## 3 Optimization of Distribution Scheme
### Optimization of Switch Times Control  
In Taiji, the three-star formation will be in orbit for five years. During this period the offset frequency needs to be switched regularly to ensure the proper operation of the detector. However, the process of regularly switching results in a loss of the laser lock and renders the observatory non-operational for a short while. In the research process of this paper, it was found that there are certain problems to be solved when there are too many or too few conversions. When the setting frequency domain is set too small, the resulting distribution scheme will involve excessive switching, and there could even be cases where the set values for a frequency group only last for one or two days. The scheme when the frequency domain is set to [7 MHz, 22 MHz] is shown in Figure 6. The program needed to switch offset frequencies 16 times in five years and switched six times between 1586 and 1622, with the longest duration being just 8 days and the shortest lasting 2 days. This number of switches seriously affects the detection of gravitational waves in this time period, so the choice of the phase-locking scheme and alignment pattern cannot be limited to the current one. When the set frequency domain is too wide, as Figure 7 shows the distribution scheme at [5 MHz, 25 MHz]. The data in the first stage have remained unchanged for 1565 days. This also results in the individual frequencies of the scheme being too close to the upper bound of 25 MHz in the frequency domain, which is not conducive to the performance requirements of other hardware systems. If the current distribution scheme does not meet the combined requirements of the current software and hardware. It can be optimized by changing the phase-locking scheme and the arrangement pattern. Twenty-four schemes are obtained by permutation, among which the optimal one is chosen. Figure 6: Raw Offset Frequency Setting of [7 MHz, 22 MHz]. Figure 8 shows the results of the generation test of the offset frequency distribution scheme for each frequency band, where the left-hand side indicates the minimum value of the set frequency domain and the upper part indicates its maximum. The test parameters were set to arm length of 3 million kilometers, Doppler shift in 5 years and most commonly used locking scheme 1. Green stands for the frequency range in which the distribution scheme can be generated properly where the number of switches between 6 and 13. The duration of each set of offset frequencies is 7 days or more. Yellow implies insufficient switches. This leads to relatively high values for the offset frequency settings corresponding to the first stage, which can be further optimized. Red means two conditions that no set of offset frequencies could be found to keep all beat frequencies within the given frequency bounds or excessive switches exist. Excessive switches will always leave the interferometric links in a long unlocked state and affect the detection accuracy. In this case, the phase-locking scheme or alignment pattern needs to be changed. Therefore, the number of conversions is judged and optimized after the scheme has been generated. The following content displays the optimization process of the frequency  
Figure 8: Possible Number of Conversions in Different Frequency Domains. Figure 7: Raw Offset Frequency Setting of [5 MHz, 25 MHz]. domain [7 MHz, 22 MHz] with excessive conversions and [5 MHz, 25 MHz] with insufficient conversions. The optimization effect is shown in Figures 9 and 10. Figure 9a-c show the comparison in the frequency domain [7 MHz, 22 MHz]. The frequency in Figure 9a needs to be converted 16 times. During the period from 1586 to 1622, the longest duration is only 8 days and the shortest is 2 days. Figure 9b uses the scheme 3 without changing the alignment pattern, which requires only nine conversions, with the longest lasting 848 days and the shortest lasting 33 days so that its switch times and durations are more reasonable.