Systems Engineering and Electronics ›› 2024, Vol. 46 ›› Issue (2): 549-560.doi: 10.12305/j.issn.1001-506X.2024.02.19
• Systems Engineering • Previous Articles
Na LYU, Maohuan WANG, Yuanfu ZHONG, Yingchao ZHANG, Lei SUN
Received:
2022-11-08
Online:
2024-01-25
Published:
2024-02-06
Contact:
Yingchao ZHANG
CLC Number:
Na LYU, Maohuan WANG, Yuanfu ZHONG, Yingchao ZHANG, Lei SUN. Weapon target allocation problem based on matching model of bipartite graphs[J]. Systems Engineering and Electronics, 2024, 46(2): 549-560.
Table 1
Description of parameters and variable symbols"
符号 | 符号含义 |
X | 作战时己方武器集合 |
xi | 第i个武器, xi∈X |
Y | 作战时对方目标集合 |
yj | 第j个目标, yj∈Y |
M | 确定有打击关系的边组成的集合 |
m | 作战时己方武器数量 |
n | 作战时对方目标数量 |
Pij | 武器i对目标j的毁伤概率, xi∈X, yj∈Y |
vj | 目标j的威胁程度, yj∈Y |
xiyj | 第i个武器与第j个目标之间的边 |
wij | 边xiyj的权重, 也是目标j被武器i打击后的威胁程度 |
Xij | 0-1决策变量, 当武器i分配给目标j时取值为1;否则为0 |
Table 2
Question dimension"
问题 | 武器数 | 目标数 | 武器数/目标数 |
WTA1 | 5 | 5 | 1 |
WTA2 | 10 | 10 | 1 |
WTA3 | 20 | 20 | 1 |
WTA4 | 30 | 30 | 1 |
WTA5 | 40 | 40 | 1 |
WTA6 | 50 | 50 | 1 |
WTA7 | 60 | 60 | 1 |
WTA8 | 70 | 70 | 1 |
WTA9 | 80 | 80 | 1 |
WTA10 | 90 | 90 | 1 |
WTA11 | 100 | 100 | 1 |
WTA12 | 200 | 200 | 1 |
WTA13 | 10 | 5 | 2 |
WTA14 | 5 | 10 | 1/2 |
WTA15 | 10 | 20 | 1/2 |
WTA16 | 20 | 10 | 2 |
WTA17 | 20 | 40 | 1/2 |
WTA18 | 20 | 80 | 1/4 |
WTA19 | 40 | 20 | 2 |
WTA20 | 80 | 20 | 4 |
Table 3
Experiment results and running time"
问题 | 计算结果 | 运行时间/s |
WTA1 | 48.364 0 | 0.005 |
WTA2 | 96.312 3 | 0.007 |
WTA3 | 142.107 0 | 0.061 |
WTA4 | 247.167 9 | 0.162 |
WTA5 | 303.534 5 | 0.291 |
WTA6 | 354.865 7 | 0.774 |
WTA7 | 416.389 3 | 0.530 |
WTA8 | 497.586 6 | 0.717 |
WTA9 | 530.931 2 | 1.335 |
WTA10 | 588.149 1 | 2.067 |
WTA11 | 690.379 7 | 1.071 |
WTA12 | 1 274.100 0 | 18.590 |
WTA13 | 36.092 5 | 0.020 |
WTA14 | 330.815 8 | 0.019 |
WTA15 | 585.064 5 | 0.028 |
WTA16 | 65.473 9 | 0.031 |
WTA17 | 1 043.500 0 | 0.083 |
WTA18 | 3 264.200 0 | 0.335 |
WTA19 | 152.172 1 | 0.184 |
WTA20 | 140.556 4 | 0.878 |
Table 4
Experimental results comparison of multiple algorithms"
问题 | 武器数 | 目标数 | 算法 | 最优值 | 平均值 | 中位数 | 标准差 | 运行时间/s |
WTA1 | 5 | 5 | KM-WTA | 48.364 0 | - | - | - | 0.005 |
FMINCON | 48.364 0 | - | - | - | 0.820 | |||
KM | 48.364 0 | - | - | - | 0.140 | |||
PSA[ | 48.364 0 | 48.364 0 | 48.364 0 | 0.00 | 19.280 | |||
PSA | 48.364 0 | 48.364 0 | 48.364 0 | 0.00 | 27.300 | |||
MCSA[ | 48.364 0 | 48.364 0 | 48.364 0 | 0.00 | 4.420 | |||
MCSA | 48.364 0 | 48.364 0 | 48.364 0 | 0.00 | 11.420 | |||
WTA2 | 10 | 10 | KM-WTA | 96.312 3 | - | - | - | 0.007 |
FMINCON | 120.118 5 | - | - | - | 1.280 | |||
KM | 96.312 3 | - | - | - | 3.660 | |||
PSA[ | 96.312 3 | 96.312 3 | 96.312 3 | 0.00 | 30.940 | |||
PSA | 96.312 3 | 100.137 1 | 101.028 8 | 3.06 | 42.720 | |||
MCSA[ | 96.312 3 | 96.312 3 | 96.312 3 | 0.00 | 5.390 | |||
MCSA | 96.312 3 | 96.843 7 | 96.312 3 | 1.12 | 12.540 | |||
WTA3 | 20 | 20 | KM-WTA | 142.107 0 | - | - | - | 0.060 |
FMINCON | 189.080 9 | - | - | - | 69.850 | |||
KM | 142.107 0 | - | - | - | 8.200 | |||
PSA[ | 142.107 0 | 142.107 0 | 142.107 0 | 0.00 | 17.560 | |||
PSA | 169.145 1 | 193.787 5 | 194.323 8 | 4.71 | 42.390 | |||
MCSA[ | 142.107 0 | 142.107 0 | 142.107 0 | 0.00 | 7.560 | |||
MCSA | 178.132 3 | 183.981 1 | 184.695 5 | 2.48 | 13.060 | |||
WTA4 | 30 | 30 | KM-WTA | 247.167 9 | - | - | - | 0.160 |
FMINCON | 304.319 5 | - | - | - | 34.870 | |||
KM | 247.167 9 | - | - | - | 17.850 | |||
PSA[ | 248.028 5 | 248.028 5 | 248.028 5 | 0.00 | 11.230 | |||
PSA | 343.677 1 | 377.720 6 | 378.685 2 | 8.28 | 78.030 | |||
MCSA[ | 248.028 5 | 248.078 1 | 248.028 5 | 0.10 | 9.860 | |||
MCSA | 350.101 4 | 357.944 5 | 358.235 2 | 5.204 2 | 13.660 | |||
WTA5 | 40 | 40 | KM-WTA | 303.534 5 | - | - | - | 0.290 |
FMINCON | 368.337 5 | - | - | - | 40.240 | |||
KM | 303.534 5 | - | - | - | 23.090 | |||
PSA[ | 305.501 6 | 305.501 6 | 305.501 6 | 0.00 | 12.150 | |||
PSA | 474.890 3 | 520.943 6 | 522.207 0 | 10.46 | 82.810 | |||
MCSA[ | 305.501 6 | 305.604 6 | 305.501 6 | 0.15 | 12.700 | |||
MCSA | 484.390 3 | 495.208 7 | 494.979 7 | 6.48 | 14.050 | |||
WTA6 | 50 | 50 | KM-WTA | 354.865 7 | - | - | - | 0.770 |
FMINCON | 409.938 0 | - | - | - | 210.130 | |||
KM | 354.865 7 | - | - | - | 54.580 | |||
PSA[ | 353.076 7 | 353.311 2 | 353.261 0 | 0.14 | 11.170 | |||
PSA | 575.185 7 | 629.167 8 | 630.491 7 | 10.89 | 81.110 | |||
MCSA[ | 353.010 2 | 353.410 4 | 353.489 3 | 0.26 | 14.860 | |||
MCSA | 592.395 8 | 606.195 2 | 607.581 4 | 7.427 9 | 14.930 | |||
WTA7 | 60 | 60 | KM-WTA | 416.389 3 | - | - | - | 0.530 |
FMINCON | 504.111 8 | - | - | - | 297.120 | |||
KM | 416.389 3 | - | - | - | 45.920 | |||
PSA[ | 415.052 8 | 415.406 8 | 415.437 1 | 0.21 | 14.090 | |||
PSA | 702.694 5 | 776.700 7 | 777.976 5 | 12.32 | 82.980 | |||
MCSA[ | 414.222 2 | 415.401 7 | 415.383 8 | 0.82 | 17.480 | |||
MCSA | 721.075 9 | 742.163 8 | 746.450 9 | 7.43 | 15.300 | |||
WTA8 | 70 | 70 | KM-WTA | 497.586 6 | - | - | - | 0.720 |
FMINCON | 581.537 8 | - | - | - | 469.930 | |||
KM | 497.586 6 | - | - | - | 67.660 | |||
PSA[ | 498.104 9 | 498.591 8 | 498.586 0 | 0.30 | 15.730 | |||
PSA | 898.514 7 | 958.680 1 | 960.763 0 | 14.26 | 84.060 | |||
MCSA[ | 496.309 5 | 497.101 2 | 497.129 7 | 0.55 | 19.840 | |||
MCSA | 906.679 3 | 918.006 1 | 918.063 6 | 9.13 | 15.600 | |||
WTA9 | 80 | 80 | KM-WTA | 530.931 2 | - | - | - | 1.340 |
FMINCON | - | - | - | - | > 3 600.000 | |||
KM | 530.931 2 | - | - | - | 80.490 | |||
PSA[ | 534.440 8 | 535.455 9 | 535.593 7 | 0.57 | 18.120 | |||
PSA | 966.850 6 | 1 040.6 | 1 043.1 | 15.44 | 86.740 | |||
MCSA[ | 531.159 2 | 533.264 7 | 532.978 2 | 1.46 | 22.260 | |||
MCSA | 979.834 2 | 998.234 9 | 998.904 6 | 12.02 | 15.860 | |||
WTA10 | 90 | 90 | KM-WTA | 588.149 1 | - | - | - | 2.070 |
FMINCON | - | - | - | - | > 3 600.000 | |||
KM | 588.149 1 | - | - | - | 125.900 | |||
PSA[ | 594.063 9 | 595.327 7 | 595.646 6 | 0.72 | 19.900 | |||
PSA | 1 114.0 | 1 188.9 | 1 190.9 | 15.95 | 89.000 | |||
MCSA[ | 589.320 9 | 592.504 2 | 592.372 5 | 1.52 | 24.370 | |||
MCSA | 1 127.4 | 1 150.6 | 1 153.7 | 13.85 | 16.520 | |||
WTA11 | 100 | 100 | KM-WTA | 690.379 7 | - | - | - | 1.070 |
FMINCON | - | - | - | - | > 3 600.000 | |||
KM | 690.379 7 | - | - | - | 93.530 | |||
PSA[ | 699.835 7 | 701.005 4 | 701.249 5 | 0.75 | 20.600 | |||
PSA | 1 338.5 | 1 402.9 | 1 405.0 | 17.51 | 90.000 | |||
MCSA[ | 694.500 9 | 696.729 9 | 696.723 5 | 1.34 | 29.080 | |||
MCSA | 1 349.6 | 1 362.8 | 1 363.0 | 9.44 | 17.120 | |||
WTA12 | 200 | 200 | KM-WTA | 1 274.1 | - | - | - | 18.590 |
FMINCON | - | - | - | - | > 3 600.000 | |||
KM | 1 274.1 | - | - | - | 248.400 | |||
PSA[ | 1 306.912 6 | 1 308.338 2 | 1 308.518 7 | 0.86 | 27.570 | |||
PSA | 2 711.5 | 2 813.0 | 2 817.7 | 26.00 | 112.400 | |||
MCSA[ | 1 290.271 2 | 1 294.494 3 | 1 294.858 3 | 1.66 | 55.720 | |||
MCSA | 2 699.0 | 2 731.4 | 2 735.9 | 19.896 5 | 23.620 | |||
WTA13 | 10 | 5 | KM-WTA | 36.092 5 | - | - | - | 0.020 |
FMINCON | 36.092 5 | - | - | - | 2.370 | |||
KM | 36.092 5 | - | - | - | 4.130 | |||
PSA | 36.092 5 | 36.095 2 | 36.095 2 | 0.00 | 40.390 | |||
MCSA | 36.092 5 | 36.095 2 | 36.095 2 | 0.00 | 20.560 | |||
WTA14 | 5 | 10 | KM-WTA | 330.815 8 | - | - | - | 0.020 |
FMINCON | 414.145 3 | - | - | - | 3.660 | |||
KM | 330.815 8 | - | - | - | 4.190 | |||
PSA | 330.815 8 | 330.815 8 | 330.815 8 | 0.00 | 44.500 | |||
MCSA | 330.815 8 | 330.815 8 | 330.815 8 | 0.00 | 20.550 | |||
WTA15 | 10 | 20 | KM-WTA | 585.064 5 | - | - | - | 0.030 |
FMINCON | 689.055 4 | - | - | - | 126.530 | |||
KM | 585.064 5 | - | - | - | 8.310 | |||
PSA | 609.248 7 | 645.344 1 | 646.466 8 | 8.86 | 47.030 | |||
MCSA | 591.111 7 | 620.861 4 | 623.042 2 | 11.87 | 39.540 | |||
WTA16 | 20 | 10 | KM-WTA | 65.473 9 | - | - | - | 0.030 |
FMINCON | 78.294 2 | - | - | - | 9.240 | |||
KM | 65.473 9 | - | - | - | 8.220 | |||
PSA | 71.242 5 | 84.707 4 | 84.575 2 | 4.73 | 46.360 | |||
MCSA | 74.074 9 | 76.847 3 | 77.130 0 | 1.51 | 39.330 | |||
WTA17 | 20 | 40 | KM-WTA | 1 043.5 | - | - | - | 0.080 |
FMINCON | 1 202.7 | - | - | - | 3 431.000 | |||
KM | 1 043.5 | - | - | - | 10.460 | |||
PSA | 1 197.8 | 1 293.5 | 1 295.3 | 14.75 | 50.350 | |||
MCSA | 1 226.3 | 1 251.5 | 1 253.7 | 12.50 | 111.400 | |||
WTA18 | 20 | 80 | KM-WTA | 3 264.2 | - | - | - | 0.330 |
FMINCON | - | - | - | - | > 3 600.000 | |||
KM | 3 264.2 | - | - | - | 14.320 | |||
PSA | 3 556.5 | 3 643.8 | 3 646.3 | 18.81 | 59.720 | |||
MCSA | 3 566.7 | 3 585.6 | 3 586.2 | 12.04 | 402.000 | |||
WTA19 | 40 | 20 | KM-WTA | 152.172 1 | - | - | - | 0.180 |
FMINCON | 160.417 9 | - | - | - | 19.140 | |||
KM | 152.172 1 | - | - | - | 13.510 | |||
PSA | 209.540 3 | 242.607 7 | 242.895 0 | 7.81 | 50.400 | |||
MCSA | 251.369 5 | 227.254 3 | 229.094 0 | 6.65 | 1 120.000 | |||
WTA20 | 80 | 20 | KM-WTA | 140.556 4 | - | - | - | 0.870 |
FMINCON | - | - | - | - | > 3 600.000 | |||
KM | 140.556 4 | - | - | - | 67.010 | |||
PSA | 196.682 9 | 225.269 8 | 225.812 9 | 7.74 | 55.760 | |||
MCSA | 204.432 2 | 212.706 9 | 213.461 1 | 4.61 | 401.000 |
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