## 2 Research Object
### Optimal Results  
The genetic algorithm used has a hybridization probability of 0.8, an algebra of 50 generations, and a population of 40 per generation. Table 2 shows the flow distribution and input power distribution for different schemes. From Table 2, it can be seen that, when multiple water pump units are operating in parallel in the pump station, and the water intake is constant, when the working flow distribution of each operating unit in the pump station is the same, the total input power of the pump station is the highest. When the difference between the maximum and minimum working flow rates assigned to each operating unit is greater, the total input power of the pump station is smaller.  
Figure 4 shows the optimal fitness and individual distribution obtained through genetic algorithms, with blue dots representing the distribution of average fitness values and red dots representing the distribution of optimal fitness values.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Total Flow**} & \multicolumn{5}{c}{**Flow Distribution (m\({}^{3}\)/s)**} & \multicolumn{5}{c}{**Total Input Power (MW)**} \\ \hline
70 m\({}^{3}\)/s & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 11.5 & 11.5 & 12.5 & 84.00999 \\ (Start six units) & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 11.5 & 12.0 & 12.0 & 84.01484 \\ \hline  & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 11.5 & 12.0 & 13.5 & 70.54607 \\  & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 11.5 & 12.5 & 13.0 & 70.58901 \\
60 m\({}^{3}\)/s (Start five units) & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 12.0 & 12.0 & 13.0 & 70.59386 \\  & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 12.0 & 12.5 & 12.5 & 70.60940 \\  & Option\({}^{\textregistered}\) & 11.5 & 12.0 & 12.0 & 12.0 & 12.5 & 70.61425 \\  & Option\({}^{\textregistered}\) & 12.0 & 12.0 & 12.0 & 12.0 & 70.61910 \\ \hline  & Option\({}^{\textregistered}\) & 11.5 & 11.5 & 13.5 & 13.5 & 57.07730 \\  & Option\({}^{\textregistered}\) & 11.5 & 12.0 & 13.0 & 13.5 & 57.12509 \\  & Option\({}^{\textregistered}\) & 11.5 & 12.5 & 12.5 & 13.5 & 57.14063 \\
50 m\({}^{3}\)/s (Start four units) & Option\({}^{\textregistered}\) & 11.5 & 12.5 & 13 & 13 & 57.14548 \\  & Option\({}^{\textregistered}\) & 12.0 & 12.0 & 12.5 & 13.5 & 57.16803 \\  & Option\({}^{\textregistered}\) & 12.0 & 12.0 & 13.0 & 13.0 & 57.17288 \\  & Option\({}^{\textregistered}\) & 12.0 & 12.5 & 12.5 & 13.0 & 57.18842 \\  & Option\({}^{\textregistered}\) & 12.5 & 12.5 & 12.5 & 12.5 & 57.20396 \\ \hline
40 m\({}^{3}\)/s (Start three units) & Option\({}^{\textregistered}\) & 13.0 & 13.5 & 13.5 & 43.65635 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Flow distribution results.  
According to Figure 4, as the number of running iterations increases, the average fitness values show a downward trend and gradually approaches the optimal fitness values. The final flow distribution results are as follows: When the diversion volume is 70 m\({}^{3}\)/s, six units need to be started, of which five have working flow rates of 11.5 m\({}^{3}\)/s and the  
Figure 4: Best fitness and best individual figure: (**a**) 70 m\({}^{3}\)/s; (**b**) 60 m\({}^{3}\)/s; (**c**) 50 m\({}^{3}\)/s; (**d**) 40 m\({}^{3}\)/s.  
other unit has a flow rate of 12.5 m\({}^{3}\)/s, at minimum input power of 84.0097 MW. When the water diversion volume is 60 m\({}^{3}\)/s, five units need to be started, of which three units have working flow rates of 11.5 m\({}^{3}\)/s; the other two units have flow rates of 12 m\({}^{3}\)/s and 13.5 m\({}^{3}\)/s, at minimum input power of 70.5458 MW. When the water diversion volume is 50 m\({}^{3}\)/s, four units must be started, of which two units have flow rates of 11.5 m\({}^{3}\)/s; the remaining two units have 13.5 m\({}^{3}\)/s, at minimum input power of 57.0771 MW. When the water intake is 40 m\({}^{3}\)/s, three units must be started with flow distribution rates of 11.5, 13.5, and 13.5 m\({}^{3}\)/s, at minimum input power of 43.6561 MW.