Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm
Abstract
:1. Introduction
2. Theory Background
2.1. Space Solar Power Station Model
2.2. Basic Differential Evolution Algorithm
- DE/rand/1
- DE/rand/2
- DE/best/1
- DE/best/2
- DE/current-to-best/1
2.3. Clustering Algorithm
3. Task Planning Model of Space-Robot Cluster
3.1. Constraints
3.2. Objective Function
4. Modified Differential Evolution Algorithm
4.1. Adaptive Control Parameter Strategy
4.2. Roulette Selection Strategy
4.3. Multi-Neighbor Operation Strategy
4.4. De-Crossover Strategy
Algorithm 1. The pseudo-code of uncrossed strategy. |
Input: path (A, B, C, D, E, A) Output: path_uncross (A, D, C, B, E, A) 1. for i←1:length(path) 2. j←i + 1 3. While j<length(path) 4. ab←path(i,i+1) 5. cd←path(j,j+1) 6. flag←Cross_judgement (ab, cd) % Judge whether cross 7. if flag=1 8. path(i+1:j)←path(j:-1:i+1) 9. end if 10. j←j+1 11. end While 12. end for 13. path_uncross←path 14. return path_uncross |
4.5. Multi-Population Integration Strategy
Algorithm 2. Pseudo-code of multi-population integration strategy. |
1. Set up the each 2. Initialize the , (Change the reward population per generation) 3. Randomly initialize to randomly distribute it in the search space 4. Initialize the and set up the 5. Set up the and 6. while do 7. ; 8. if 9. 10. 11. end if 12. According to is randomly divided into 13. Set up the and 14. for to 15. for to 16. switch 17. case 1: %Perform the first mutation strategy DE/rand-to-pbest/1 in 18. 19. case 2: %Perform the second mutation strategy DE/current-to-rand/1 in 20. 21. case 3: %Perform the third mutation strategy DE/pbad-to-pbest/1 in 22. 23. end switch 24. Perform crossover operations and boundary condition processing 25. if 26. 27. else 28. 29. end if 30. end for 31. 32. end while |
4.6. Algorithm Flow
- First, generating the coordinates of the maintenance node, the maintenance level and the revenue and determine the number of space robots and the origin coordinates;
- Cluster the maintenance nodes to obtain the coordinates of the cluster center point, the revenue within the cluster and the number of target points within the cluster;
- Generate the energy loss matrix between clusters and the distance energy loss matrix from the space robot to each cluster center;
- Modified differential evolution algorithm.
- (1)
- Initialize the multi-population parameters;
- (2)
- Randomized population;
- (3)
- Adaptive differential evolution operator ;
- (4)
- The reward subpopulation is assigned to the population, set and , where ;
- (5)
- carry out their respective strategy differential evolution operations;
- (6)
- Population combination, judge whether the end condition is satisfied and output the robot cluster optimization result if it is satisfied, otherwise repeat steps (3)–(5).
5. Experimental Results
5.1. Space Maintenance Point Clustering
5.2. Comparison Experiment of Optimal-Path Model Optimization
5.2.1. Experimental Comparison
5.2.2. Parameter Analysis
5.3. Comparison Experiment of Modified Differential Evolution Algorithm
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Num | (x, y) | NPC | IC | Num | (x, y) | NPC | IC |
---|---|---|---|---|---|---|---|
1 | (−88.5, −28.2) | 6 | 110 | 51 | (51.5, 24.0) | 9 | 170 |
2 | (−23.5, −12.0) | 18 | 350 | 52 | (40.0, 2.4) | 11 | 220 |
3 | (−80.0, −6.6) | 13 | 220 | 53 | (68.5, 9.6) | 3 | 80 |
4 | (−46.5, −6.0) | 8 | 130 | 54 | (56.5, 4.2) | 16 | 340 |
5 | (−56.5, −8.4) | 7 | 130 | 55 | (−82.0, −24.0) | 4 | 70 |
6 | (−40.0, −16.8) | 14 | 310 | 56 | (−75.5, 2.4) | 9 | 220 |
7 | (−13.5, −13.2) | 7 | 110 | 57 | (−63.0, −2.4) | 5 | 80 |
8 | (−10.0, −3.6) | 15 | 300 | 58 | (2.5, −8.4) | 5 | 120 |
9 | (−6.5, −18.6) | 9 | 160 | 59 | (−67.0, −16.8) | 9 | 190 |
10 | (−38.5, −6.0) | 16 | 290 | 60 | (−4.5, 18.0) | 7 | 130 |
11 | (−50.0, −27.6) | 6 | 110 | 61 | (−34.0, 26.4) | 13 | 300 |
12 | (−88.5, 1.8) | 10 | 210 | 62 | (−31.5, 10.8) | 6 | 100 |
13 | (−23.5, 18.0) | 6 | 130 | 63 | (9.5, −22.8) | 9 | 220 |
14 | (−80.0, 23.4) | 16 | 330 | 64 | (17.5, −3.6) | 7 | 170 |
15 | (−46.5, 24.0) | 17 | 340 | 65 | (81.5, −24.0) | 5 | 70 |
16 | (−56.5, 21.6) | 8 | 130 | 66 | (89.5, −15.6) | 9 | 160 |
17 | (−40.0, 13.2) | 20 | 370 | 67 | (43.5, −22.2) | 11 | 260 |
18 | (−16.5, 3.6) | 7 | 130 | 68 | (24.0, −18.0) | 8 | 170 |
19 | (−60.0, 10.2) | 17 | 290 | 69 | (9.5, 9.0) | 6 | 80 |
20 | (−66.5, 25.2) | 6 | 120 | 70 | (15.0, 6.0) | 3 | 60 |
21 | (−13.5, 16.8) | 14 | 260 | 71 | (82.0, 16.2) | 6 | 120 |
22 | (−10.0, 26.4) | 20 | 430 | 72 | (59.0, 24.6) | 5 | 100 |
23 | (−6.5, 11.4) | 9 | 220 | 73 | (31.5, 4.8) | 3 | 50 |
24 | (−50.0, 2.4) | 9 | 200 | 74 | (18.0, −9.6) | 6 | 80 |
25 | (−21.5, 9.6) | 5 | 70 | 75 | (18.5, 16.8) | 11 | 200 |
26 | (−33.5, 4.2) | 8 | 140 | 76 | (39.0, 12.6) | 6 | 150 |
27 | (−73.5, 10.2) | 4 | 80 | 77 | (−15.5, −21.0) | 7 | 130 |
28 | (66.5, −12.0) | 12 | 250 | 78 | (−6.0, 3.6) | 4 | 110 |
29 | (10.0, −6.6) | 5 | 80 | 79 | (−30.5, −21.0) | 4 | 70 |
30 | (43.5, −6.0) | 6 | 100 | 80 | (−22.5, 26.4) | 5 | 110 |
31 | (33.5, −8.4) | 12 | 260 | 81 | (−70.5, 18.6) | 6 | 140 |
32 | (50.0, −16.8) | 12 | 200 | 82 | (57.5, −8.4) | 5 | 70 |
33 | (23.5, −4.8) | 7 | 130 | 83 | (60.0, −22.2) | 7 | 150 |
34 | (76.5, −13.2) | 14 | 250 | 84 | (92.5, 18.0) | 5 | 120 |
35 | (80.0, −3.6) | 14 | 270 | 85 | (60.0, 13.8) | 8 | 120 |
36 | (51.5, −6.0) | 7 | 140 | 86 | (−30.0, −5.4) | 3 | 50 |
37 | (68.5, −20.4) | 6 | 90 | 87 | (−31.5, −15.0) | 3 | 60 |
38 | (1.5,1.8) | 5 | 90 | 88 | (−52.5, −18.6) | 6 | 110 |
39 | (66.5, 18.0) | 7 | 120 | 89 | (2.0, 12.0) | 5 | 130 |
40 | (10.0, 23.4) | 17 | 340 | 90 | (10.5, −1.2) | 4 | 100 |
41 | (43.5, 24.0) | 9 | 200 | 91 | (84.0, 3.0) | 10 | 220 |
42 | (33.5, 21.6) | 9 | 170 | 92 | (39.0, 29.4) | 4 | 110 |
43 | (50.0, 13.2) | 18 | 350 | 93 | (−73.5, −19.8) | 1 | 10 |
44 | (70.0,25.2) | 11 | 210 | 94 | (1.5, −28.2) | 1 | 30 |
45 | (73.5, 3.6) | 6 | 150 | 95 | (73.5, −26.4) | 1 | 10 |
46 | (30.0, 10.2) | 6 | 130 | 96 | (30.0, −19.8) | 1 | 30 |
47 | (23.5, 25.2) | 3 | 80 | 97 | (83.5, −18.6) | 1 | 30 |
48 | (76.5, 16.8) | 12 | 290 | 98 | (40.0, −27.6) | 1 | 10 |
49 | (80.0, 26.4) | 10 | 230 | 99 | (−24.5, 5.4) | 1 | 30 |
50 | (83.5, 11.4) | 10 | 190 | 100 | (19.0, 28.8) | 1 | 20 |
Robot Number | Robot 1 | Robot 2 | Robot 3 | Robot 4 | Robot 5 |
---|---|---|---|---|---|
Total capacity 5000 | 1200 | 950 | 950 | 950 | 950 |
Total capacity 6000 | 1500 | 1125 | 1125 | 1125 | 1125 |
Total capacity 7000 | 1800 | 1300 | 1300 | 1300 | 1300 |
Type | Robot | Consumption | Income | Number of Tasks | Income Rate |
---|---|---|---|---|---|
Multirobot optimal-path model | R1 | 945.53 | 10,370 | 525 | 65.34% |
R2 | 753.56 | ||||
R3 | 738.72 | ||||
R4 | 741.71 | ||||
R5 | 752.41 | ||||
Multirobot shortest-path model | R1 | 934.61 | 6830 | 345 | 43.04% |
R2 | 658.22 | ||||
R3 | 751.03 | ||||
R4 | 692.13 | ||||
R5 | 686.65 |
Type | Robot | Consumption | Income | Number of Tasks | Income Rate |
---|---|---|---|---|---|
Multirobot optimal-path model | R1 | 1184.51 | 12,640 | 632 | 79.65% |
R2 | 890.12 | ||||
R3 | 888.59 | ||||
R4 | 899.01 | ||||
R5 | 896.14 | ||||
Multirobot shortest-path model | R1 | 1184.70 | 9160 | 466 | 57.84% |
R2 | 865.95 | ||||
R3 | 845.31 | ||||
R4 | 843.96 | ||||
R5 | 880.99 |
Type | Robot | Consumption | Income | Number of Tasks | Income Rate |
---|---|---|---|---|---|
Multirobot optimal-path model | R1 | 1433.22 | 14,540 | 730 | 91.62% |
R2 | 1035.71 | ||||
R3 | 1024.98 | ||||
R4 | 1036.98 | ||||
R5 | 1021.90 | ||||
Multirobot shortest-path model | R1 | 1273.64 | 10,650 | 543 | 67.11% |
R2 | 961.64 | ||||
R3 | 935.14 | ||||
R4 | 1001.92 | ||||
R5 | 1018.60 |
Num | Maximum Income | Maintenance Points | ||
---|---|---|---|---|
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 |
Algorithms | Objective Function Value | Total Income | Maintenance Points |
---|---|---|---|
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 |
Algorithms | Objective Function Value | Maximum Income | Maintenance Points |
---|---|---|---|
GA | 5794.99 | 6470 | 321 |
ACO | 7049.01 | 7790 | 396 |
ABC | 10,246.18 | 11,200 | 561 |
modified DE | 11,688.33 | 12,640 | 632 |
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Xiao, P.; Ju, H.; Li, Q.; Chen, F. Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm. Appl. Sci. 2020, 10, 5000. https://doi.org/10.3390/app10145000
Xiao P, Ju H, Li Q, Chen F. Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm. Applied Sciences. 2020; 10(14):5000. https://doi.org/10.3390/app10145000
Chicago/Turabian StyleXiao, Pengfei, Hehua Ju, Qidong Li, and Feifei Chen. 2020. "Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm" Applied Sciences 10, no. 14: 5000. https://doi.org/10.3390/app10145000
APA StyleXiao, P., Ju, H., Li, Q., & Chen, F. (2020). Task Planning of Space-Robot Clusters Based on Modified Differential Evolution Algorithm. Applied Sciences, 10(14), 5000. https://doi.org/10.3390/app10145000