## 5 Conclusions  
The present study investigates an offset frequency distribution scheme to mitigate the impact of Doppler shift between spacecraft in the orbital position of the three-star system. Firstly, by analyzing the potential reasonable frequency domains, the overall process of the improved genetic algorithm is elucidated. The generation of the offset frequency distribution scheme under the [6 MHz, 22 MHz] range is enumerated. After conducting 200 individuals per generation and reproducing for 20 generations, the final scheme needs to be switched 10 times and can last for a maximum duration of 966 days and a minimum duration of 16 days. This ensures effective long-term detection of gravitational waves. Secondly, three optimization strategies based on the initial scheme are proposed: frequency domain selection extension strategy, switch times control strategy and low-frequency optimization strategy. The first optimization strategy verifies the feasibility of each phase-locking scheme and alignment pattern. It also identifies the frequency setting minimum thresholds as [5 MHz, 15 MHz] and [7 MHz, 17 MHz]. The number of conversions for distribution schemes corresponding to the frequency domains [6 MHz, 17 MHz] and above can be controlled to be between 6 and 13 conversions after switch times optimization. Low-frequency optimization results in a general reduction of 25.4% of  
Figure 14: Beat Frequency Curve of [7 MHz, 21 MHz]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Start** & \(\Delta\)**f1** & \(\Delta\)**f2** & \(\Delta\)**f3** & \(\Delta\)**f4** & \(\Delta\)**f5** & **Last** \\ \hline
0 & 8.48 & 14.00 & 12.23 & \(-\)11.81 & \(-\)14.93 & 208 \\
208 & 12.49 & 12.50 & \(-\)12.31 & 14.79 & 10.33 & 1015 \\
1223 & 12.11 & \(-\)14.07 & 9.56 & 7.53 & \(-\)7.88 & 118 \\
1341 & 7.56 & \(-\)12.26 & 15.04 & 8.80 & 10.50 & 182 \\
1523 & \(-\)12.44 & \(-\)13.84 & \(-\)9.44 & \(-\)14.53 & 10.62 & 56 \\
1579 & 16.06 & 14.06 & 10.76 & \(-\)16.09 & \(-\)11.40 & 98 \\
1677 & 14.41 & 13.13 & 10.54 & \(-\)8.65 & \(-\)8.85 & 147 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Offset Frequency Distribution Scheme of 7 MHz–21 MHz. Figure 13: Beat Frequency Curve of [5 MHz, 25 MHz]. offset frequencies. Finally, the above methods are used to enumerate the offset frequency distribution schemes for heterodyne interference of the [5 MHz, 25 MHz] and [7 MHz, 21 MHz] frequency domains. These schemes will provide reliable references for further optimization of frequency distribution issues for Program Taiji. However, the schemes provided in this paper are mainly based on simulation, and specific experimental verification is not included. Due to the complexity of the interstellar gravitational wave detection observatory, it is still difficult for the ground to simulate the exact same environment as the Universe during the five-year operational cycle for the validation of the simulation data. The technical challenges of the ground simulation are mainly related to phase-locking and inter-satellite optical links. On the one hand, the ground is unable to simulate the loss of laser lock and identify the positive and negative of the beat frequency. On the other hand, the loss of phase lock in inter-satellite optical links can result in the failure of differential wavefront sensing (DWS) technology, thereby leading to the failure of acquisition tracking and pointing (ATP). These challenges require strategies such as high-precision sensors, adaptive algorithms and advanced digital signal processing techniques and need to be discussed in detail in the following work. Conceptualization, H.L. and X.L. ; Data curation, W.Y. ; Methodology, L.Z. and W.Y. ; Project administration, J.W. and X.L. ; Software, L.Z. ; Supervision, X.L. ; Writing--original draft, L.Z. ; Writing--review & editing, X.L. All authors have read and agreed to the published version of the manuscript. This work is supported by the fund: National Key Research and Development Program of China (Grant No. 2023 YFC2205401). Not applicable.