# Light-Weighting of Planetary Gearbox Based on Multi-Strategy Optimization Sparrow Search Algorithm
## 4 Application, Results, and Discussion
### Comparative Analysis and Discussion  
The MSOSSA is compared with the SSA and the Grey Wolf algorithm (GWO). The main parameters of algorithms are set as shown in Table 3. Each of the three algorithms is run 30 times to complete the transmission ratio light-weighting. Every algorithm has some dependence on the initial solution. A high-quality initial solution can better help the algorithm to find the global optimal solution. When the initial solution is far away from the optimal value neighborhood, the global optimal solution may not be computed in a finite number of iterations. The program may be limited to the neighborhood of the current solution during the search process. Therefore, generating uniform and reliable initial solutions is an important step. The best initial solution produced by each run of the three algorithms was recorded. Figure 10a-c shows the fitness values or objective function values of the best initial solutions over 30 runs. From Figure 10a, it can be seen that because of the introduction of the improved Circle mapping optimization strategy, the MSOSSA improves the probability of generating initial solutions with low fitness values in a complex solution space. The MSOSSA is six times more likely than the \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Main Parameters** \\ \hline MSOSSA & N = 400, n1:n2:n3 = 7:1:2; Max iter = 6 \\ SSA & N = 400, n1:n2:n3 = 7:1:2; Max iter = 6 \\ GWO & N = 400; Max iter = 6 \\ \hline \hline \end{tabular} Where N is the number of populations, n1:n2:n3 is the ratio of the three types of sparrows, and Max iter is the maximum number of iterations.  
\end{table} 
Table 3: The main parameters of algorithms. Figure 9: Volume of the original gearbox and the light-weight gearbox. SSA and GWO to produce initial solutions with low fitness values in this set of 30 runs. This helps to help the procedure to compute the global optimal solution. The speed of convergence is related to the number of iterations to converge. Algorithms are expected to give relatively accurate values using a small number of iterations. Figure 10: (**a**) The best initial solution over the 30 runs by MSOSA. (**b**) The best initial solution over the 30 runs by SSA. (**c**) The best initial solution over the 30 runs by GWO. The average number of iterations to reach convergence is counted. The solution space of the planetary gearbox light-weighting problem is very complex. The procedure has the possibility of falling into a local optimum solution. So, the number of convergence to local optimal solutions is also counted, as shown in Figure 11. Obviously, GWO has the slowest convergence rate. The convergence speed of SSA is faster than that of GWO, but it often converges to the local optimal solution. The MSOSSA inherits the characteristic of fast convergence of the SSA. Moreover, the convergence speed is improved again by introducing the nonlinear weight factor optimization strategy and native alterter behavior optimization strategy. The introduction of the simulated annealing optimization strategy significantly improves the ability of the MSOSSA to jump out of local optima. The solutions obtained by the metaheuristics are often not the true optimal solution of the problem, but close to the original optimal solution. From the experimental results, all three algorithms can produce suitable solutions. Figure 12 shows that the MSOSSA has the best ability among them to produce global optima and produces the highest quality solutions. The magnification penalty function optimization strategy improves the ability of the MSOSSA to find the global optimal solution. It makes the result easy to distinguish whether it is a local optima. From the above results and analyses, it can be concluded that the optimization strategies have a positive effect on improving the ability to generate high-quality initial solutions, the speed of convergence, the ability to converge, and the quality of the solution. Figure 11: Visual representation of the convergence. Figure 12: Results of optimization.