# A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions

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## Abstract

**:**

## 1. Introduction

## 2. Review of the Improved Clustering Algorithm

- In the cluster graph, select the edge with the largest number of common neighbors in the edge set.
- If the edge is not unique, select the edge that needs to delete the least number of edges after merging.
- If the edge is still not unique, select two vertices with higher priority and smaller clustering task slew angle to form the edge.
- Combine the two vertices of the edge into a new virtual vertex and delete the edges associated with the merged vertex to create a new edge. Update the vertex and edge collections.

## 3. Task Planning Model and Solving Algorithm

#### 3.1. Task Planning Model

#### 3.1.1. Main Constraints of the Planning Model

^{th}orbit, $\mathrm{Obser}{E}_{i}\_u$ represents the observation end time, and ${d}_{u}=\mathrm{Obser}{E}_{i\_u}-\mathrm{Obser}{\mathrm{S}}_{i\_u}$ represents the observation time of task ${\complement}_{i}^{c}\_u$. $T{W}_{i}^{c}=\left\{T{W}_{i\_1}^{c},T{W}_{i\_2}^{c},\dots ,T{W}_{i\_N}^{c}\right\}$ represents a set of visible time windows for all clustering tasks ${\complement}_{i}^{c}$, $T{W}_{i\_u}^{c}=\left[TW{s}_{i\_u}^{c},TW{e}_{i\_u}^{c}\right]$, where $u$ is the number of clustering tasks. The observation time window constraint ensures that the task performs observations within a visible time window.

#### 3.1.2. Optimization Objective Function

#### 3.2. Optimization Solving Algorithm

## 4. Experimental Simulation

#### 4.1. Simulation Condition

#### 4.2. Simulation Analysis

^{−7}. When the original number of tasks is 100, the fitness average value is 0.3712 and variance value is approximately 1.343 × 10

^{−7}. When the original number of tasks is 150, the average fitness value is 0.28978, and the variance value is approximately 3.846 × 10

^{−7}. It can be seen from the simulation results that the GA–SA algorithm can obtain a better solution than the other two algorithms, and the average fitness value is relatively high. The variance in the GA-SA algorithm is lower than the other two algorithms, so the algorithm is more stable. This is because the GA-SA algorithm combines the advantages of the two algorithms and has parallel and serial search functions. It has stronger search ability and more sufficient search, so it can find the optimal solution within the global scope even though entering the local optimal solution is not easy. The drawback of this hybrid algorithm is longer computation times, since the GA-SA algorithm is a combination of GA and SA algorithms and the GA is especially slow. It was found that when the original number of tasks is 50, the GA algorithm runs in 1.6084 s, the SA algorithm runs in 25.4347 s, and the GA-SA algorithm runs in 171.6045 s. When the original number of tasks is 100, the GA algorithm runs in 6.6718 s, the SA algorithm runs in 33.8040 s, and the GA-SA algorithm runs in 221.0182 s. When the original number of tasks is 150, the GA algorithm runs in 9.941 s, then SA algorithm runs in 56.1382 s, and the GA-SA algorithm runs in 362.8693 s. However, for the next-generation intelligent satellite, the computation time will be determined by carrying on the high-performance OBC, which is also the main research point for our team. The combination between the GA-SA algorithm and the high-performance OBC will be studied in our future research.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Task clustering diagram [1].

**Figure 2.**Illustration of minimal clique partition for cluster graph [1].

a (km) | e | i | Ω | $\mathit{\omega}$ | $\mathit{\upsilon}$ |
---|---|---|---|---|---|

7000 | 0 | 60 | 285 | 0 | 0 |

FOV (°) | $\mathbf{max}\mathit{T}\text{}\left(\mathbf{s}\right)$ | $\mathbf{max}\mathit{\theta}\text{}\left(\text{\xb0}\right)$ |
---|---|---|

10 | 150 | ±40 |

No. | Time Window Start (s) | Time Window End (s) | Slew Angle (°) | Priority | Observation Duration | No. | Time Window Start (s) | Time Window End (s) | Slew Angle (°) | Priority | Observation Duration |
---|---|---|---|---|---|---|---|---|---|---|---|

1 | 0 | 0 | 0 | 2 | 15 | 26 | 755.31 | 921.78 | -30.62 | 10 | 9 |

2 | 0 | 0 | 0 | 2 | 8 | 27 | 761.24 | 943.91 | 24.16 | 3 | 14 |

3 | 0 | 0 | 0 | 3 | 14 | 28 | 765.82 | 967.39 | 1.37 | 10 | 12 |

4 | 0 | 0 | 0 | 4 | 13 | 29 | 773.18 | 870.23 | 42.05 | 4 | 10 |

5 | 597.31 | 797.68 | -0.92 | 1 | 7 | 30 | 774.55 | 970.67 | 13.88 | 2 | 13 |

6 | 616.36 | 799.20 | -23.48 | 6 | 15 | 31 | 775.45 | 965.48 | -19.60 | 8 | 8 |

7 | 626.61 | 823.31 | -11.83 | 4 | 14 | 32 | 776.70 | 958.86 | 24.48 | 3 | 13 |

8 | 638.59 | 819.65 | -24.50 | 3 | 7 | 33 | 781.49 | 954.96 | 28.35 | 2 | 12 |

9 | 645.73 | 801.74 | -33.28 | 4 | 11 | 34 | 788.95 | 883.36 | 42.28 | 6 | 10 |

10 | 650.16 | 802.55 | -34.14 | 5 | 8 | 35 | 789.16 | 933.76 | 36.10 | 8 | 13 |

11 | 664.20 | 847.74 | -23.27 | 3 | 13 | 36 | 795.37 | 993.48 | -11.44 | 2 | 10 |

12 | 668.63 | 832.54 | -31.21 | 5 | 14 | 37 | 802.47 | 856.06 | 44.54 | 7 | 13 |

13 | 673.04 | 842.09 | 29.65 | 7 | 8 | 38 | 803.60 | 920.39 | 40.19 | 6 | 14 |

14 | 677.64 | 870.96 | -16.21 | 8 | 11 | 39 | 810.20 | 934.45 | 39.30 | 0 | 10 |

15 | 692.36 | 877.29 | -22.59 | 1 | 6 | 40 | 812.67 | 1012.95 | 7.53 | 1 | 10 |

16 | 692.96 | 844.41 | 34.53 | 8 | 14 | 41 | 816.26 | 1015.43 | 9.86 | 2 | 10 |

17 | 700.43 | 888.42 | -20.69 | 1 | 8 | 42 | 827.59 | 1000.99 | 28.50 | 7 | 11 |

18 | 701.47 | 902.48 | 1.82 | 2 | 8 | 43 | 831.90 | 954.35 | 39.56 | 8 | 8 |

19 | 707.94 | 909.03 | -1.39 | 5 | 7 | 44 | 843.73 | 1031.98 | 21.17 | 3 | 15 |

20 | 710.33 | 846.91 | -37.25 | 7 | 6 | 45 | 844.04 | 980.46 | 37.60 | 4 | 12 |

21 | 717.58 | 918.66 | 2.14 | 10 | 8 | 46 | 844.39 | 918.45 | 43.66 | 7 | 9 |

22 | 734.11 | 914.19 | -25.33 | 1 | 7 | 47 | 848.81 | 1032.19 | 24.10 | 4 | 13 |

23 | 742.31 | 902.24 | 32.57 | 2 | 9 | 48 | 848.82 | 1036.36 | 21.66 | 7 | 12 |

24 | 748.16 | 929.55 | 24.77 | 1 | 10 | 49 | 851.04 | 1029.37 | 26.55 | 1 | 11 |

25 | 753.34 | 925.03 | 28.94 | 6 | 10 | 50 | 853.69 | 1040.94 | 21.87 | 6 | 9 |

$\mathit{e}\mathit{i}$ | ${\mathit{\epsilon}}_{\mathit{u}\mathit{v}}$ | $\mathit{c}\mathit{i}$ | $\mathit{E}$ | $\mathit{M}$ | $\mathbf{CountMax}$ |
---|---|---|---|---|---|

1 | 0.5 | 1 | 1200 | 600 | 60 |

N | T_{0} | K | ${\mathit{P}}_{\mathit{S}\mathit{A}}$ | eps |
---|---|---|---|---|

20 | 500 | 20 | 0.85 | ${10}^{-5}$ |

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**MDPI and ACS Style**

Long, X.; Wu, S.; Wu, X.; Huang, Y.; Mu, Z.
A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions. *Algorithms* **2019**, *12*, 231.
https://doi.org/10.3390/a12110231

**AMA Style**

Long X, Wu S, Wu X, Huang Y, Mu Z.
A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions. *Algorithms*. 2019; 12(11):231.
https://doi.org/10.3390/a12110231

**Chicago/Turabian Style**

Long, Xiangyu, Shufan Wu, Xiaofeng Wu, Yixin Huang, and Zhongcheng Mu.
2019. "A GA-SA Hybrid Planning Algorithm Combined with Improved Clustering for LEO Observation Satellite Missions" *Algorithms* 12, no. 11: 231.
https://doi.org/10.3390/a12110231