Acta Armamentarii ›› 2025, Vol. 46 ›› Issue (4): 240172-.doi: 10.12382/bgxb.2024.0172
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YAN Jiang1, YIN Peng1,2, LIU Yan1,2,*(), ZHANG Wenyu3, HUANG Fenglei1
Received:
2024-03-11
Online:
2025-04-30
Contact:
LIU Yan
CLC Number:
YAN Jiang, YIN Peng, LIU Yan, ZHANG Wenyu, HUANG Fenglei. An Efficient Aiming Points Optimization Algorithm for Joint Missiles Dstroying Area Targets with Complex Shapes[J]. Acta Armamentarii, 2025, 46(4): 240172-.
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导弹类型及 瞄准点位 | 瞄准点序号 | |||||
---|---|---|---|---|---|---|
1 | 2 | … | 8 | … | 15 | |
导弹类型 | 1 | 2 | … | 2 | … | 1 |
瞄准点位 | 10 | 50 | … | 138 | … | 328 |
Table 1 Examples of numbering representations of variables to be optimized
导弹类型及 瞄准点位 | 瞄准点序号 | |||||
---|---|---|---|---|---|---|
1 | 2 | … | 8 | … | 15 | |
导弹类型 | 1 | 2 | … | 2 | … | 1 |
瞄准点位 | 10 | 50 | … | 138 | … | 328 |
导弹类型 | Rdrt/m | Ridt/m | 弹着点分布标准差/m |
---|---|---|---|
1 | 20 | 10 | 7.5 |
2 | 40 | 20 | 15.0 |
Table 2 Damage capabilities of the missiles used
导弹类型 | Rdrt/m | Ridt/m | 弹着点分布标准差/m |
---|---|---|---|
1 | 20 | 10 | 7.5 |
2 | 40 | 20 | 15.0 |
用例 | 宽/m | 高/m | 面积/m2 | s | |||
---|---|---|---|---|---|---|---|
6 | 8 | 10 | 12 | ||||
1 | 172 | 143 | 12672 | 351 | 200 | 127 | 87 |
2 | 224 | 127 | 20581 | 565 | 328 | 214 | 159 |
3 | 181 | 153 | 13788 | 383 | 218 | 137 | 96 |
4 | 143 | 153 | 15874 | 425 | 247 | 151 | 117 |
5 | 112 | 151 | 6758 | 188 | 104 | 69 | 48 |
6 | 172 | 159 | 14571 | 408 | 228 | 145 | 94 |
Table 3 Statistics on target size and number of aiming point candidates in the 6 test cases
用例 | 宽/m | 高/m | 面积/m2 | s | |||
---|---|---|---|---|---|---|---|
6 | 8 | 10 | 12 | ||||
1 | 172 | 143 | 12672 | 351 | 200 | 127 | 87 |
2 | 224 | 127 | 20581 | 565 | 328 | 214 | 159 |
3 | 181 | 153 | 13788 | 383 | 218 | 137 | 96 |
4 | 143 | 153 | 15874 | 425 | 247 | 151 | 117 |
5 | 112 | 151 | 6758 | 188 | 104 | 69 | 48 |
6 | 172 | 159 | 14571 | 408 | 228 | 145 | 94 |
算法 | 瞄准点优化结果 | 毁伤概率二维图 | 毁伤概率三维图 | 优化过程收敛曲线 |
---|---|---|---|---|
EAPOA-annealing | | | | |
EAPOA-greedy | | | | |
SEGA | | | | |
Table 4 Optimized results of EAPOA and SEGA on test case 2
算法 | 瞄准点优化结果 | 毁伤概率二维图 | 毁伤概率三维图 | 优化过程收敛曲线 |
---|---|---|---|---|
EAPOA-annealing | | | | |
EAPOA-greedy | | | | |
SEGA | | | | |
测试用例 | 采样步长 | EAPOA-annealing | EAPOA-greedy | SEGA | |||
---|---|---|---|---|---|---|---|
毁伤概率 | 时间/s | 毁伤概率 | 时间/s | 毁伤概率 | 时间/s | ||
1 | 6 | 0.868 | 2.35 | 0.868 | 2.56 | 0.861 | 8.20 |
8 | 0.872 | 1.37 | 0.872 | 1.51 | 0.861 | 7.99 | |
10 | 0.863 | 1.19 | 0.867 | 0.99 | 0.858 | 10.29 | |
12 | 0.861 | 0.82 | 0.848 | 0.52 | 0.857 | 8.82 | |
2 | 6 | 0.728 | 8.92 | 0.728 | 5.92 | 0.746 | 16.74 |
8 | 0.738 | 5.84 | 0.733 | 4.14 | 0.720 | 16.60 | |
10 | 0.731 | 1.52 | 0.732 | 1.64 | 0.726 | 10.97 | |
12 | 0.740 | 1.14 | 0.740 | 1.29 | 0.701 | 11.86 | |
3 | 6 | 0.880 | 2.76 | 0.879 | 3.03 | 0.878 | 10.42 |
8 | 0.869 | 1.60 | 0.869 | 2.16 | 0.868 | 8.67 | |
10 | 0.872 | 0.76 | 0.871 | 0.87 | 0.864 | 10.36 | |
12 | 0.871 | 0.56 | 0.871 | 0.44 | 0.861 | 8.00 | |
4 | 6 | 0.801 | 1.94 | 0.801 | 2.21 | 0.789 | 8.79 |
8 | 0.802 | 1.57 | 0.802 | 1.72 | 0.785 | 9.21 | |
10 | 0.797 | 0.70 | 0.797 | 0.54 | 0.785 | 9.03 | |
12 | 0.807 | 0.75 | 0.807 | 0.60 | 0.775 | 9.64 | |
5 | 6 | 0.916 | 1.01 | 0.916 | 1.15 | 0.927 | 7.24 |
8 | 0.929 | 1.67 | 0.929 | 1.93 | 0.924 | 6.20 | |
10 | 0.926 | 0.63 | 0.921 | 0.66 | 0.925 | 6.44 | |
12 | 0.918 | 0.31 | 0.928 | 0.24 | 0.926 | 5.49 | |
6 | 6 | 0.863 | 3.74 | 0.863 | 3.18 | 0.858 | 8.71 |
8 | 0.857 | 1.61 | 0.857 | 1.73 | 0.857 | 7.72 | |
10 | 0.862 | 1.03 | 0.864 | 1.21 | 0.857 | 7.38 | |
12 | 0.856 | 0.91 | 0.857 | 0.92 | 0.852 | 7.93 |
Table 5 Comparison of algorithm performances with the total amount of 8 ammunitions
测试用例 | 采样步长 | EAPOA-annealing | EAPOA-greedy | SEGA | |||
---|---|---|---|---|---|---|---|
毁伤概率 | 时间/s | 毁伤概率 | 时间/s | 毁伤概率 | 时间/s | ||
1 | 6 | 0.868 | 2.35 | 0.868 | 2.56 | 0.861 | 8.20 |
8 | 0.872 | 1.37 | 0.872 | 1.51 | 0.861 | 7.99 | |
10 | 0.863 | 1.19 | 0.867 | 0.99 | 0.858 | 10.29 | |
12 | 0.861 | 0.82 | 0.848 | 0.52 | 0.857 | 8.82 | |
2 | 6 | 0.728 | 8.92 | 0.728 | 5.92 | 0.746 | 16.74 |
8 | 0.738 | 5.84 | 0.733 | 4.14 | 0.720 | 16.60 | |
10 | 0.731 | 1.52 | 0.732 | 1.64 | 0.726 | 10.97 | |
12 | 0.740 | 1.14 | 0.740 | 1.29 | 0.701 | 11.86 | |
3 | 6 | 0.880 | 2.76 | 0.879 | 3.03 | 0.878 | 10.42 |
8 | 0.869 | 1.60 | 0.869 | 2.16 | 0.868 | 8.67 | |
10 | 0.872 | 0.76 | 0.871 | 0.87 | 0.864 | 10.36 | |
12 | 0.871 | 0.56 | 0.871 | 0.44 | 0.861 | 8.00 | |
4 | 6 | 0.801 | 1.94 | 0.801 | 2.21 | 0.789 | 8.79 |
8 | 0.802 | 1.57 | 0.802 | 1.72 | 0.785 | 9.21 | |
10 | 0.797 | 0.70 | 0.797 | 0.54 | 0.785 | 9.03 | |
12 | 0.807 | 0.75 | 0.807 | 0.60 | 0.775 | 9.64 | |
5 | 6 | 0.916 | 1.01 | 0.916 | 1.15 | 0.927 | 7.24 |
8 | 0.929 | 1.67 | 0.929 | 1.93 | 0.924 | 6.20 | |
10 | 0.926 | 0.63 | 0.921 | 0.66 | 0.925 | 6.44 | |
12 | 0.918 | 0.31 | 0.928 | 0.24 | 0.926 | 5.49 | |
6 | 6 | 0.863 | 3.74 | 0.863 | 3.18 | 0.858 | 8.71 |
8 | 0.857 | 1.61 | 0.857 | 1.73 | 0.857 | 7.72 | |
10 | 0.862 | 1.03 | 0.864 | 1.21 | 0.857 | 7.38 | |
12 | 0.856 | 0.91 | 0.857 | 0.92 | 0.852 | 7.93 |
测试用例 | 采样步长 | EAPOA-annealing | EAPOA-greedy | SEGA | |||
---|---|---|---|---|---|---|---|
毁伤概率 | 时间/s | 毁伤概率 | 时间/s | 毁伤概率 | 时间/s | ||
1 | 6 | 0.947 | 4.82 | 0.947 | 4.06 | 0.945 | 18.04 |
8 | 0.937 | 1.58 | 0.940 | 1.93 | 0.940 | 14.75 | |
10 | 0.948 | 1.43 | 0.948 | 0.78 | 0.939 | 15.78 | |
12 | 0.942 | 1.04 | 0.940 | 0.83 | 0.940 | 15.46 | |
2 | 6 | 0.868 | 9.54 | 0.844 | 39.46 | 0.851 | 23.22 |
8 | 0.866 | 6.83 | 0.856 | 4.82 | 0.845 | 21.85 | |
10 | 0.859 | 8.34 | 0.859 | 3.41 | 0.853 | 22.04 | |
12 | 0.865 | 4.55 | 0.863 | 3.85 | 0.843 | 20.29 | |
3 | 6 | 0.951 | 15.06 | 0.948 | 4.42 | 0.947 | 17.10 |
8 | 0.948 | 3.62 | 0.951 | 3.82 | 0.943 | 14.74 | |
10 | 0.949 | 1.93 | 0.949 | 2.00 | 0.942 | 12.24 | |
12 | 0.951 | 1.07 | 0.951 | 1.16 | 0.944 | 13.28 | |
4 | 6 | 0.910 | 6.69 | 0.910 | 6.03 | 0.894 | 12.45 |
8 | 0.909 | 2.73 | 0.909 | 1.78 | 0.896 | 10.70 | |
10 | 0.898 | 0.99 | 0.898 | 1.49 | 0.884 | 10.04 | |
12 | 0.904 | 0.81 | 0.902 | 0.90 | 0.893 | 11.34 | |
5 | 6 | 0.979 | 1.84 | 0.975 | 1.22 | 0.976 | 10.18 |
8 | 0.973 | 1.11 | 0.973 | 0.68 | 0.977 | 8.54 | |
10 | 0.972 | 0.42 | 0.968 | 0.94 | 0.973 | 8.29 | |
12 | 0.966 | 0.31 | 0.966 | 0.46 | 0.974 | 7.62 | |
6 | 6 | 0.942 | 3.90 | 0.942 | 5.29 | 0.934 | 11.51 |
8 | 0.941 | 2.20 | 0.944 | 3.65 | 0.933 | 14.06 | |
10 | 0.939 | 2.25 | 0.942 | 2.73 | 0.939 | 11.25 | |
12 | 0.935 | 1.23 | 0.935 | 0.79 | 0.936 | 11.83 |
Table 6 Comparison of algorithm performances with the total amount of 12 ammunitions
测试用例 | 采样步长 | EAPOA-annealing | EAPOA-greedy | SEGA | |||
---|---|---|---|---|---|---|---|
毁伤概率 | 时间/s | 毁伤概率 | 时间/s | 毁伤概率 | 时间/s | ||
1 | 6 | 0.947 | 4.82 | 0.947 | 4.06 | 0.945 | 18.04 |
8 | 0.937 | 1.58 | 0.940 | 1.93 | 0.940 | 14.75 | |
10 | 0.948 | 1.43 | 0.948 | 0.78 | 0.939 | 15.78 | |
12 | 0.942 | 1.04 | 0.940 | 0.83 | 0.940 | 15.46 | |
2 | 6 | 0.868 | 9.54 | 0.844 | 39.46 | 0.851 | 23.22 |
8 | 0.866 | 6.83 | 0.856 | 4.82 | 0.845 | 21.85 | |
10 | 0.859 | 8.34 | 0.859 | 3.41 | 0.853 | 22.04 | |
12 | 0.865 | 4.55 | 0.863 | 3.85 | 0.843 | 20.29 | |
3 | 6 | 0.951 | 15.06 | 0.948 | 4.42 | 0.947 | 17.10 |
8 | 0.948 | 3.62 | 0.951 | 3.82 | 0.943 | 14.74 | |
10 | 0.949 | 1.93 | 0.949 | 2.00 | 0.942 | 12.24 | |
12 | 0.951 | 1.07 | 0.951 | 1.16 | 0.944 | 13.28 | |
4 | 6 | 0.910 | 6.69 | 0.910 | 6.03 | 0.894 | 12.45 |
8 | 0.909 | 2.73 | 0.909 | 1.78 | 0.896 | 10.70 | |
10 | 0.898 | 0.99 | 0.898 | 1.49 | 0.884 | 10.04 | |
12 | 0.904 | 0.81 | 0.902 | 0.90 | 0.893 | 11.34 | |
5 | 6 | 0.979 | 1.84 | 0.975 | 1.22 | 0.976 | 10.18 |
8 | 0.973 | 1.11 | 0.973 | 0.68 | 0.977 | 8.54 | |
10 | 0.972 | 0.42 | 0.968 | 0.94 | 0.973 | 8.29 | |
12 | 0.966 | 0.31 | 0.966 | 0.46 | 0.974 | 7.62 | |
6 | 6 | 0.942 | 3.90 | 0.942 | 5.29 | 0.934 | 11.51 |
8 | 0.941 | 2.20 | 0.944 | 3.65 | 0.933 | 14.06 | |
10 | 0.939 | 2.25 | 0.942 | 2.73 | 0.939 | 11.25 | |
12 | 0.935 | 1.23 | 0.935 | 0.79 | 0.936 | 11.83 |
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