# Path Optimization of Two-Posture Manipulator of Apple Packing Robots
## 4 Results and Discussion  
### Comparative Study of the Improved Performance  
The experiments were conducted from 2019 to 2020. Tests were repeated 10 times using four genetic algorithms, namely, the traditional genetic algorithm with empirical parameters, the improved genetic algorithm in Section 3.1 with empirical parameters, the traditional genetic algorithm with the optimal parameter selection algorithm in Section 3.2,  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Population Size**} & \multirow{2}{*}{**Crossover Probability\%**} & \multirow{2}{*}{**Mutation Probability\%**} & \multirow{2}{*}{**Comparison Substitution Coefficient\%**} & \multirow{2}{*}{**Target Path Time\%**} & \multirow{2}{*}{**Program Running Time\%**} \\  & & & & & & \\ \hline
1 & 33 & 0.92 & 0.93 & 0.13 & 23.19 & 1.52 \\
2 & 59 & 0.77 & 0.17 & 0.52 & 27.58 & 1.74 \\
3 & 13 & 0.29 & 0.10 & 0.69 & 32.28 & 0.25 \\
4 & 20 & 0.57 & 0.32 & 0.75 & 29.95 & 0.51 \\
5 & 77 & 0.30 & 0.51 & 0.33 & 26.22 & 0.93 \\
6 & 13 & 0.58 & 0.98 & 0.51 & 27.06 & 0.53 \\
7 & 76 & 0.81 & 0.74 & 0.36 & 23.90 & 2.12 \\
8 & 54 & 0.75 & 0.34 & 0.22 & 24.12 & 1.81 \\
9 & 22 & 0.26 & 0.29 & 0.58 & 29.66 & 0.35 \\
10 & 16 & 0.54 & 0.03 & 0.53 & 32.17 & 0.37 \\ \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\
361 & 63 & 0.2 & 0.7 & 0.88 & 28.12 & 0.60 \\
362 & 46 & 0.61 & 0.73 & 0.53 & 27.78 & 1.08 \\
363 & 63 & 0.27 & 0.39 & 0.60 & 28.54 & 0.76 \\
364 & 17 & 0.75 & 0.13 & 0.28 & 28.63 & 0.55 \\
365 & 18 & 0.07 & 0.84 & 0.31 & 28.02 & 0.14 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters and corresponding time.  
Figure 11: Standardized residuals: (**a**) normalized residuals of target path time; (**b**) normalized residuals of program running time.  
and the improved genetic algorithm fused with the optimal parameter selection algorithm, to verify the improved performance of the genetic algorithm based on the optimal parameter selection algorithm. In these tests, four grasping points and fourteen placing points were found, and apples were continuously supplied at every grasping point. The angular velocities of the two rotatory joints of the manipulator were 40\({}^{\circ}\)/s and 50\({}^{\circ}\)/s, respectively, and the final iteration times were set to 100.  
Traditional genetic algorithms frequently select good or poor chromosomes on the basis of roulette operators. Crossover and mutation probabilities are constantly fixed in crossover and mutation operations. On the basis of the empirical parameters of the traditional genetic algorithm, the population size was set to 50, the crossover probability was set to 0.8, and the mutation probability was set to 0.2. The average time of target paths was 27.13 s, the average running time of the program was 1.38 s, and the total time was 28.51 s.  
The improved genetic algorithm using empirical parameter values was tested to compare the performance of the improved genetic algorithm mentioned in Section 3.1 with that of the traditional genetic algorithm. The average time of target paths was 24.84 s, the average running time of the program was 1.61 s, and the total time was 26.45 s.  
Similarly, we tested the performance of the traditional genetic algorithm fused with the optimal parameter selection algorithm to verify the improvement effect of the optimal parameter selection algorithm. The average time of target paths was 25.04 s, the average running time of the program was 1.80 s, and the total time was 26.84 s.  
The iterative results of the improved genetic algorithm fused with the proposed optimal parameter selection algorithm were as follows. The optimal parameter selection algorithm gradually and completely converged when the number of iterations reached 70. The average time of the optimal target paths was 22.34 s, the average running time of the program was 1.52 s, and the average total time was 23.86 s.