# Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm
## 5 Experimental Results
### Comparison Experiment of Modified Differential Evolution Algorithm  
In order to verify the superiority of the algorithm in this experiment, taking the total energy of the space-robot cluster is 6000 as an example, the basic differential evolution algorithm (DE), the adaptive differential evolution algorithm (JDE), the multi-population integrated differential evolution algorithm (MPEDE) and the modified differential evolution algorithm (modified DE) are used, respectively to solve the optimal path of the maintenance task of the large SSPS. The test results are shown in Table 7.  
Some conclusions can be drawn by comparing the different types of algorithms in Table 7. The modified differential evolution algorithm is more effective than DE, JDE and MPEDE in the objective function value, the maximum profit and the number of maintenance points of the space-robot cluster. In terms of the total maintenance revenue of space-robot clusters, the modified differential evolution algorithm is 2.45 times that of DE, 1.32 times that of JDE and 1.28 times that of MPEDE. In the total maintenance points of space-robot cluster, the modified differential evolution algorithm is 2.52 times of DE, 1.35 times of JDE and 1.26 times of MPEDE. This shows that the modified difference algorithm proposed in this paper is better than the existing methods in solving the optimal-path model of spatial robot clusters. Figure 6 shows the comparison of the maximum income of the space-robot cluster, Figure 7 shows the comparison of the maximum maintenance points. Figure 8 shows the comparison of the objective function value. At the beginning, due to the existence of the penalty coefficient, the objective function is negative, and it will be very large, which makes the graph display not obvious. In order to make it clear, we have truncated the vertical coordinate of Figure 8.  
It can be seen from Figures 6-8 that the number of iterations of the modified differential evolution algorithm is significantly less than that of DE, JDE and MPEDE in solving the optimal solution of the maximum benefit, the number of maintenance points and the objective function value of the space-robot cluster. The convergence effect of the modified differential evolution algorithm is better than that of other algorithms. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Num** & \(\lambda\) & \(ng\) & **Maximum Income** & **Maintenance Points** \\ \hline
1 & 0.10 & 20 & 11,660 & 585 \\
2 & 0.15 & 20 & 12,030 & 606 \\
3 & 0.20 & 20 & 12,240 & 605 \\
4 & 0.25 & 20 & 12,640 & 632 \\
5 & 0.25 & 10 & 12,180 & 609 \\
6 & 0.25 & 30 & 11,640 & 580 \\
7 & 0.25 & 40 & 11,450 & 565 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The influence of \(\lambda\) and \(ng\) on the modified differential evolution algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithms** & **Objective Function Value** & **Total Income** & **Maintenance Points** \\ \hline DE & 4300.27 & 5150 & 251 \\ JDE [40] & 8705.85 & 9590 & 468 \\ MPEDE [41] & 8906.75 & 9850 & 502 \\ Modified DE & 11,688.33 & 12,640 & 632 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison of different types of algorithms. Figure 6: Total income when the space-robot cluster energy is 6000. Figure 7: Total task points completed when the space-robot cluster energy is 6000. In this paper, the variation factor of differential evolution algorithm is improved, the diversity of individuals is maintained in the early stage, the mutation operator is reduced in the later stage and the probability of searching the global optimal solution is increased. The combination of roulette and multi-neighborhood operations is used to ensure the optimal value of the population and avoid falling into the local optimal; the convergence of the model is accelerated by the de-crossing strategy; the multi-population strategy-integration method is used to obtain more computational resources in the evolution of better mutation strategies.