the National Natural Science Foundation of China (Grant No. 12072242 and 12172263) and the Natural Science Foundation of Hubei Province (Grant No. 2020 CFB816).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data are contained within the article. On behalf of all authors, the corresponding author states that the results presented in this paper can be reproduced by implementation details provided herein.  
**Conflicts of Interest:** On behalf of all authors, the corresponding author states that there was no conflict of interest.