## 4 Multi-Objective Optimization and Experimental Verification
### Preliminary Selection of Optimization Range  
Based on the optimized flow chart and the established optimization agent model, the second-generation non-genetic algorithm, NSGA-II, was selected to optimize the three design variables of inlet pressure, return pressure, and reset spring stiffness, taking the minimum values of the four objective functions, the unloader ejection speed, withdrawal speed, displacement deviation, and work deviation of the flow control system, as objective functions. The initial range of design variables, constraints for adjusting performance deviations, and the parameters of the optimization algorithm are listed in Table 4.  
This study performed the first optimization and key parameter range screening under full-load conditions. The screening process is illustrated using 80%, 60%, and 40% scenarios (Figure 12). According to the optimization criteria, the Pareto front represents all non-inferior solutions after optimization; these are represented by green dots. Owing to the different load approximation models, the shapes of the Pareto fronts were different, and the following conclusions were drawn:  
1. The ejection and withdrawal speeds changed negatively; the ejection speed decreased and the withdrawal speed increased. This was because the power and resistance sources in the two processes were opposite; that is, the ejection power source became the resistance source of withdrawal.
2. The regulation deviation of the flow control system was positively related, both of which increased and decreased simultaneously, and the value of the load reduction deviation increased. This can be explained by the fact that the lower the load was, the more sensitive the control system was to the change in withdrawal speed, which was consistent with the sensitivity analysis above.
3. The deviations of regulation performance were within the constraints and were all less than \(<\)\(\pm\)5%, which indicated that the optimization results can fully satisfy the system regulation accuracy required by the project.  
The objective of optimization was to reduce the unloader ejection and withdrawal speeds and ensure a minimum adjustment deviation. Auxiliary lines with different percentages of speed drop were plotted in the speed diagram, to preliminarily select the optimum range for different loads. The range of the key parameters under different loads was selected according to the maximum reduction ratio of the speed (Table 5). The range data were used as the initial value ranges for the second optimization, to prepare for the final selection.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Value Range** & **NSGA-II Parameter Setting** \\ \hline
**Name** & **Value** & **Name** & **Value** \\ \hline \(K_{mu}\) & 46,000–80,000 & Population size & 60 \\ \(p_{in}\) & 60–80 & Number of generations & 50 \\ \(p_{bf}\) & 0–12 & Crossover probability & 0.9 \\ \(Error\_V\) & \(-\)10–10\% & Crossover distribution index & 10 \\ \(Error\_W\) & \(-\)10–10\% & Mutation distribution index & 20 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimum algorithm for setting parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Load** & \(K_{mu}\) **(N/m)** & \(p_{in}\) **(bar)** & \(p_{bf}\) **(bar)** &  
Figure 12: First optimization result. (**a**) Optimized speed at 80% load; (**b**) optimized adjustment deviation at 80% load; (**c**) optimized speed at 60% load; (**d**) optimized adjustment deviation at 60% load; (**e**) optimized speed at 40% load; (**f**) optimized adjustment deviation at 40% load.