## 1 Introduction  
The space gravitational wave [1; 2] antenna program Taiji consists of three spacecrafts flying in a heliocentric [3], with separations of \(L=3\times 10^{9}\) m [4]. Each spacecraft (SC) contains two proof masses that are shielded from external disturbances. Bidirectional laser links are maintained between all SC in the constellation for exchanging laser beams to interferometrically measure the pathlength variations at the picometer level caused by gravitational waves [5; 6]. During the mission operation, spaceborne interferometers will be affected by Doppler shifts [7]. Thus, the interferometers in Taiji are based on heterodyne interferometry, where two laser beams from local and remote SC are combined to yield a beat note, the phase of which is used to lock and track the remote laser [8]. However, the Doppler shift due to the inter-spacecraft motion varies with time. This will cause the beat frequency to enter some disallowed frequency bands over the five-year operational cycle and stop probing [9]. In particular, the laser relative intensity noise (RIN) [10] and phase readout circuit sampling frequency [11; 12] limit the minimum and maximum of the allowed frequency bands respectively. For the Taiji program, The lower bound of the beat frequency is 5 MHz, and the upper is 25 MHz [13]. In order to address this issue, current research commonly adds offset frequencies into the interferometric link to control the beat frequency [14; 15]. The fixed offset frequency method is mainly used to control the beat frequency within the reasonable range of [5 MHz, 25 MHz]. A crucial challenge of the method is the reasonable distribution of the offset frequency. Once the current offset frequency is unable to keep the beat frequency within a reasonable range, the offset frequency needs to be switched, and the interferometry needs to be restarted, which will inevitably lead to the interruption of observation data. [PERSON] [9] proposed a frequency distribution scheme of [7 MHz, 23 MHz], requiring 24 switches. The offset frequencies theoretically did not require changing for a maximum of 177 days within the specified constraints. Due to the need for prolonged uninterrupted detection by the system, excessive switching and insufficient duration can lead to probing errors. Additionally, [PERSON] utilized a linear programming (LP) algorithm [13] and a two-stage optimization algorithm [14] to solve the setting strategy of the offset frequencies. The LP algorithm provided an offset frequency distribution scheme that can remain unchanged for up to 1931 days over a six-year period. The two-stage optimization algorithm reduced the upper bound to 16 MHz and provided a scheme that the offset frequency changes nine times with a minimum and maximum offset frequency duration of 90 days and 713 days, respectively. Based on the above research, this paper makes appropriate improvements. A high-precision fitness genetic algorithm is adopted to generate an initial distribution scheme. Three optimization strategies for the initial scheme are analyzed and proposed. The final scheme obtained by this distribution technique and these strategies have fewer switching times and lower offset frequency setting values. Additionally, this paper can lower the upper bound to 15 MHz to reduce the performance requirements of hardware devices such as phase readout circuits. Section 2 of this paper elaborates on the operation process of a high-precision fitness genetic algorithm and presents offset frequency distribution schemes for the [6 MHz, 22 MHz] frequency domain. Within the frequency bounds and for a five-year mission, only 10 frequency switches are necessary. The shortest duration without a switch is 16 days, and the longest undisturbed measurement run would be 966 days. Section 3 shows that optimizing the frequency domain selection can narrow the reasonable frequency domain setting to [7 MHz, 17 MHz]. If the lower bound is not raised, the frequency domain can be controlled between [5 MHz and 15 MHz].