## 3 Optimization of Distribution Scheme
### Optimization of Low Frequency  
The phase readout circuit is used to demodulate the beat notes received by each laser heterodyne interferometry platform. Due to the accuracy requirements for Program Taiji, the lower the frequency band, the lower the phase noise. Therefore, in order to improve the phase readout accuracy and increase its signal resolution sensitivity, the low-frequency band is optimized on the basis of the originally generated frequency distribution scheme.  
In the scheme generation described above, the individual adaptation is determined by the degree of convergence dispersion of the frequencies of the nine beat frequencies with respect to the median value. This leads to higher values for some offset frequency settings. For distribution schemes with wider frequency domains and the number of switches below the reasonable range, it is more necessary to optimize. According to the statistical analysis index, its concentration trend is used to bring the reproductive offspring in the genetic algorithm closer to the low-frequency band. This method does not have a significant impact on the number of conversions and the duration of the distribution plan. That is to say, it is applicable in the full frequency range.  
In this paper, the genetic algorithm produces the last generation of high-quality individuals with extremely close values of the offset frequency. So, we distinguish individual differences more carefully by appropriately increasing the accuracy of the fitness function. Under the reasonable frequency domain setting [\(f_{min}\), \(f_{max}\)], we further modify the deviation calculation in the fitness function, and the result is shown in example (7).  
\[F_{N}=F_{N-1}+\frac{\sum_{\overline{t}=1}^{N}(f_{n}-\overline{f})^{3}}{9\times (\overline{f})^{3}}, \tag{7}\]  
\(\overline{f}\) is the convergence value, which represents the current frequency value that we would like the nine-beat notes to be close. It can be set through the parameter interface and is calculated as shown in example (8).  
\[\overline{f}=\frac{f_{max}-f_{min}}{x}+f_{min} \tag{8}\]  
Since four of the nine beat notes change with each day's Doppler shift, the degree of deviation is calculated for each day and summed. \(F_{N}\) represents the sum of all deviations from the convergence value up to the current day number. \(F_{N-1}\) represents the sum until the previous day. N is the overall number of days that the set of offset frequency groups can be maintained. The fractional equation calculates the mean square deviation of the nine beat notes with respect to the convergence value to measure the degree of deviation of the beat notes. Finally, \(F_{N}\) and N need to be divided to calculate the average fitness which is used to compare individuals with the same number of days N. The smaller the value of the average degree of deviation of an individual under this method of calculation, the higher the population fitness of the individual and the higher the survival rate.  
Accordingly, a further optimization comparison of the solutions is shown in Figure 12 in the same reasonable frequency domain, phase-locking scheme and arrangement. The graph is represented by the average of the frequency groups' absolute values. We can obtain such significant optimization results.