Journal of System Simulation ›› 2024, Vol. 36 ›› Issue (3): 595-607.doi: 10.16182/j.issn1004731x.joss.22-1252
• Papers • Previous Articles Next Articles
Li Gaoyang(), Li Xiangfeng(
), Zhao Kang, Jin Yuchao, Yi Zhidong, Zuo Dunwen
Received:
2022-10-19
Revised:
2023-01-07
Online:
2024-03-15
Published:
2024-03-14
Contact:
Li Xiangfeng
E-mail:a78989@qq.com;fxli@nuaa.edu.com
CLC Number:
Li Gaoyang, Li Xiangfeng, Zhao Kang, Jin Yuchao, Yi Zhidong, Zuo Dunwen. Three-Dimensional Path Planning of UAV Based on All Particles Driving Wild Horse Optimizer Algorithm[J]. Journal of System Simulation, 2024, 36(3): 595-607.
Table 3
Algorithm test results
函数 | 指标 | PSO | GA | GWO | SSA | WHO | APDWHO |
---|---|---|---|---|---|---|---|
f1(x) | Min | 6.485 1E-08 | 1.342 2E+00 | 5.923 0E-30 | 2.499 2E-08 | 1.295 4E-51 | 0.000 0E+00 |
Max | 1.178 1E-04 | 9.464 9E+00 | 2.002 4E-26 | 1.747 3E-06 | 9.508 9E-43 | 4.331 2E-270 | |
Avg | 7.613 1E-06 | 1.886 1E+00 | 1.602 1E-27 | 2.079 6E-07 | 3.736 8E-44 | 4.337 7E-272 | |
Std | 3.253 1E-05 | 3.432 0E+00 | 2.820 2E-27 | 2.989 9E-07 | 1.739 5E-43 | 0.000 0E+00 | |
Rank | 5 | 6 | 3 | 4 | 2 | 1 | |
f2(x) | Min | 5.236 0E-05 | 3.535 0E-01 | 1.297 6E-17 | 1.024 4E-03 | 1.415 3E-28 | 1.211 7E-166 |
Max | 3.140 2E-01 | 6.546 7E-01 | 2.939 6E-16 | 7.390 8E+00 | 6.327 8E-23 | 4.013 8E-125 | |
Avg | 1.650 3E-02 | 4.654 3E-01 | 9.798 5E-17 | 1.925 6E+00 | 3.473 8E-24 | 4.013 8E-127 | |
Std | 6.401 2E-02 | 8.453 5E-2 | 6.846 0E-17 | 1.560 8E+00 | 1.316 4E-23 | 4.013 8E-126 | |
Rank | 4 | 5 | 3 | 6 | 2 | 1 | |
f 3(x) | Min | 5.785 0E+01 | 2.744 3E+03 | 1.743 1E-08 | 2.785 2E+02 | 1.891 4E-34 | 1.368 2E-137 |
Max | 3.978 4E+02 | 9.543 0E+03 | 8.911 5E-04 | 5.633 5E+03 | 6.607 0E-24 | 2.228 1E-78 | |
Avg | 1.506 1E+02 | 4.543 2E+03 | 3.135 7E-05 | 1.621 4E+03 | 2.986 6E-25 | 2.237 8E-80 | |
Std | 8.789 1E+01 | 1.345 3E+03 | 1.293 61E-04 | 9.399 0E+02 | 1.237 4E-24 | 2.22 8E-79 | |
Rank | 4 | 6 | 3 | 5 | 2 | 1 | |
f 4(x) | Min | 7.610 2E-01 | 5.045 3E+00 | 7.799 9E-08 | 4.049 5E+00 | 8.390 1E-2 | 2.681 1E-144 |
Max | 4.754 1E+00 | 1.434 5E+01 | 8.354 3E-06 | 2.009 6E+01 | 1.032 0E-15 | 4.088 4E-65 | |
Avg | 2.501 2E+00 | 8.854 2E+00 | 9.004 8E-07 | 1.128 1E+01 | 5.111 3E-17 | 4.089 2E-67 | |
Std | 7.541 4E-01 | 2.543 7E+00 | 1.088 9E-06 | 3.323 7E+00 | 1.906 8E-16 | 4.088 3E-66 | |
Rank | 4 | 5 | 3 | 6 | 2 | 1 | |
f5(x) | Min | 1.359 9E+01 | 1.241 3E+02 | 2.584 6E+01 | 2.639 5E+01 | 2.545 4E+01 | 2.667 3E+01 |
Max | 1.589 4E+02 | 1.242 9E+03 | 2.874 8E+01 | 2.049 2E+03 | 8.208 7E+01 | 2.788 3E+01 | |
Avg | 4.907 3E+01 | 3.986 7E+02 | 2.705 4E+01 | 2.990 4E+02 | 2.884 9E+01 | 2.644 3E+01 | |
Std | 3.448 6E+01 | 2.322 1E+02 | 7.638 0E-01 | 4.376 6E+02 | 1.013 5E+01 | 2.004 9E-01 | |
Rank | 4 | 6 | 2 | 5 | 3 | 1 | |
f 6(x) | Min | 9.284 7E-08 | 1.576 3E+00 | 1.265 8E-04 | 1.480 8E-08 | 7.585 6E-06 | 2.181 4E-06 |
Max | 1.621 4E-05 | 1.398 9E+01 | 2.002 2E+00 | 2.341 2E-06 | 3.289 0E-01 | 3.769 1E-05 | |
Avg | 1.887 3E-06 | 4.457 3E+00 | 7.833 2E-01 | 2.128 6E-07 | 1.420 0E-02 | 1.076 6E-05 | |
Std | 2.934 6E-06 | 2.568 0E+00 | 3.672 7E-01 | 3.204 9E-07 | 6.010 0E-02 | 6.752 3E-06 | |
Rank | 2 | 6 | 5 | 1 | 4 | 3 | |
f 7(x) | Min | 1.210 0E-02 | 4.500 0E-02 | 4.026 0E-04 | 4.444 9E-02 | 5.168 4E-05 | 1.123 3E-04 |
Max | 4.080 0E-02 | 2.489 0E-01 | 8.670 5E-03 | 4.614 5E-01 | 9.600 0E-03 | 3.270 5E-03 | |
Avg | 2.380 0E-02 | 1.302 0E-01 | 2.050 2E-03 | 1.671 1E-01 | 1.300 0E-03 | 8.813 9E-04 | |
Std | 8.200 0E-03 | 4.040 0E-02 | 1.206 3E-03 | 7.759 6E-02 | 1.700 0E-03 | 5.601 8E-04 | |
Rank | 4 | 5 | 3 | 6 | 2 | 1 | |
F 8(x) | Min | 2.116 4E+00 | -1.145 7E+04 | -7.835 4E+03 | -9.807 1E+03 | -1.049 1E+04 | -1.065 4E+04 |
Max | 2.116 4E+00 | -1.024 9E+04 | -4.287 3E+03 | -5.697 3E+03 | -7.939 7E+03 | -7.327 8E+03 | |
Avg | 2.116 4E+00 | -1.023 4E+04 | -5.988 9E+03 | -7.471 9E+03 | -9.024 7E+03 | -9.110 4E+03 | |
Std | 2.116 4E+00 | 3.342 4E+02 | 7.0599 E+02 | 7.642 6E+02 | 6.513 2E+02 | 5.515 5E+02 | |
Rank | 6 | 1 | 5 | 4 | 3 | 2 | |
F 9(x) | Min | 2.143 2E+00 | 3.423 2E+00 | 0.000 0E+00 | 1.492 4E+01 | 0.000 0E+00 | 0.000 0E+00 |
Max | 1.096 4E+02 | 1.249 8E+01 | 2.001 5E+01 | 1.094 4E+02 | 3.386 6E-07 | 0.000 0E+00 | |
Avg | 4.814 4E+01 | 8.022 9E+00 | 2.882 7E+00 | 5.652 1E+01 | 1.369 4E-08 | 0.000 0E+00 | |
Std | 2.156 4E+01 | 2.005 6E+00 | 4.214 0E+00 | 1.631 8E+01 | 6.277 3E-08 | 0.000 0E+00 | |
Rank | 5 | 4 | 3 | 6 | 2 | 1 | |
F 10(x) | Min | 9.496 6E-05 | 2.234 0E-01 | 6.483 7E-14 | 8.323 9E-02 | 8.8818E-16 | 8.881 8e-16 |
Max | 2.322 2E+00 | 1.653 2E+00 | 1.501 1E-13 | 5.412 6E+00 | 4.4409E-15 | 4.440 9e-15 | |
Avg | 1.134 6E+00 | 8.003 4E-01 | 1.037 7E-13 | 2.646 2E+00 | 1.5987E-15 | 4.014 6e-15 | |
Std | 8.146 1E-01 | 4.271 3E-01 | 1.917 5E-14 | 9.145 9E-01 | 1.4454E-15 | 1.160 3e-15 | |
Rank | 5 | 4 | 3 | 6 | 1 | 2 | |
F 11(x) | Min | 9.613 3E-08 | 8.514 0E-01 | 0.000 0E+00 | 4.637 0E-04 | 0.0000E+00 | 0.000 0E+00 |
Max | 2.121 0E-01 | 1.057 2E+00 | 3.196 4E-02 | 6.416 9E-02 | 0.0000E+00 | 0.000 0E+00 | |
Avg | 2.852 0E-02 | 1.015 9E+00 | 2.944 2E-03 | 1.838 7E-02 | 0.0000E+00 | 0.000 0E+00 | |
Std | 4.320 0E-02 | 5.370 0E-02 | 6.742 4E-03 | 1.271 3E-02 | 0.0000E+00 | 0.000 0E+00 | |
Rank | 5 | 6 | 3 | 4 | 1.5 | 1.5 | |
F 12(x) | Min | 1.117 6E-08 | 3.600 0E-03 | 1.265 2E-02 | 1.132 9E+00 | 1.0591E-05 | 6.474 3E-08 |
Max | 5.153 0E-01 | 2.267 0E-01 | 2.849 1E-01 | 2.548 2E+01 | 1.0420E-01 | 1.945 8E-06 | |
Avg | 5.823 0E-02 | 3.408 0E-02 | 4.739 3E-02 | 8.270 6E+00 | 1.0600E-02 | 4.065 2E-07 | |
Std | 1.114 0E-01 | 4.698 0E-02 | 3.213 0E-02 | 3.800 1E+00 | 3.1600E-02 | 3.037 9E-07 | |
Rank | 5 | 4 | 2 | 6 | 3 | 1 | |
F13(x) | Min | 7.397 7E-08 | 1.436 9E-01 | 1.034 7E-01 | 2.178 2E-02 | 3.1600E-02 | 1.288 2E-06 |
Max | 2.422 3E-01 | 7.533 0E-01 | 1.288 7E+00 | 6.058 6E+01 | 4.6828E-06 | 1.100 0E-02 | |
Avg | 1.850 0E-02 | 3.460 0E-01 | 6.291 6E-01 | 1.730 0E+01 | 1.6370E-01 | 7.808 1E-04 | |
Std | 4.447 0E-02 | 1.383 0E-01 | 2. 181 6E-01 | 1.517 4E+01 | 3.4000E-02 | 3.157 7E-03 | |
Rank | 2 | 4 | 5 | 6 | 3 | 1 |
Table 4
Performance indexes of each algorithm
环境模型 | 测试设置 | 指标 | GA | PSO | SRM-PSO | WHO | APDWHO | |
---|---|---|---|---|---|---|---|---|
30峰 | 种群规模 | 100 | 最优值 | 181.36 | 163.34 | 162.29 | 162.52 | 162.42 |
平均值 | 207.93 | 175.42 | 166.29 | 179.32 | 166.17 | |||
迭代次数 | 30 | 方差 | 50.64 | 9.21 | 4.21 | 15.49 | 4.19 | |
有效路径率/% | 100 | 100 | 100 | 100 | 100 | |||
收敛到200适应度平均用时/s | — | 5.72 | 6.41 | 14.12 | 6.37 | |||
40峰 | 种群规模 | 100 | 最优值 | 192.73 | 182.09 | 181.06 | 180.40 | 180.84 |
平均值 | 43 062.78 | 70 986.66 | 53 179.16 | 19 461.87 | 185.97 | |||
迭代次数 | 100 | 方差 | 71 715.43 | 89 461.54 | 61130.46 | 11.03 | 5.17 | |
有效路径率/% | 76 | 56 | 67 | 93 | 100 | |||
收敛到220适应度平均用时/s | — | — | — | — | 12.62 | |||
50峰 | 种群规模 | 100 | 最优值 | 187.76 | 180.58 | 179.40 | 179.35 | 179.36 |
平均值 | 17 752.22 | 74 209.84 | 64 432.96 | 26 154.86 | 180.60 | |||
迭代次数 | 100 | 方差 | 21 046.31 | 96 072.86 | 79 053.39 | 9.00 | 0.83 | |
有效路径率/% | 90 | 54 | 60 | 85 | 100 | |||
收敛到220适应度平均用时/s | — | — | — | — | 7.31 |
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