## 3 System Model and Problem Formulations
### Advanced Load Balancing Scheme Based on Optimized GA
(2) The crossover factor and mutation factor in GAs are proposed to optimize with prior information such as the periodicity of satellite movement and the proposed model of DoU, which can better improve the efficiency of GAs and the performance of load balancing in S-IoT-N than other existing methods. (3) Based on the proposed improved GA, we obtained the optimal load balancing scheme under the conditions of adaptation from the local balancing scheme to global balancing and the selection of Ser-Beam access. In the scenario of extremely non-uniform DoU and dynamic density variances, advances in beam-hopping were fully realized. The proposed load balancing scheme has many application scenarios in S-IoT-N. For example, S-IoT-N can make up for the lack of terrestrial networks caused by earthquakes and other natural disasters; this scheme can effectively relieve the sudden increase of traffic load pressure and keep the communication link unblocked. Moreover, when using sensors to monitor and transmit the circuit status information through S-IoT-N, this scheme can ensure the timeliness of the information, so as to take timely measures for various emergencies. **Author Contributions:** Conceptualization, W.L., Z.D., K.W. and D.W. ([PERSON]); methodology, W.L., Z.D., K.W. and D.W. ([PERSON]); software, Z.D. ; validation, Z.D., W.L., K.W. and D.W. ([PERSON]); formal analysis, Z.D., Y.L. ([PERSON]), Y.D. and D.W. ([PERSON]); investigation, Z.D. ; resources, Z.D., W.L., Y.L. ([PERSON]) and B.X. ; data curation, Z.D. ; writing--original draft preparation, Z.D. ; writing--review and editing, Z.D., W.L, Y.L. ([PERSON]) and G.W. ; visualization, Z.D. ; supervision, W.L., K.W. and D.W. ([PERSON]); project administration, W.L., Z.D., K.W. and D.W. ([PERSON]); funding acquisition, W.L., K.W. and D.W. ([PERSON]). All authors have read and agreed to the published version of the manuscript. This work was supported by the China National Key Research and Development Plan (2022 YFB2902605 and 2020 YFB1808005), Science and Technology on Communication Networks Laboratory Foundation project (HHX22641X003), the Science and Technology on Communication Networks Laboratory Foundation project (FFX22641X010), the 13 th 5-year plan Civil Aerospace Technology Advance Research Project (D030301), the Hebei Province High-level Talent Funding Project (B2021003032), and the New technology research university cooperation project (SKX212010010). Not applicable. **Confics of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. ## References

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